QUANTITATIVE METHODS
Rates & Returns
Required Rate of Return (Build-Up)
Required Rate of Return\[ r = r_{rf} + \text{Inflation Premium} + \text{Default Premium} + \text{Liquidity Premium} + \text{Maturity Premium} \]
Approximation\[ r_{\text{nominal}} \approx r_{\text{real}} + r_{\text{inflation}} \]
Exact (Fisher)\[ (1 + r_{\text{nominal}}) = (1 + r_{\text{real}})(1 + r_{\text{inflation}}) \]
Holding Period Return (HPR)
Holding Period Return\[ HPR = \frac{P_1 - P_0 + CF_1}{P_0} \]
Multi-period\[ R = \prod_{t=1}^{n}(1 + R_t) - 1 \]
HPR is NOT annualised by default.
Key: HPR is not annualised by default. A 20% HPR over 4 years ≠ 20% per year.
Three Mean Returns — When to Use Each Critical
Arithmetic Mean — expected return over 1 future period\[ \bar{R}_A = \frac{1}{T}\sum_{t=1}^{T} R_t \]
Geometric Mean — actual historical compound growth rate\[ \bar{R}_G = \left[\prod_{t=1}^{T}(1+R_t)\right]^{1/T} - 1 \]
Harmonic Mean — dollar-cost averaging (equal \(\$ \) per period)\[ \bar{R}_H = \frac{N}{\displaystyle\sum_{i=1}^{N}\frac{1}{R_i}} \]
⚠ Trap: With volatile returns: Arithmetic ≥ Geometric ≥ Harmonic. Equality only when all values are identical. Also: Arithmetic × Harmonic = (Geometric)².
Trap: If returns are volatile, Arithmetic ≥ Geometric ≥ Harmonic (equality only when all values identical). Also: Arithmetic × Harmonic = (Geometric)²
| Scenario | Use |
|---|---|
| Year 1: +50%, Year 2: −50% | Arithmetic = 0% (misleading!), Geometric = −13.4% (reality) |
| Buy $500 of stock each month | Harmonic mean of prices gives average cost per share |
Money-Weighted vs Time-Weighted Return Critical
| MWR (IRR) | TWR | |
|---|---|---|
| Method | IRR of all cash flows | Geometric mean of sub-period HPRs |
| Affected by investor CF timing? | Yes | No |
| Manager controls CFs? | Use MWR | Use TWR |
| CFA benchmark standard | No | Yes |
Classic Exam Trap: If investor adds money before a bad period → MWR < TWR. If adds before good period → MWR > TWR. TWR eliminates this timing effect.
EAR / APR Conversions
Effective Annual Rate (discrete compounding)\[ EAR = \left(1 + \frac{r_{\text{stated}}}{m}\right)^{m} - 1 \]
EAR (continuous compounding)\[ EAR_{\text{cont}} = e^{r_s} - 1 \]
m = number of compounding periods per year.
Key: More frequent compounding → higher EAR for same APR. APR and EAR are equal only when m = 1.
Real vs Nominal Returns (Fisher Equation)
Fisher Equation (exact)\[ 1 + r_{\text{real}} = \frac{1 + r_{\text{nominal}}}{1 + r_{\text{inflation}}} \]
Approximation (valid for small rates)\[ r_{\text{real}} \approx r_{\text{nominal}} - r_{\text{inflation}} \]
Leveraged Return
Leveraged Return\[ R_L = R_P + \frac{V_B}{V_E}(R_P - r_D) \]
\(V_B\) = borrowed capital, \(V_E\) = equity capital, \(r_D\) = cost of debt.
If R_P > r_D: leverage amplifies gains. If R_P < r_D: leverage amplifies losses.
Time Value of Money
FV / PV Core Formulas
Future / Present Value\[ FV_N = PV \cdot (1 + r)^{N} \qquad PV = \frac{FV_N}{(1+r)^{N}} \]
Periodic compounding (m periods/year)\[ FV_N = PV \left(1 + \frac{r_s}{m}\right)^{mN} \]
Continuous compounding\[ FV_N = PV \cdot e^{r_s \cdot N} \]
Annuities
Ordinary Annuity PV\[ PV = PMT \times \frac{1 - (1+r)^{-N}}{r} \]
Ordinary Annuity FV\[ FV = PMT \times \frac{(1+r)^{N} - 1}{r} \]
Annuity Due PV\[ PV_{\text{due}} = PV_{\text{ordinary}} \times (1 + r) \]
Use BGN mode on BA II Plus for annuity due.
Fixed-Income Instruments
Coupon Bond PV\[ PV = \sum_{t=1}^{N}\frac{PMT}{(1+r)^{t}} + \frac{FV}{(1+r)^{N}} \]
Zero-Coupon Bond\[ PV = \frac{FV}{(1+r)^{N}} \]
Implied YTM from price\[ r = \left(\frac{FV}{PV}\right)^{1/N} - 1 \]
Equity Instruments & TVM
Perpetuity (constant dividend)\[ PV = \frac{D}{r} \]
Gordon Growth Model\[ PV = \frac{D_1}{r - g} = \frac{D_0(1+g)}{r - g} \]
Implied required return\[ r = \frac{D_1}{PV} + g \]
NPV and IRR
Net Present Value\[ NPV = \sum_{t=0}^{N}\frac{CF_t}{(1+r)^{t}} \]
Accept if NPV > 0. IRR is the rate r where NPV = 0; accept if IRR > hurdle rate.
When NPV and IRR conflict on mutually exclusive projects: ALWAYS follow NPV. NPV directly measures value creation. IRR can give misleading rankings due to scale and timing differences.
Calculator tip (BA II Plus): Always CLR TVM before new calculation. For bonds: PMT and FV same sign (positive), PV opposite sign (negative). BGN mode for annuity due.
Statistical Measures of Asset Returns
Central Tendency
Sample Mean\[ \bar{X} = \frac{1}{n}\sum_{i=1}^{n} X_i \]
Weighted Mean\[ \bar{X}_w = \sum_{i=1}^{n} w_i X_i \quad \text{where } \textstyle\sum w_i = 1 \]
Skewed distributions: Mean is pulled toward the tail. For negatively skewed (long left tail): Mean < Median < Mode. Most equity portfolios are negatively skewed.
Measures of Dispersion
Mean Absolute Deviation\[ MAD = \frac{1}{n}\sum_{i=1}^{n}\bigl|X_i - \bar{X}\bigr| \]
Sample Variance\[ s^2 = \frac{\sum_{i=1}^{n}(X_i - \bar{X})^2}{n-1} \]
Denominator n−1 is Bessel's correction for unbiased estimation.
Measures of Location (Percentiles)
Location of y-th Percentile\[ L_y = (n+1)\times\frac{y}{100} \]
Interquartile Range\[ IQR = Q_3 - Q_1 \]
Skewness & Kurtosis Critical
Skewness\[ SK \approx \frac{1}{n}\sum_{i=1}^{n}\frac{(X_i - \bar{X})^3}{s^3} \]
Kurtosis\[ KU \approx \frac{1}{n}\sum_{i=1}^{n}\frac{(X_i - \bar{X})^4}{s^4} \]
Excess Kurtosis\[ \text{Excess Kurtosis} = KU - 3 \]
| Type | Excess Kurtosis | Tails vs Normal | Finance Implication |
|---|---|---|---|
| Leptokurtic | > 0 | Fatter tails | More extreme events (crashes) than normal predicts |
| Mesokurtic | = 0 | Normal | Theoretical benchmark |
| Platykurtic | < 0 | Thinner tails | Rare in finance |
Most financial return series are leptokurtic (fat tails) and negatively skewed. Standard deviation ALONE understates tail risk.
Covariance & Correlation
Sample Covariance\[ s_{XY} = \frac{\sum_{i=1}^{n}(X_i-\bar{X})(Y_i-\bar{Y})}{n-1} \]
Correlation Coefficient\[ r_{XY} = \frac{s_{XY}}{s_X \cdot s_Y} \qquad -1 \leq r \leq +1 \]
Correlation ≠ Causation. r = +1: perfect positive co-movement. r = 0: no linear relationship. r = −1: perfect opposite movement (max diversification benefit).
Probability Trees & Portfolio Mathematics
Expected Value & Variance
Expected Value\[ E(X) = \sum_i P(X_i)\,X_i \]
Variance\[ \sigma^2(X) = \sum_i P(X_i)\bigl[X_i - E(X)\bigr]^2 \]
Portfolio Expected Return & Variance
Portfolio Expected Return\[ E(R_p) = \sum_i w_i E(R_i) \]
2-Asset Portfolio Variance\[ \sigma^2(R_p) = w_A^2\sigma_A^2 + w_B^2\sigma_B^2 + 2\,w_A w_B\,\rho_{AB}\,\sigma_A\sigma_B \]
Roy's Safety-First Ratio
Roy's Safety-First Ratio\[ SFR = \frac{E(R_p) - R_L}{\sigma_p} \]
Probability of shortfall\[ P(R_p < R_L) = N(-SFR) \]
✓ Use when: Maximise SFR to minimise the probability of falling below threshold return \(R_L\).
Maximise SFRatio to minimise probability of falling below the threshold. The formula is identical to Sharpe ratio with Rₗ replacing Rᶠ.
Diversification Insight
Correlation effect on portfolio risk:
ρ = +1.0: σₚ = weighted average (no diversification)
ρ = 0.5: σₚ < weighted average (some benefit)
ρ = 0.0: substantial risk reduction
ρ = −1.0: risk can be eliminated entirely
Only SYSTEMATIC risk is rewarded. Unsystematic risk can be diversified away at no cost — the market does not compensate it.
Simulation Methods
Lognormal Distribution
Lognormal Distribution\[ \text{If } Y \sim \text{Lognormal, then } \ln Y \sim \text{Normal} \]
Used to model asset prices (bounded at zero). Returns can be negative; prices cannot.
Why lognormal for prices? Prices can't be negative. The lognormal distribution is right-skewed and bounded at zero — perfect for modelling asset prices. Returns (not prices) can be normal.
Monte Carlo vs Historical Simulation
| Monte Carlo | Historical Simulation | |
|---|---|---|
| Data source | Generated from assumed distribution | Actual historical data |
| Captures fat tails? | Only if model includes them | Yes — reflects actual past crises |
| Limitation | Model risk: garbage-in, garbage-out | Past may not repeat |
Estimation & Inference
Sampling Methods
| Method | How |
|---|---|
| Simple random | Every element equally likely |
| Systematic | Every kth observation |
| Stratified | Random samples from each sub-group |
| Cluster | Mini-representations of population |
| Convenience | Based on accessibility |
| Judgmental | Researcher expertise |
Central Limit Theorem (CLT)
Central Limit Theorem\[ \bar{X} \sim N\!\left(\mu,\; \frac{\sigma^2}{n}\right) \quad \text{for } n \geq 30 \]
Standard Error of the Mean\[ SE = \frac{\sigma}{\sqrt{n}} \approx \frac{s}{\sqrt{n}} \]
CLT does NOT require the population to be normal. It only says the SAMPLING DISTRIBUTION of the mean approaches normal as n grows. With n < 30, use the t-distribution unless the population is known to be normal.
Bootstrap & Jackknife
Bootstrap: Resample WITH replacement; repeat many times → builds empirical sampling distribution without distributional assumptions.
Jackknife: Leave out one observation at a time (without replacement).
Sampling Biases — Critical for Finance
| Bias | Mechanism | Effect |
|---|---|---|
| Survivorship | Only surviving funds in database | Overstates average returns |
| Look-ahead | Uses data not available at the time | Overstates strategy returns |
| Time-period | Results depend on specific period studied | Non-generalisable conclusions |
| Data mining | Testing too many variables until something works | Spurious correlations |
Hypothesis Testing
Decision Framework
| Type | H₀ | Hₐ | Reject H₀ if |
|---|---|---|---|
| One-tailed (upper) | μ ≤ μ₀ | μ > μ₀ | t > +critical |
| One-tailed (lower) | μ ≥ μ₀ | μ < μ₀ | t < −critical |
| Two-tailed | μ = μ₀ | μ ≠ μ₀ | |t| > critical |
Type I error (α): Reject H₀ when H₀ is TRUE — false positive.
Type II error (β): Fail to reject H₀ when H₀ is FALSE — false negative.
Statistical Power\[ \text{Power} = 1 - \beta \]
p-value = smallest α at which H₀ is rejected.
When Type I and Type II errors trade off: Reducing α (less likely to falsely reject) increases β (more likely to miss a true effect). The only way to reduce both simultaneously is to increase sample size.
Test for Single Mean (t-test)
One-Sample t-Test\[ t = \frac{\bar{X} - \mu_0}{s/\sqrt{n}}, \quad df = n-1 \]
✓ Use when: Use when population variance is unknown (almost always in practice).
Tests for Differences Between Means
Independent Samples t-Test (pooled variance)\[ t = \frac{(\bar{X}_1 - \bar{X}_2) - (\mu_1 - \mu_2)}{\sqrt{s_p^2/n_1 + s_p^2/n_2}} \]
Pooled Variance\[ s_p^2 = \frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2}, \quad df = n_1+n_2-2 \]
Test for Variance (Chi-Square)
Chi-Square Test (single variance)\[ \chi^2 = \frac{(n-1)s^2}{\sigma_0^2}, \quad df = n-1 \]
Test for Equality of Two Variances (F-test)
F-Test (equality of variances)\[ F = \frac{s_1^2}{s_2^2}, \quad df_1 = n_1-1,\; df_2 = n_2-1 \]
⚠ Trap: By convention, place the larger variance in the numerator → always right-tailed test.
Parametric vs Nonparametric Tests
| Parametric | Nonparametric Alternative |
|---|---|
| t-test for mean | Wilcoxon signed-rank test |
| t-test for diff in means | Mann-Whitney U test |
| Pearson correlation (r) | Spearman rank correlation (rₛ) |
Use nonparametric when: Distribution assumptions violated, data has outliers, data are ranked (ordinal), or hypothesis doesn't concern a parameter.
Tests for Correlation
Pearson Correlation t-Test\[ t = \frac{r\sqrt{n-2}}{\sqrt{1-r^2}}, \quad df = n-2 \]
Spearman Rank Correlation\[ r_s = 1 - \frac{6\sum d_i^2}{n(n^2-1)} \]
Simple Linear Regression
Model Specification & OLS Estimates
OLS Regression Line\[ \hat{Y} = \hat{b}_0 + \hat{b}_1 X \]
Slope Estimate\[ \hat{b}_1 = \frac{\text{Cov}(Y,X)}{\text{Var}(X)} = \frac{\sum(Y_i-\bar{Y})(X_i-\bar{X})}{\sum(X_i-\bar{X})^2} \]
Intercept\[ \hat{b}_0 = \bar{Y} - \hat{b}_1\bar{X} \]
OLS Assumptions: Linear relationship; homoscedasticity (constant residual variance); independence of X and Y; normality of residuals. Violations → biased/inefficient estimates.
ANOVA Decomposition
Total Sum of Squares\[ SST = SSR + SSE \]
Coefficient of Determination\[ R^2 = \frac{SSR}{SST} \]
F-Statistic\[ F = \frac{MSR}{MSE} = \frac{SSR/k}{SSE/(n-k-1)} \]
Hypothesis Tests on Coefficients
t-Test for Slope\[ t = \frac{\hat{b}_1 - b_1}{s_{\hat{b}_1}}, \quad s_{\hat{b}_1} = \frac{s_e}{\sqrt{\sum(X_i-\bar{X})^2}} \]
Prediction
Variance of Forecast Error\[ s_f^2 = s_e^2\left[1 + \frac{1}{n} + \frac{(X-\bar{X})^2}{(n-1)s_X^2}\right] \]
Prediction interval is wider than confidence interval for the conditional mean.
Functional Forms
| Model | Form | Slope Interpretation |
|---|---|---|
| Lin-Lin (standard) | Y = b₀ + b₁X | ΔY per unit ΔX |
| Log-Lin | ln(Y) = b₀ + b₁X | % ΔY per unit ΔX |
| Lin-Log | Y = b₀ + b₁ln(X) | ΔY per % ΔX |
| Log-Log | ln(Y) = b₀ + b₁ln(X) | % ΔY per % ΔX (elasticity) |
Tests of Independence (Contingency Tables)
Chi-Square Test of Independence\[ \chi^2 = \sum_{i,j}\frac{(O_{ij} - E_{ij})^2}{E_{ij}} \]
Big Data & Machine Learning
Big Data: Volume, Velocity, Variety. Alternative data sources include social media, satellite, credit card transactions, IoT sensors.
| ML Type | What It Does | Examples |
|---|---|---|
| Supervised learning | Learns from labelled data to predict outcomes | Regression, classification (spam filter) |
| Unsupervised learning | Finds patterns in unlabelled data | Clustering, dimensionality reduction (PCA) |
| Deep learning | Neural networks with many layers; learns features automatically | Image recognition, NLP (text analysis) |
ECONOMICS
Firms & Market Structures
Universal Profit-Maximisation Rule
Profit Maximisation (all market structures)\[ MR = MC \]
Step 1: find Q* where MR = MC. Step 2: read P* from demand curve at Q*.
Four Market Structures Compared Critical
| Feature | Perfect Competition | Monopolistic Competition | Oligopoly | Monopoly |
|---|---|---|---|---|
| Firms | Many | Many | Few | One |
| Product | Homogeneous | Differentiated | Homogeneous or differentiated | Unique |
| Entry barriers | None | Low | High | Very high |
| Pricing power | None (price taker) | Some (narrow range) | Significant (interdependent) | Considerable (price maker) |
| Long-run economic profit | Zero | Zero (entry erodes) | Positive possible | Positive possible |
| Demand curve | Horizontal (perfectly elastic) | Downward sloping (elastic) | Kinked demand | Market demand (inelastic) |
Shutdown Decision
| Condition | Short-Term | Long-Term |
|---|---|---|
| TR ≥ TC | Stay | Stay |
| TVC < TR < TC | Stay (covers variable costs) | Exit market |
| TR < TVC | Shut down | Exit market |
Logic: In the short run, fixed costs are sunk — operate if TR covers at least the variable costs. In the long run, all costs must be covered.
Oligopoly Specifics
Kinked demand (oligopoly): price increase → elastic response (rivals don't match) → large volume loss. Price decrease → inelastic response (rivals match) → small volume gain.
Price collusion more likely when: Few firms, similar products, similar cost structures, frequent small orders, credible retaliation threats.
Market Power Measures
Herfindahl-Hirschman Index\[ HHI = \sum_{i=1}^{n} s_i^2 \quad \text{(sum of squared market shares)} \]
N-firm concentration ratio = sum of market shares of N largest firms.
Economies of Scale
Each expansion stage has its own short-run ATC curve. The long-run ATC is the envelope of all short-run ATC curves. Minimum efficient scale (MES) = lowest point on the long-run ATC — the scale at which average costs are minimised. Firms must reach MES to be competitive.
Understanding Business Cycles
Four Cycle Phases Critical
| Phase | Economy | Employment | Inflation | Capital Spending |
|---|---|---|---|---|
| Recovery | Going through trough; output below potential but increasing | Layoffs slow; firms extend overtime before rehiring full-time | Moderate | Low but rising; efficiency over capacity |
| Expansion | Above-average growth rates; output above potential | Full-time rehiring; overtime increases | Moderate but rising | Focused on capacity expansion |
| Slowdown | Going through peak; growth decelerates | Hiring slows | Accelerating | Strong but inventory building as sales slow |
| Contraction | Weakening; may enter recession | Hiring freeze, then layoffs | Decelerating (with a lag) | New orders halted; maintenance scaled back |
Economic Indicators
Leading indicators turn BEFORE the economy: stock indexes, building permits, money supply, yield curve slope.
Coincident: real income, industrial production, employment. Lagging: average duration of unemployment, inflation, bank prime rate.
Key exam point: The unemployment rate is a lagging indicator — employers wait before hiring/firing. Stock prices are a leading indicator — markets anticipate future conditions.
Fiscal Policy
Fiscal Tools
Fiscal tools: transfer payments, current spending, capital investment, taxation.
Fiscal Multiplier
Fiscal Multiplier\[ \text{Multiplier} = \frac{1}{1 - MPC(1-t)} \]
MPC = marginal propensity to consume; t = tax rate.
A €1 increase in government spending increases aggregate demand by €2.5 (multiplier effect). Higher MPC or lower taxes → larger multiplier.
Execution Lags
| Lag Type | Description |
|---|---|
| Recognition lag | Time for government to recognise the economic problem |
| Action lag | Time to formulate, debate, and pass policy |
| Impact lag | Time for policy to actually affect the economy |
Fiscal policy is slower than monetary policy due to legislative requirements. By the time fiscal measures take effect, the cycle may have already shifted. This is why automatic stabilisers (unemployment benefits) are preferred — they act immediately without legislative action.
Ricardian Equivalence (Counter-argument)
If households anticipate future tax increases to repay deficit spending, they save the extra income today → fiscal multiplier = 0. In practice, the multiplier is positive but smaller than simple models suggest.
Monetary Policy
Roles of Central Banks
- Supplier of currency
- Banker to government and bankers' bank
- Lender of last resort (LOLR)
- Regulator of payments system
- Conductor of monetary policy
- Supervisor of banking system
- Maintain foreign currency and gold reserves
Policy Tools — Expansionary vs Contractionary
| Tool | Expansionary Action | Contractionary Action |
|---|---|---|
| Open market operations | Buy bonds from commercial banks (↑ money supply) | Sell bonds (↓ money supply) |
| Policy rate | Set below neutral rate | Set above neutral rate |
| Reserve requirement | Reduce required reserves | Increase required reserves |
Neutral Interest Rate & Policy Stance
Neutral Policy Rate\[ r^* = r_{\text{real neutral}} + \pi^e \approx \text{Long-run GDP growth} + \text{Inflation target} \]
Taylor Rule Critical
Taylor Rule\[ \text{Policy Rate} = r^* + \pi^* + 0.5(\pi - \pi^*) + 0.5\left(\frac{Y - Y^*}{Y^*}\right) \]
Where: r* = neutral real rate; π* = inflation target (typically 2%); π = actual inflation; (Y − Y*)/Y* = output gap.
Worked example: Neutral rate = 2%, inflation target = 2%, actual inflation = 4%, output gap = 0.
Policy Rate = 2% + 2% + 0.5(4% − 2%) + 0.5(0) = 4% + 1% = 5%.
Inflation is 2pp above target → rate raised by 1pp above neutral. Policy is restrictive.
Policy Rate = 2% + 2% + 0.5(4% − 2%) + 0.5(0) = 4% + 1% = 5%.
Inflation is 2pp above target → rate raised by 1pp above neutral. Policy is restrictive.
Monetary policy limitations: Zero lower bound (ZLB) prevents deep cuts; liquidity trap means cuts stop stimulating; 12–18 month transmission lag makes it easy to over-steer; broken credit channel if banks are undercapitalised.
Quantitative Easing (QE)
Non-conventional monetary policy used when policy rate hits the zero lower bound. Central bank purchases longer-term assets (government bonds, MBS) to lower long-term yields and stimulate lending/investment. Increases bank reserves. Tapering = reducing asset purchases.
Interaction: Fiscal vs Monetary Policy
| Fiscal | Monetary | Effect |
|---|---|---|
| Expansionary | Expansionary | Strongest stimulus (rarely simultaneous) |
| Expansionary | Contractionary | Fiscal boosts demand; monetary limits inflation → mixed |
| Contractionary | Expansionary | Monetary stimulates; fiscal brakes → mixed |
Introduction to Geopolitics
State actors: possess authority to deploy national security resources (governments). Non-state actors: IMF, multinationals, NGOs, terrorist organisations.
Assessing Geopolitical Threats
| Dimension | Questions to Ask |
|---|---|
| Likelihood | How probable is the event? |
| Velocity | How quickly will it impact markets? |
| Size/Nature of impact | How large and widespread is the effect? |
Event risks with high velocity demand immediate portfolio hedging. Thematic risks develop slowly — allowing gradual repositioning. The exam may ask you to categorise a geopolitical risk and recommend an appropriate investor response.
International Trade & Capital Flows
Trade Restrictions & Their Effects
| Restriction | Mechanism |
|---|---|
| Tariff | Tax on imported goods |
| Quota | Quantity limit on imports |
| Export subsidy | Government payment to exporters |
| Min domestic content | Require % of product made domestically |
| Voluntary export restraint | Exporting country self-limits |
Tariff Welfare Analysis (price rises from P* to P_t)\[ \Delta\text{Consumer surplus} = -(A+B+C+D) \]
\[ \Delta\text{Producer surplus} = +A \qquad \text{Government revenue} = +C \]
Net welfare loss\[ \text{DWL} = -(B+D) \]
Regional Trading Blocs
| Type | What Members Have |
|---|---|
| FTA (Free Trade Area) | Free trade among members only |
| Customs Union (CU) | FTA + common external trade policy |
| Common Market (CM) | CU + free movement of factors of production |
| Economic Union (EU) | CM + common economic institutions and policies |
| Monetary Union (MU) | EU + common currency |
Trade Balance Identity
Current Account Identity\[ X - M = (S - I) + (T - G) \]
X−M = trade surplus/deficit. A trade deficit requires net capital imports.
Classic exam question: If a country has a persistent current account deficit, what must be true? Either private investment exceeds savings, OR the government has a fiscal deficit (or both). You can't have a current account deficit without a corresponding capital account surplus.
Benefits & Costs of International Trade
Gains from trade: comparative advantage, economies of scale, diffusion of technology. Costs: structural unemployment, income inequality.
Capital Flows & Exchange Rate Calculations
FX Notation & Real Exchange Rate
Quote Convention "A/B"\[ \text{Units of } A \text{ per 1 unit of } B \]
Real Exchange Rate\[ q_{A/B} = S_{A/B} \times \frac{CPI_B}{CPI_A} \]
Forward Rate (Interest Rate Parity)
Interest Rate Parity (Covered)\[ \frac{F_{A/B}}{S_{A/B}} = \frac{1 + i_A}{1 + i_B} \]
Forward Rate\[ F_{A/B} = S_{A/B}\times\frac{1 + i_A}{1 + i_B} \]
⚠ Trap: If \(i_A > i_B\): currency A is at a forward discount (depreciates forward).
Interest rate parity prevents arbitrage. High-interest-rate currencies must trade at a forward discount. If they didn't, you could borrow in the low-rate currency, invest in the high-rate currency, and hedge the FX risk — earning a riskless profit.
Exchange Rate Regimes
| Regime | Description |
|---|---|
| Dollarisation | Adopt another country's currency (most fixed) |
| Monetary union | Adopt a common currency (euro) |
| Currency board | Fixed rate; central bank must hold FX reserves to cover all domestic currency |
| Fixed peg | Pegged within ±1% margin |
| Target zone | Fixed peg with wider bands |
| Crawling peg | Peg adjusted periodically (rate of crawl announced) |
| Crawling bands | Margin widens over time |
| Managed floating | No official target; central bank intervenes discretionally |
| Independently floating | Market-determined (most flexible) |
Ideal Currency Regime — The Impossible Trinity
You CANNOT simultaneously have all three:
(1) Fixed exchange rate
(2) Free capital flows
(3) Independent monetary policy
Any two out of three is feasible. The Eurozone chose 1 and 2 (sacrificing 3). The US chose 2 and 3 (floating rate).
CORPORATE ISSUERS
Organisational Forms & Ownership
| Feature | Sole Proprietorship | General Partnership | Limited Partnership | Corporation |
|---|---|---|---|---|
| Separate legal entity? | No | No | No | Yes |
| Owner–operator separation | No | No | Partial (LPs passive) | Yes (board hires mgmt) |
| Liability | Unlimited | Unlimited (all partners) | GPs: unlimited; LPs: limited | Limited (shareholders) |
| Tax treatment | Personal income | Personal income | Personal income (pass-through) | Potential double taxation |
| Capital access | Very limited | Limited | Better (LP capital) | Best (equity + debt markets) |
Corporation is the ONLY form with a separate legal identity from owners. This enables limited liability, perpetual existence, and easy share transferability — which is why it dominates capital markets.
Private vs Public Companies
| Private Limited | Public Limited | |
|---|---|---|
| Taxation | Personal income level | Double taxation (corporate + personal dividend) |
| Owner count | Restricted | Unlimited |
| Transfer of ownership | Requires votes | Transferable anytime |
Going Public / Going Private
Go public: IPO, Direct Listing, SPAC, Acquisition. Go private: LBO. Raise capital privately via Private Placement Memorandum (PPM).
Investors & Other Stakeholders
| Equity (Shareholders) | Debt (Creditors) | |
|---|---|---|
| Upside potential | Unlimited | Limited to promised payments |
| Maximum loss | Cannot exceed investment value | Cannot exceed investment value |
| Investment risk | Higher | Lower |
| Investment interest | Maximise company value | Timely repayment of principal + interest |
| Priority in liquidation | Last (residual claim) | First (secured); before equity |
Key tensions:
• Equity owners prefer growth and higher risk tolerance (upside is unlimited)
• Creditors prefer stability and limited downside risk
• This conflict shapes debt covenants — creditors add restrictions on dividend payments, additional debt issuance, and asset sales to protect themselves
Corporate Governance: Conflicts, Mechanisms, Risks & Benefits
Principal–Agent Conflicts
| Conflict | Nature |
|---|---|
| Shareholder vs Manager | Entrenchment (avoid risky projects to protect job), Empire building (make unjustified acquisitions for size/pay), Excessive risk taking (gamble to boost stock-based comp) |
| Controlling vs Minority shareholder | Concentrated ownership may extract private benefits; multiple-class shares give disproportionate voting power |
| Shareholder vs Creditor | Shareholders want growth/risk; creditors want stability — debt covenants manage this |
Board Committees
- Audit committee — Financial reporting oversight
- Governance committee — Board practices and structure
- Remuneration/Compensation committee — Executive pay
- Nomination committee — Board candidate selection
- Risk committee — Enterprise risk oversight
- Investment committee — Capital allocation decisions
Shareholder Mechanisms
- Corporate reporting and transparency
- Shareholder meetings (cumulative voting, proxy voting)
- Shareholder activism and engagement
- Derivative lawsuits (shareholders sue on behalf of company)
- Corporate takeovers (proxy contests, tender offers, hostile takeovers)
Governance Risks & Benefits
| Poor Governance Risk | Good Governance Benefit |
|---|---|
| Weak control systems | Lower cost of capital |
| Ineffective decision-making | Better operating performance |
| Higher default/bankruptcy risk | Lower bankruptcy risk |
| Higher borrowing costs | Better equity returns long-term |
Working Capital & Liquidity
Cash Conversion Cycle (CCC)
Cash Conversion Cycle\[ CCC = DOH + DSO - DPO \]
Days of Inventory on Hand\[ DOH = \frac{365}{\text{Inventory Turnover}} \]
Days Sales Outstanding\[ DSO = \frac{365}{\text{Receivables Turnover}} \]
Days Payable Outstanding\[ DPO = \frac{365}{\text{Payables Turnover}} \]
Shorter CCC = better efficiency. Collect faster (lower DSO), sell inventory quickly (lower DOH), pay suppliers slowly (higher DPO).
Trade Credit EAR
Cost of Trade Credit (EAR)\[ EAR = \left(1 + \frac{d}{1-d}\right)^{\!\frac{365}{\text{Pay period} - \text{Discount period}}} - 1 \]
Example: 2/10 net 30 → 2% discount if paid within 10 days, otherwise due in 30.
Liquidity Ratios
Current Ratio\[ \text{Current Ratio} = \frac{CA}{CL} \]
Quick Ratio\[ \text{Quick Ratio} = \frac{\text{Cash} + \text{Mkt Sec} + \text{Receivables}}{CL} \]
Cash Ratio\[ \text{Cash Ratio} = \frac{\text{Cash} + \text{Mkt Sec}}{CL} \]
Sources of Liquidity
Primary: free cash flows, bank balances. Secondary: committed credit lines. Tertiary (dragonfly): asset sales, debt restructuring.
Working Capital Strategy Trade-Off
| Conservative | Aggressive | |
|---|---|---|
| Funding approach | Long-term financing; excess cash held | Short-term financing; minimal cash buffer |
| Rollover risk | Low | High |
| Financing cost | Higher | Lower (under upward yield curve) |
| Flexibility | Lower (covenants, lead times) | Higher (borrow as needed) |
Capital Investments & Capital Allocation
NPV & IRR Decisions
NPV Rule\[ NPV = \sum_{t=0}^{N}\frac{CF_t}{(1+r)^t} > 0 \implies \text{Accept} \]
When NPV and IRR conflict on mutually exclusive projects, prefer NPV (assumes reinvestment at cost of capital, which is more realistic).
Return on Invested Capital (ROIC)
Return on Invested Capital\[ ROIC = \frac{(1-t)\times\text{Operating Profit}}{\text{Avg Invested Capital}} \]
✓ Use when: If ROIC > WACC, the company is creating economic value.
Real Options
| Type | What It Is |
|---|---|
| Timing option | Delay investment until conditions improve |
| Sizing option | Expand, grow, or abandon based on outcomes |
| Flexibility option | Alter operations (prices, inputs, production) |
| Fundamental option | Future decision depends on event (e.g., drill based on oil price) |
Capital Allocation Pitfalls
- Internal forecasting errors (overoptimistic projections)
- Ignoring opportunity cost of internal financing
- Inconsistent treatment of inflation (mix real and nominal)
- Inertia (continuing bad projects to avoid sunk cost recognition)
- Basing decisions on earnings metrics rather than cash flows
- Pet projects (manager bias toward personally favoured ideas)
- Failing to consider alternatives
Investment Types
Real option types: Timing (delay investment), Sizing (expand or contract), Flexibility (switch inputs/outputs), Fundamental (abandon project).
Capital Structure
Weighted Average Cost of Capital (WACC)
Weighted Average Cost of Capital\[ WACC = w_d\,r_d(1-t) + w_p\,r_p + w_e\,r_e \]
Weights should be market-value based. Use target capital structure if available.
Modigliani & Miller (MM) Propositions
Modigliani-Miller Proposition I (no taxes)\[ V_L = V_U \quad \text{(capital structure irrelevant)} \]
MM I (with corporate taxes)\[ V_L = V_U + t \cdot D \]
Static Trade-Off Theory
Static Trade-Off Theory\[ V_L = V_U + t\cdot D - PV(\text{financial distress costs}) \]
Optimal structure: increase debt until marginal distress cost = marginal tax shield.
Pecking Order Theory
Managers prefer capital sources that reveal the least information:
- Internally generated earnings (BEST — no information revealed)
- New debt issuance
- New equity issuance (WORST — signals manager thinks stock is overpriced)
Estimating Target Capital Structure
- Assume company maintains its CURRENT capital structure
- Infer target weights from recent trend (direction of movement)
- Use the industry average as a proxy
Business Models
Pricing Strategy Types
Pricing strategies: tiered, dynamic, value-based, auction, bundling, razors-and-blades, freemium, penetration pricing.
Value Chain vs Supply Chain
Value chain: systems within the firm that create customer value. Supply chain: external steps to prepare a product for sale. Unit economics: revenue and cost per unit.
FINANCIAL STATEMENT ANALYSIS
Introduction to Financial Statement Analysis
| Step | Activity |
|---|---|
| 1. State objective | Define the question (creditworthiness? equity valuation? M&A?) |
| 2. Gather data | Financial statements, footnotes, MD&A, industry data |
| 3. Process data | Calculate ratios, common-size statements, adjustments |
| 4. Analyse & interpret | Draw conclusions — the "so what?" |
| 5. Report | Communicate findings, comply with Code & Standards |
| 6. Update | Revise periodically as company changes |
IOSCO: global securities regulation standard-setter. SEC: US capital markets regulator (GAAP). IASB: sets IFRS. FASB: sets US GAAP.
MD&A is NOT audited. It's management's perspective — treat with more scepticism than audited footnotes. Footnotes are audited and often reveal the most important information.
The Three Statements — Structure & Interconnections Critical
| Statement | What It Answers | Time Coverage | Key Equation |
|---|---|---|---|
| Income Statement | How much did the company earn? | Over a period | Revenue − Expenses = Net Income |
| Balance Sheet | What does the company own and owe? | Point in time (snapshot) | Assets = Liabilities + Equity |
| Cash Flow Statement | Where did cash come from and go? | Over a period (same as IS) | ΔCash = CFO + CFI + CFF |
Four Bridges (exam favourite):
| Bridge | What Flows |
|---|---|
| IS → BS | Net Income adds to Retained Earnings: Ending RE = Beginning RE + NI − Dividends. D&A reduces carrying value of PP&E and intangibles. |
| IS → CFS | Net Income is the starting point for CFO (indirect method). Non-cash items (D&A, unrealised gains) are reversed; accruals are converted to cash. |
| CFS → BS | Ending cash on CFS = Cash & equivalents on the Balance Sheet. CapEx (CFI outflow) increases PP&E; debt issued (CFF inflow) increases liabilities. |
| BS → CFS | Changes in working capital accounts drive CFO adjustments: ↑AR subtracts from CFO; ↑AP adds to CFO. Period-over-period BS changes are the raw material for the CFS. |
Memory anchor: Net Income is the hub — it grows equity (IS → BS), and it's the starting point for reconciling accrual profit to actual cash (IS → CFS). Ending cash links the CFS back to the BS.
Analysing Income Statements
Income Statement Structure
Top Line Revenue (Net Sales) $X,XXX
− Returns, discounts & allowances (XXX)
= Net Revenue $X,XXX
Gross Profit − Cost of Goods Sold (COGS) (X,XXX)
= Gross Profit → Gross Margin = GP / Revenue $X,XXX
Operating Income − SG&A, R&D, D&A, other operating expenses (XXX)
= Operating Income (EBIT) → Op. Margin = EBIT / Revenue $XXX
Pre-Tax Income + Interest / investment income XXX
− Interest expense (XXX)
+/− Non-operating gains / losses ±XX
= Pre-Tax Income (EBT) $XXX
Bottom Line − Income Tax Expense (XXX)
= Net Income $XXX
− Preferred Dividends / ÷ Shares = EPS $X.XX
EBITDA = EBIT + D&A. Non-GAAP measure used as a cash generation proxy. Does NOT equal CFO — it ignores working capital changes, taxes paid in cash, and capex.
Accrual vs. Cash: The IS uses accrual accounting — revenue earned ≠ cash received, expense incurred ≠ cash paid. The gap between NI and CFO is what the Cash Flow Statement reconciles.
Revenue Recognition (IFRS 15 / ASC 606 — 5-Step Model)
5-step model: (1) Identify contract, (2) Identify performance obligations, (3) Determine transaction price, (4) Allocate price to obligations, (5) Recognise revenue when/as each obligation is satisfied.
Revenue NOT recognised unless: risks of ownership transferred, amount reliably measurable, collection likely, and transaction unlikely to be reversed.
Capitalising vs Expensing
| Treatment | Effect on Balance Sheet | Effect on P&L (Near-term) |
|---|---|---|
| Capitalise | Increases assets; investing outflow | Higher NI (cost spread over time) |
| Expense | No asset; operating outflow | Lower NI (cost recognised immediately) |
Capitalising inflates near-term earnings and assets. Compare capitalising vs expensing decisions across competitors — a key quality-of-earnings flag.
Basic EPS
Basic EPS\[ EPS_{\text{basic}} = \frac{NI - \text{Preferred Dividends}}{WA \text{ Shares Outstanding}} \]
Diluted EPS Critical
Diluted EPS\[ EPS_{\text{diluted}} = \frac{NI - \text{Pref Div} + \text{Conv Pref Div} + \text{Conv Debt Interest}(1-t)}{WA\text{ Shares} + \text{Shares from conversions}} \]
Separately Reported Items
| Item | IFRS | US GAAP |
|---|---|---|
| Unusual/infrequent items | Reported within continuing operations; footnote disclosure | Reported separately within continuing operations |
| Discontinued operations | Reported separately, net of tax | Same — reported separately, net of tax |
Analysing Balance Sheets
Balance Sheet Structure Overview Critical
Assets = Liabilities + Shareholders' Equity
| ASSETS — What the company owns or controls | LIABILITIES + EQUITY — How assets are funded |
|---|---|
|
Current Assets (convert to cash < 1 yr) Cash & cash equivalents Short-term investments / marketable securities Accounts receivable (net of allowance) Inventory Prepaid expenses & other current assets Non-Current Assets (benefit > 1 yr) PP&E (net of accumulated depreciation) Right-of-use assets (leases) Intangible assets (patents, trademarks) Goodwill Long-term investments / equity-method investments Deferred tax assets (DTA) |
Current Liabilities (due < 1 yr) Accounts payable Accrued liabilities (wages, interest, taxes) Short-term debt / current portion of LT debt Unearned (deferred) revenue Non-Current Liabilities (due > 1 yr) Long-term debt / bonds payable Deferred tax liabilities (DTL) Finance lease obligations Pension / post-retirement obligations Shareholders' Equity Common stock + Additional paid-in capital (APIC) Retained earnings Accumulated OCI (AOCI) Treasury stock (contra — reduces equity) |
Retained Earnings bridge (IS → BS): Ending RE = Beginning RE + Net Income − Dividends Declared. Every dollar of NI not paid as a dividend accumulates here. This is the primary link between the income statement and the balance sheet.
Working Capital = Current Assets − Current Liabilities. Positive = short-term liquidity buffer. Negative can be fine (e.g. supermarkets) or a red flag — context matters.
Key Non-Current Assets
- Intangible assets: Patents, trademarks, customer lists (have finite or indefinite life)
- Goodwill: Premium paid in acquisition over fair value of net identifiable assets; not amortised (IFRS and US GAAP); tested for impairment annually
- Financial instruments: Measured at fair value or amortised cost depending on classification
Intangible Assets & Goodwill Critical
| Type | Treatment | Key Rule |
|---|---|---|
| Internally created intangibles | Expensed as incurred | IFRS: research expensed; development may be capitalised. US GAAP: both expensed |
| Purchased intangibles (finite life) | Capitalised, then amortised | Similar to tangible assets |
| Purchased intangibles (indefinite life) | Not amortised; impairment-tested annually | Includes goodwill |
Goodwill\[ \text{Goodwill} = \text{Purchase Price} - \text{Fair Value of Identifiable Net Assets} \]
Goodwill only arises from acquisitions — you cannot create it internally. It represents the premium paid for brand, customer loyalty, and synergies. Under both IFRS and US GAAP, goodwill is not amortised but tested for impairment at least annually.
| Financial Asset Classification | Balance Sheet | Unrealised Gains/Losses |
|---|---|---|
| Held-to-maturity (debt only) | Amortised cost | Not recognised |
| Available-for-sale / FVOCI | Fair value | OCI (bypasses P&L) |
| Trading / FVPL | Fair value | Income statement |
Key Non-Current Liabilities
- Long-term financial liabilities: Bonds payable, long-term loans, finance lease obligations
- Deferred tax liabilities: Taxes owed in the future (timing differences between book and tax income)
Goodwill impairment: Under IFRS and US GAAP, goodwill is impaired when carrying amount exceeds recoverable amount (IFRS) or fair value (US GAAP). US GAAP: a two-step test. IFRS: single-step. Impairment is a non-cash charge that reduces earnings and book value.
Analysing Statements of Cash Flows
Cash Flow Statement Structure
Unlike the income statement (accrual basis), the cash flow statement tracks actual cash movements. Its ending cash balance must equal the Cash line on the balance sheet — the hard-wired CFS → BS link.
Operating Activities (CFO) — core business cash generation Net Income (indirect method starting point) $X,XXX
+ Depreciation & amortisation (non-cash add-back) XXX
− Unrealised gains / + unrealised losses ±XXX
− Increase in accounts receivable ← earned but not collected (XXX)
− Increase in inventory ← cash tied up in stock (XXX)
+ Increase in accounts payable ← owe but haven't paid yet XXX
+ Increase in deferred tax liabilities XX
= Cash Flow from Operations (CFO) $X,XXX
Investing Activities (CFI) — long-term asset transactions − Capital expenditures / CapEx (purchase of PP&E) (X,XXX)
+ Proceeds from sale of PP&E or investments XXX
− Acquisitions (net of cash acquired) (X,XXX)
= Cash Flow from Investing (CFI) $(X,XXX)
Financing Activities (CFF) — capital structure transactions + Proceeds from long-term debt / equity issuance X,XXX
− Debt repaid + share repurchases + dividends paid (X,XXX)
= Cash Flow from Financing (CFF) $(X,XXX)
Net Change in Cash → links to Balance Sheet Net Change in Cash = CFO + CFI + CFF $±XXX
+ Beginning Cash (from prior balance sheet) X,XXX
= Ending Cash = Cash & equivalents on Balance Sheet $X,XXX
CFO pattern signals: (+CFO, −CFI, −CFF) = mature healthy firm. (−CFO, −CFI, +CFF) = growth / startup burning cash. (−CFO, +CFI, +CFF) = distressed — selling assets to fund losses. Consistently NI > CFO = earnings quality warning.
CFO — Indirect Method (Most Common)
CFO (Indirect Method)\[ CFO = NI + \text{Non-cash charges} - \Delta WC \]
Add: depreciation, amortisation, impairments. Subtract: gains on asset sales. Adjust for changes in working capital.
Memory trick: Source of cash: ↑ liabilities, ↓ assets. Use of cash: ↓ liabilities, ↑ assets. Depreciation is added back because it reduced NI but involved no cash payment.
Free Cash Flow Formulas
Free Cash Flow to Firm\[ FCFF = NI + NCC + I(1-t) - FCI - WCI \]
FCFF from CFO\[ FCFF = CFO + I(1-t) - FCI \]
Free Cash Flow to Equity\[ FCFE = CFO - FCI + \text{Net Borrowing} \]
Direct Method — Calculating Cash Flow Items Critical
Take the accrual IS item → remove non-cash pieces → adjust for the related BS account change.
| Cash Item | Formula |
|---|---|
| Cash received from customers | Revenue − Δ Accounts Receivable ↑ AR = earned but not collected → less cash in |
| Cash paid to suppliers | Step 1: Purchases = COGS + Δ Inventory Step 2: Cash Paid = Purchases − Δ Accounts Payable ↑ AP = bought on credit → less cash out |
| Cash paid to employees | Salaries Expense − Δ Salaries Payable |
| Cash paid for interest | Interest Expense − Δ Interest Payable |
| Cash paid for taxes | Tax Expense − Δ Taxes Payable − Δ Deferred Tax Liability |
Worked examples:
Revenue $500k, AR ↑ $20k → Cash received = $500k − $20k = $480k
COGS $300k, Inventory ↑ $10k, AP ↑ $5k → Purchases = $310k; Cash paid = $310k − $5k = $305k
Revenue $500k, AR ↑ $20k → Cash received = $500k − $20k = $480k
COGS $300k, Inventory ↑ $10k, AP ↑ $5k → Purchases = $310k; Cash paid = $310k − $5k = $305k
Converting Indirect → Direct Method
| Step | Action |
|---|---|
| 1. Start with accrual IS item | Use the revenue or expense line as reported |
| 2. Remove non-cash components | Strip out D&A and unrealised gains/losses — no cash counterpart |
| 3. Adjust for BS account changes | Apply Δ in the related working capital account (AR, Inventory, AP, Payables) |
Same total, different presentation. Indirect starts with NI and adjusts to cash; direct starts with cash receipts and payments. Both must arrive at the same CFO figure.
Cash Flow Linkages
Cash Collected from Customers\[ \text{Cash} = \text{Beginning AR} + \text{Revenue} - \text{Ending AR} \]
Cash Paid to Suppliers (two-step)\[ \text{Purchases} = COGS + \Delta\text{Inventory} \qquad \text{Cash Paid} = \text{Purchases} - \Delta AP \]
IFRS vs US GAAP — Cash Flow Classification
| Item | IFRS | US GAAP |
|---|---|---|
| Interest received | Operating OR Investing | Operating |
| Interest paid | Operating OR Financing | Operating |
| Dividends received | Operating OR Investing | Operating |
| Dividends paid | Operating OR Financing | Financing |
| Bank overdrafts | Part of cash & equivalents | Financing |
IFRS gives more flexibility; US GAAP is more prescriptive. Interest paid and dividends paid are the most commonly tested differences. Under IFRS, a company can classify interest paid as either operating or financing.
Quality Signals from Cash Flows
| Signal | Implication |
|---|---|
| CFO ≫ NI consistently | Good quality: earnings converting to cash |
| NI ≫ CFO persistently | Warning: accruals building; earnings quality low |
| CFO turns negative while NI positive | Red flag: business consuming cash despite reported profit |
Analysis of Inventories
Inventory Methods
| Method | US GAAP | IFRS |
|---|---|---|
| FIFO | Allowed | Allowed |
| LIFO | Allowed | Prohibited |
| Weighted Average | Allowed | Allowed |
| Specific Identification | Allowed | Allowed |
LIFO is unique to US GAAP — not permitted under IFRS. The "LIFO reserve" = FIFO inventory value − LIFO inventory value. Adding the LIFO reserve back to LIFO inventory restates it to FIFO equivalent.
Inventory Valuation
IFRS: Inventory at lower of cost or NRV. Reversal of write-downs allowed. US GAAP: lower of cost or market (= replacement cost); LIFO allowed; no write-down reversals.
| Standard / Method | Inventory Measurement |
|---|---|
| IFRS (all methods) | Lower of cost and NRV |
| US GAAP — FIFO or weighted average | Lower of cost and NRV |
| US GAAP — LIFO or retail | Lower of cost or market |
What "Market" Means (US GAAP LIFO / Retail)
Market = middle value of three amounts:
\[ \text{Market} = \text{median}(\text{Replacement Cost},\ \text{NRV},\ \text{NRV} - \text{Normal Profit Margin}) \]
\[ \text{Inventory Value} = \min(\text{Cost},\ \text{Market}) \]
Ceiling = NRV (no overstatement above recoverable amount). Floor = NRV − normal profit margin (no artificial future profit). Replacement cost is used as market only if it falls within that range.
FIFO vs LIFO Impact (Rising Prices) Critical
| If prices rising | FIFO | LIFO |
|---|---|---|
| Ending Inventory | Higher | Lower |
| COGS | Lower | Higher |
| Net Income | Higher | Lower |
| Income Tax Expense | Higher | Lower |
| Operating Cash Flow | Lower | Higher (tax savings) |
Intuition: Under FIFO, older (cheaper) costs go to COGS; newer (expensive) costs stay in inventory. Under LIFO, newer (expensive) costs go to COGS; older (cheap) costs stay in inventory. In rising price environments, LIFO gives more realistic COGS but understated inventory.
Analysis of Long-Term Assets
Depreciation Methods
Straight-Line Depreciation\[ Dep = \frac{\text{Cost} - \text{Salvage}}{\text{Useful Life}} \]
Double-Declining Balance\[ Dep_t = \frac{BV_t}{\text{Useful Life}} \times 2 \]
Units of Production\[ Dep_t = \frac{\text{Cost} - \text{Salvage}}{\text{Total Output}} \times \text{Output}_t \]
PP&E Impairment
| IFRS | US GAAP | |
|---|---|---|
| Model permitted | Cost AND Revaluation | Cost ONLY |
| Impairment test | Annual; if indicators exist | Only if impairment likely |
| Impairment loss | Carrying − Recoverable amount | Carrying − Fair value |
| Recoverable amount | Greater of (Fair Value − Costs to sell) and Value-in-use (PV of future CFs) | Fair value |
| Loss reversals | Allowed (up to original carrying value) | NOT allowed |
Lease Classification & Lessee Accounting Critical
Finance lease indicators (any one): ownership transfers; purchase option likely to be exercised; lease term = major part of asset life; PV of payments ≈ fair value; specialised asset.
| Finance Lease (US GAAP) | Operating Lease (US GAAP) | IFRS (all leases) | |
|---|---|---|---|
| Balance sheet | Right-of-use asset + lease liability | Right-of-use asset + lease liability | Right-of-use asset + lease liability |
| Income statement | Depreciation + interest (front-loaded) | Single lease expense (straight-line) | Depreciation + interest |
| CFO impact | Higher (only interest portion in CFO) | Lower (all payments in CFO) | Higher (interest component in CFO) |
IFRS treats ALL leases as finance leases. US GAAP still distinguishes operating vs finance. This can create comparability issues when comparing IFRS and US GAAP companies' leverage ratios.
Impairment — IFRS vs. U.S. GAAP Critical
| Feature | IFRS | U.S. GAAP |
|---|---|---|
| Test | Carrying value > recoverable amount | Step 1: Carrying value > undiscounted future cash flows |
| Write-down to | Recoverable amount (higher of fair value less selling costs OR value in use) | Fair value (or discounted CF if FV unknown) |
| Reversal allowed? | Yes (limited to original loss) | No (for assets held for use) |
Intuition — Impairment charges are a backdoor for earnings management. Management can time them during "bad" years (big bath), making future years look better — lower asset base means lower depreciation, higher ROA and ROE going forward. Watch for clusters of impairments when new management takes over.
Analysis of Income Taxes
Deferred Tax Assets & Liabilities Critical
DTL: taxable income < accounting income → will pay MORE tax in future. DTA: taxable income > accounting income → will pay LESS tax in future.
| Comparison | Result |
|---|---|
| Asset carrying amount > Tax base | DTL (paid more for book, less for tax) |
| Asset carrying amount < Tax base | DTA |
| Liability carrying amount > Tax base | DTA |
| Liability carrying amount < Tax base | DTL |
Tax Rate Changes
Tax rate increase → both DTA and DTL increase. Tax rate decrease → both decrease. Valuation allowance (US GAAP): reduces DTA if benefits unlikely to be realised.
Three Tax Rates
| Rate | Definition |
|---|---|
| Statutory rate | The legal corporate income tax rate in the jurisdiction |
| Effective tax rate | Income tax expense / EBT (as reported on P&L) |
| Cash tax rate | Taxes actually paid / EBT (real cash out the door) |
Pension Accounting (Defined Benefit Plans)
Net Pension Asset / Liability Critical
Net Pension Position\[ \text{Net} = \text{Fair Value of Plan Assets} - PBO \]
| Result | Balance Sheet Treatment |
|---|---|
| Plan assets > PBO | Net pension asset (non-current asset) |
| PBO > Plan assets | Net pension liability (non-current liability) |
PBO (Projected Benefit Obligation): Present value of all future benefits employees have earned to date, assuming future salary increases. The most comprehensive and most commonly used obligation measure.
Three Components of Pension Cost
| Component | Description | Cash Flow Statement |
|---|---|---|
| Service cost | Present value of benefits earned by employees this period | CFO |
| Interest cost | Unwinding of discount on PBO (PBO × discount rate) | CFO (IFRS: may be CFO or CFF) |
| Expected return on plan assets | Expected earnings on assets held in the fund (reduces pension cost) | CFO |
IFRS vs US GAAP — Pension
| IFRS | US GAAP | |
|---|---|---|
| Actuarial gains/losses | Through OCI (never recycled to P&L) | Through OCI, then amortised to P&L via corridor method |
| Past service cost | Recognised immediately in P&L | Amortised over service period |
| Balance sheet | Full fair-value recognition of net pension position | Full fair-value recognition (post-SFAS 158) |
Analyst adjustment: If a company has an underfunded DB plan, add the unfunded obligation back to debt when assessing leverage. Pension liabilities are "hidden debt" — economically similar to debt but often excluded from headline debt metrics.
Financial Analysis Techniques & Ratios
Activity Ratios
Total Asset Turnover\[ = \frac{\text{Revenue}}{\text{Avg Total Assets}} \]
Fixed Asset Turnover\[ = \frac{\text{Revenue}}{\text{Avg Net Fixed Assets}} \]
Working Capital Turnover\[ = \frac{\text{Revenue}}{\text{Avg Working Capital}} \]
Inventory Turnover\[ = \frac{COGS}{\text{Avg Inventory}} \]
Receivables Turnover\[ = \frac{\text{Revenue}}{\text{Avg Receivables}} \]
Payables Turnover\[ = \frac{\text{Purchases}}{\text{Avg Trade Payables}} \]
Cash Conversion Cycle\[ CCC = DSO + DOH - DPO \]
Solvency Ratios
Debt-to-Equity\[ = \frac{\text{Total Debt}}{\text{Total Equity}} \]
Debt-to-Capital\[ = \frac{\text{Total Debt}}{\text{Total Debt} + \text{Equity}} \]
Debt-to-Assets\[ = \frac{\text{Total Debt}}{\text{Total Assets}} \]
Financial Leverage\[ = \frac{\text{Avg Total Assets}}{\text{Avg Total Equity}} \]
Debt-to-EBITDA\[ = \frac{\text{Total Debt}}{EBITDA} \]
Interest Coverage\[ = \frac{EBIT}{\text{Interest Payments}} \]
Fixed Charge Coverage\[ = \frac{EBIT + \text{Lease Pmts}}{\text{Interest} + \text{Lease Pmts}} \]
Profitability Ratios
Gross Profit Margin\[ = \frac{\text{Gross Profit}}{\text{Revenue}} \]
Operating Profit Margin\[ = \frac{EBIT}{\text{Revenue}} \]
Net Profit Margin\[ = \frac{NI}{\text{Revenue}} \]
Return on Assets\[ ROA = \frac{NI}{\text{Avg Total Assets}} \]
Return on Equity\[ ROE = \frac{NI}{\text{Avg Total Equity}} \]
Defensive Interval Ratio\[ = \frac{\text{Cash} + \text{Mkt Sec} + \text{Receivables}}{\text{Avg Daily Expenditures}} \]
DuPont Analysis Critical
3-Factor DuPont\[ ROE = \underbrace{\frac{NI}{\text{Rev}}}_{\text{NPM}} \times \underbrace{\frac{\text{Rev}}{\text{Assets}}}_{\text{Asset TO}} \times \underbrace{\frac{\text{Assets}}{\text{Equity}}}_{\text{Leverage}} \]
5-Factor DuPont\[ ROE = \frac{NI}{\text{EBT}}\times\frac{\text{EBT}}{EBIT}\times\frac{EBIT}{\text{Rev}}\times\frac{\text{Rev}}{\text{Assets}}\times\frac{\text{Assets}}{\text{Equity}} \]
High ROE driven by leverage is dangerous. Always decompose: is ROE high because of good margins, efficient asset use, or excessive debt? A 25% ROE driven by 5× leverage is very different from 25% ROE driven by strong margins.
Depreciation Methods for FSA
Straight-Line\[ Dep = \frac{\text{Cost} - \text{Salvage}}{\text{Useful Life}} \]
DDB\[ Dep_t = \frac{2 \cdot BV_t}{\text{Useful Life}} \]
Units of Production\[ Dep_t = \frac{\text{Cost} - \text{Salvage}}{\text{Total Output}}\times\text{Output}_t \]
Behavioural Finance Biases in Forecasting
Common analyst forecasting biases: Overconfidence, Illusion of control, Conservatism (fail to update with new info), Representativeness (pattern-match too quickly), Confirmation (seek confirming evidence). Porter's Five Forces: Threat of substitutes, Rivalry, Bargaining power of suppliers/customers, Threat of new entrants.
EQUITY
Market Organisation & Structure
Market Functions
- Saving — move wealth to the future
- Borrowing — move future income to present
- Raising Equity Capital — companies sell ownership stakes
- Managing Risk — transfer risk to those willing to bear it
- Price Discovery — markets aggregate information into prices
- Liquidity Provision — assets can be converted to cash
Leveraged Positions & Margin Calls
Leverage Ratio\[ \text{Leverage} = \frac{\text{Position Value}}{\text{Equity}} \]
Max Initial Leverage\[ = \frac{1}{\text{Initial Margin }\%} \]
Margin call triggered when equity falls below maintenance margin.
Short Selling Critical
Borrow shares → sell at current price → hope price falls → buy back (cover) → return shares to lender. Maximum gain = short price (stock goes to zero). Maximum loss = unlimited (price can rise without bound).
Short Selling Profit\[ \text{Profit} = P_{\text{short}} - P_{\text{cover}} - \text{Dividends Paid} - \text{Borrowing Costs} \]
Margin Call Price (Short Position)\[ P_{\text{call}} = P_{\text{short}} \times \frac{1 + \text{Initial Margin \%}}{1 + \text{Maintenance Margin \%}} \]
Worked example: Short 100 shares at $80, initial margin 50%, maintenance margin 30%.
Margin call price = $80 × (1 + 0.50) / (1 + 0.30) = $80 × 1.1538 = $92.31
The price RISES above the short price to trigger a call — the short is losing money as price climbs.
Margin call price = $80 × (1 + 0.50) / (1 + 0.30) = $80 × 1.1538 = $92.31
The price RISES above the short price to trigger a call — the short is losing money as price climbs.
Key trap: Short sellers must pay dividends declared on borrowed shares to the lender. A $2 dividend reduces short P&L by $2/share.
Order Types
| Type | Description | Price Certainty |
|---|---|---|
| Market order | Fill immediately at market price | None |
| Limit order | Buy ≤ limit or sell ≥ limit | Certain |
| All-or-nothing | Cancel if not fully filled | N/A |
| Hidden | Visible to brokers, not traders | N/A |
| Iceberg | Only fraction of size visible | N/A |
Market Structures
| Structure | How Trades Execute | Examples |
|---|---|---|
| Quote-driven (dealer) | Dealers post bid/ask; trade with own inventory | OTC bond markets, FX |
| Order-driven | Exchange matches buyer and seller orders | NYSE, NASDAQ, CME |
| Brokered | Broker finds counterparty | Real estate, illiquid securities |
| Call market | Periodic single-price auctions; illiquid between calls | Open/close auctions |
Broker vs Dealer: A broker acts as AGENT (charges commission, takes no position). A dealer acts as PRINCIPAL (takes position, profits from spread). Confusing these is a classic trap.
Trade Pricing Rules
- Uniform pricing: Call markets — all trades at price that maximises quantity traded
- Discriminatory pricing: Continuous markets — most aggressive orders filled first, at their own prices
- Derivative pricing: Crossing networks — trade at midpoint of external market quotes
Security Market Indexes
Return Calculations
Single-Period Price Return\[ PR_i = \frac{P_{i,1} - P_{i,0}}{P_{i,0}} \]
Total Return\[ TR_i = \frac{P_{i,1} - P_{i,0} + \text{Inc}_i}{P_{i,0}} \]
Index Return (weighted)\[ PR_I = \sum_i w_i \cdot PR_i \]
Index Weighting Methods
| Method | Weight | Advantage | Disadvantage |
|---|---|---|---|
| Price-weighted | w_i = P_i / ΣP_j | Simple | Arbitrary (split-affected); bias toward high-price stocks |
| Equal-weighted | w_i = 1/N | Simple; emphasises small caps | Frequent rebalancing; underweights large caps |
| Cap-weighted (float-adj) | w_i = Q_iP_i / ΣQ_jP_j | Reflects market reality | Overweights possibly overvalued large caps |
| Fundamentally-weighted | Fundamental metric (sales, book value) | Value tilt; contrarian rebalancing | More complex; active bets |
Price-weighted index adjustment for stock splits: If one stock splits 2-for-1, its price is halved — but its economic weight should be unchanged. The divisor is DECREASED to keep the index value constant. This is the mechanical process behind index maintenance.
Float-adjustment: Removes shares held by insiders and governments from the weight calculation — only shares available for public trading are used. More realistic representation of investable universe.
Market Efficiency
Forms of the EMH Critical
| Form | Past Market Data Reflected? | All Public Info? | Private Info? |
|---|---|---|---|
| Weak | ✓ Yes | No | No |
| Semi-strong | ✓ Yes | ✓ Yes | No |
| Strong | ✓ Yes | ✓ Yes | ✓ Yes |
Weak EMH: past prices are fully reflected → technical analysis cannot earn abnormal profits.
Semi-strong EMH: all public information is reflected → fundamental analysis cannot earn abnormal profits.
Strong EMH: all information (including private) is reflected → no one can earn abnormal profits.
Market Anomalies & Behavioral Biases
| Anomaly | Description | Explanation |
|---|---|---|
| Momentum (3–12m) | Recent winners keep winning | Behavioral: underreaction/overconfidence |
| Value (long-run) | Low P/E, P/B outperform | Risk-based or mispricing |
| Small-cap effect | Small caps outperform historically | Liquidity risk premium; possible data mining |
| Post-earnings drift | Prices drift after earnings surprises for weeks | Strong challenge to semi-strong efficiency |
| Long-run reversal | Extreme losers outperform over 3–5 years | Behavioral: overreaction |
Behavioral Biases Affecting Market Prices
| Bias | Mechanism | Market Effect |
|---|---|---|
| Loss aversion | Losses hurt ~2× as much as gains feel good | Disposition effect: hold losers, sell winners |
| Overconfidence | Overestimate own ability/precision | Excessive trading, momentum |
| Representativeness | Extrapolate recent patterns as permanent | Overreaction, bubbles, then reversal |
| Conservatism | Fail to update beliefs with new information | Underreaction to earnings news (post-earnings drift) |
| Herding | Follow the crowd against private information | Amplifies bubbles and crashes |
Overview of Equity Securities
Common Share Voting Methods
Statutory voting: 1 vote per share per director seat. Cumulative voting: total votes = shares × seats, concentratable on one candidate — favours minority shareholders.
Preference Shares — Key Types Critical
| Type | Key Feature | Favours |
|---|---|---|
| Cumulative | Missed dividends accumulate; common can't be paid until preference is current | Investor |
| Non-cumulative | Missed dividends are lost permanently | Issuer |
| Participating | Fixed dividend PLUS share in residual earnings above a threshold | Investor |
| Convertible | Can convert into common shares at conversion ratio | Investor |
| Callable | Issuer can redeem at preset price | Issuer |
| Putable | Investor can force redemption at preset price | Investor |
Preference shares are EQUITY — dividends are NOT deductible. Common confusion: preference dividends look like interest but are paid from after-tax income. This is why WACC uses after-tax cost of debt but pre-tax cost of preferred stock (since preferred dividends are not tax-deductible).
Equity Return Components
Total Return Decomposition\[ TR = \underbrace{\frac{D_1}{P_0}}_{\text{Dividend Yield}} + \underbrace{\frac{P_1-P_0}{P_0}}_{\text{Capital Gain}} \]
Book Value per Share\[ BVPS = \frac{\text{Total Equity} - \text{Preference Equity}}{\text{Shares Outstanding}} \]
Depository Receipts
| Type | Description | Key Feature |
|---|---|---|
| Sponsored ADR | Foreign company participates; SEC disclosure required | Investor has same voting rights as local shareholders |
| Unsponsored ADR | Depository bank creates it without company involvement | Bank retains voting rights |
| GDR (Global) | Listed on multiple global exchanges; often USD-denominated | Cannot list on US exchanges; US investors via private placement |
| Global Registered Share (GRS) | Trades on multiple exchanges including domestic; multi-currency | Actual ownership interest (unlike DRs which are receipts) |
Company Analysis: Past, Present & Forecasting
Operating Leverage & Financial Leverage
Operating Income\[ \text{EBIT} = Q(P - VC) - FC \]
Degree of Operating Leverage\[ DOL = \frac{\%\Delta\,\text{EBIT}}{\%\Delta\,\text{Sales}} = \frac{Q(P-VC)}{Q(P-VC)-FC} \]
Degree of Financial Leverage\[ DFL = \frac{\%\Delta\,EPS}{\%\Delta\,EBIT} \]
Degree of Total Leverage\[ DTL = DOL \times DFL \]
High fixed costs → high operating leverage → profits amplified when revenues rise; amplified losses when revenues fall. Debt magnifies this further via DFL. Companies with both high DOL and DFL are extremely sensitive to economic cycles.
DuPont ROE Decomposition (see FSA section)
ROE exam diagnostic: When comparing two companies with similar ROE, always decompose. Company A: thin margins but high turnover (Walmart model). Company B: high margins but low turnover (luxury brand model). Both can achieve 15% ROE through very different strategies.
Porter's Five Forces (Industry Analysis)
| Force | High Force Means | Key Drivers |
|---|---|---|
| Rivalry among competitors | Price/margin pressure | # competitors, differentiation, exit barriers |
| Threat of new entrants | Competitive pressure on margins | Capital requirements, brand loyalty, regulation |
| Threat of substitutes | Price ceiling on the industry | Relative price-performance, switching costs |
| Buyer bargaining power | Margin compression | Buyer concentration, volume, switching costs |
| Supplier bargaining power | Input cost increases | Supplier concentration, input uniqueness |
Industry Life Cycle Stages
| Stage | Growth Rate | Profitability | Competition |
|---|---|---|---|
| Embryonic | Slow | Low/Negative | Few early movers |
| Growth | Rapid | Rising | Increasing |
| Shakeout | Slowing | Declining (price wars) | Intense; weak players exit |
| Mature | GDP-like | Stable | Moderate (oligopoly) |
| Decline | Negative | Low | Reducing; players exit |
Equity Valuation: Concepts & Basic Tools
Dividend Discount Models (DDM)
General DDM\[ V_0 = \sum_{t=1}^{\infty}\frac{D_t}{(1+r)^t} \]
Multi-period with Terminal Value\[ V_0 = \sum_{t=1}^{n}\frac{D_t}{(1+r)^t} + \frac{P_n}{(1+r)^n} \]
Multistage DDM
Terminal Value (Gordon Growth)\[ P_n = \frac{D_{n+1}}{r - g_L} \]
✓ Use when: Use when firm transitions from high growth to stable long-run growth \(g_L\).
Price Multiples
Forward P/E Justified by DDM\[ \frac{P_0}{E_1} = \frac{\text{Payout Ratio}}{r - g} \]
P/B = Price per share / Book value per share. P/CF = Price / Cash flow per share. P/S = Price / Sales per share.
P/E interpretation: High P/E implies high expected growth, low risk, or both. P/E relative to growth = PEG ratio. A stock with P/E = 20 and growth = 10% has PEG = 2. Lower PEG can suggest better value.
Enterprise Value (EV)
Enterprise Value\[ EV = MV_E + MV_{PS} + MV_D - \text{Cash} - \text{ST Investments} \]
EV/EBITDA is popular for comparing firms across capital structures.
FIXED INCOME
Fixed-Income Features, Cash Flows & Issuance
Cash Flow Structures
| Structure | Description |
|---|---|
| Bullet bond | Fixed coupons; 100% principal at maturity (most common) |
| Zero-coupon bond | No coupons; issued at discount; Duration = Maturity (most rate-sensitive) |
| Fully amortised | Equal annuity payments (interest + principal mixed); like a mortgage |
| Partially amortised | Some principal repaid periodically; lump sum ("balloon") at maturity |
| Sinking fund | Fixed % of principal retired each year |
| Floating-rate note (FRN) | Coupon = Reference rate (MRR) + Quoted Margin; resets periodically |
| Step-up bond | Coupon rate increases on a preset schedule |
| Inflation-linked bond | Principal indexed to CPI; coupon applied to adjusted principal |
| Deferred coupon bond | No coupons in early years; higher coupons in later years |
| PIK (Payment-in-Kind) | Coupons paid in additional bonds rather than cash |
Embedded Options Critical
Callable Bond Price\[ V_{\text{callable}} = V_{\text{bullet}} - V_{\text{call option}} \]
Putable Bond Price\[ V_{\text{putable}} = V_{\text{bullet}} + V_{\text{put option}} \]
Seniority Ranking (Waterfall)
| Priority | Claim Type |
|---|---|
| 1st | First Lien — Senior Secured (highest recovery) |
| 2nd | Second Lien — Secured |
| 3rd | Senior Unsecured |
| 4th | Senior Subordinated |
| 5th | Subordinated |
| 6th | Junior Subordinated |
| Last | Equity (residual claim; typically 0% recovery in default) |
Pari passu: Claims of equal seniority rank equally regardless of maturity. All senior unsecured bonds share recovery pro-rata.
Fixed-Income Markets
Repurchase (Repo) Agreements Critical
Repo Terminal Price\[ P_{\text{terminal}} = P_{\text{purchase}}\times\left(1 + r_{\text{repo}}\times\frac{\text{Days}}{360}\right) \]
Haircut\[ \text{Haircut} = \frac{\text{Security Price} - \text{Purchase Price}}{\text{Security Price}} \]
Factors that INCREASE repo rate: Lower-quality collateral, longer term, more unique/illiquid collateral, physical (rather than electronic) delivery.
Commercial Paper
Key risk: Rollover risk. CP is short-term (≤270 days). If market freezes (like 2008), company can't issue new CP to repay maturing CP → forced default. Mitigation: maintain committed backup revolving credit lines.
Sovereign vs Non-Sovereign Debt
| Type | Issuer | Key Feature |
|---|---|---|
| On-the-run sovereign | National governments | Most recent issue; most liquid; benchmark rate |
| Off-the-run sovereign | National governments | Less liquid than on-the-run |
| Municipal (GO) | Sub-national; backed by taxing power | Often tax-exempt interest; generally safer |
| Municipal (Revenue) | Sub-national; backed by project revenue | Risk depends on project success |
| Quasi-government/Agency | Government-backed agencies | Implicit or explicit government guarantee |
| Supranational | IMF, World Bank, ECB | Multi-government backing |
Bond Valuation: Prices, Yields & Term Structure
Bond Pricing with Market Discount Rate
Bond Price (general)\[ PV = \sum_{t=1}^{N}\frac{PMT}{(1+r)^t} + \frac{FV}{(1+r)^N} \]
PMT = r → PV = FV (par). PMT < r → PV < FV (discount). PMT > r → PV > FV (premium). Pull-to-par as maturity approaches.
The #1 Fixed Income Rule: Bond prices and yields move in OPPOSITE directions. ALWAYS. This is non-negotiable. A rise in market yield → price falls. A fall in yield → price rises.
Full Price, Flat Price & Accrued Interest
Full Price (Dirty)\[ P_{\text{full}} = P_{\text{flat}} + AI \]
Full Price Between Coupon Dates\[ P_{\text{full}} = PV \times (1+r)^{t/T} \]
Accrued Interest\[ AI = \frac{t}{T}\times PMT \]
Bond Price Properties (Key Relationships)
| Effect | Description |
|---|---|
| Inverse effect | Price moves opposite to yield — always |
| Convexity effect | Yield decrease has LARGER price impact than equivalent increase (positive convexity) |
| Coupon effect | Lower-coupon bonds are more sensitive to yield changes |
| Maturity effect | Longer-maturity bonds are more sensitive to yield changes |
| Pull to par | As maturity approaches, price converges to 100 regardless of starting price |
Yield Measures Critical
| Measure | Definition | Key Limitation |
|---|---|---|
| Current yield | Annual coupon / Flat price | Ignores capital gains and time value |
| YTM | IRR: discount rate making PV of CFs = price | Assumes hold-to-maturity AND reinvest at YTM |
| Yield-to-call (YTC) | YTM using call date as maturity | Only relevant if called |
| Yield-to-worst (YTW) | min(YTM, YTC1, YTC2, …) | Most conservative; always use for callables |
Effective Annual Yield (from semi-annual)\[ EAY = \left(1 + \frac{YTM_{\text{semi}}}{2}\right)^2 - 1 \]
Simple Yield\[ = \frac{\text{Annual Coupon} + \text{Amortised Gain/Loss}}{\text{Flat Price}} \]
Yield Spread Measures
G-Spread\[ G\text{-spread} = YTM - \text{Government Bond Yield} \]
I-Spread\[ I\text{-spread} = YTM - \text{Swap Rate} \]
Z-spread: constant spread added to ALL spot rates so bond PV = price. OAS = Z-spread − option value (removes embedded option cost).
| Bond Type | OAS vs Z-spread | Reason |
|---|---|---|
| Callable | OAS < Z-spread | Issuer's call option removes value from investor |
| Putable | OAS > Z-spread | Investor's put option adds value — investor "pays" via lower yield |
| Straight (option-free) | OAS = Z-spread | No option to adjust for |
FRN Pricing (Quoted Margin vs Discount Margin)
FRN Coupon\[ C = MRR + QM \]
FRN PV (using Discount Margin)\[ PV = \sum_{t=1}^{N}\frac{MRR + QM}{(1+\frac{MRR+DM}{m})^t} + \frac{FV}{(1+\frac{MRR+DM}{m})^N} \]
QM is fixed at issuance. DM is the market's required spread over MRR.
Money Market Instruments
Discount Rate (DR) Basis — T-Bills\[ PV = FV\left(1 - \frac{\text{Days}}{360}\times DR\right) \]
Add-On Rate (AOR) Basis — CDs, LIBOR\[ PV = \frac{FV}{1 + \frac{\text{Days}}{360}\times AOR} \]
Bond Equivalent Yield (BEY) from DR\[ BEY = \frac{365\times DR}{360 - DR\times\text{Days}} \]
Spot Rates, Forward Rates & Yield Curves
Bond Pricing with Spot Rates\[ PV = \frac{PMT}{(1+z_1)} + \frac{PMT}{(1+z_2)^2} + \cdots + \frac{PMT+FV}{(1+z_N)^N} \]
Forward Rate from Spot Rates\[ IFR_{A,\,B-A} = \left[\frac{(1+z_B)^B}{(1+z_A)^A}\right]^{1/(B-A)} - 1 \]
| Yield Curve Shape | Spot vs Par Curve | Forward Curve |
|---|---|---|
| Upward sloping (normal) | Par curve BELOW spot | Forward curve ABOVE spot |
| Flat | All three equal | All three equal |
| Inverted | Par curve ABOVE spot | Forward curve BELOW spot |
Fixed-Income Risk & Returns: Duration & Convexity
Macaulay Duration
Macaulay Duration (approximate)\[ D_{\text{Mac}} = \frac{\sum_{t=1}^N t \cdot \dfrac{CF_t}{(1+r)^t}}{PV_{\text{full}}} \]
Exact closed-form: accounts for coupon rate, YTM, maturity, and time since last coupon.
Modified Duration & Price Sensitivity
Modified Duration\[ D_{\text{mod}} = \frac{D_{\text{Mac}}}{1 + r} \]
Price Change Approximation\[ \%\Delta PV \approx -D_{\text{mod}}\times\Delta YTM \]
Approximate Modified Duration\[ D_{\text{mod}} \approx \frac{PV_- - PV_+}{2\times\Delta y\times PV_0} \]
Money Duration (PVBP)\[ PVBP = D_{\text{mod}}\times PV\times 0.0001 \]
Convexity Adjustment
Full Price Change with Convexity\[ \%\Delta PV \approx -D_{\text{mod}}\cdot\Delta y + \tfrac{1}{2}\cdot C\cdot(\Delta y)^2 \]
Approximate Convexity\[ C \approx \frac{PV_- + PV_+ - 2\,PV_0}{(\Delta y)^2\cdot PV_0} \]
⚠ Trap: Convexity is always positive for straight bonds → price rises more than duration predicts when yields fall, and falls less when yields rise.
Positive convexity (straight bonds): When yields fall, price rises MORE than duration predicts. When yields rise, price falls LESS. Convexity is always beneficial — more is better. Callable bonds exhibit negative convexity at low yields.
Duration Properties Summary
| Factor | Effect on Duration |
|---|---|
| Longer maturity | Higher duration |
| Lower coupon rate | Higher duration |
| Lower YTM | Higher duration |
| Zero-coupon bond | Duration = Maturity (maximum) |
| Callable bond | Lower duration than equivalent straight bond |
Effective Duration & Convexity (Bonds with Options)
Effective Duration\[ D_{\text{eff}} = \frac{PV_- - PV_+}{2\times\Delta\text{Curve}\times PV_0} \]
Effective Convexity\[ C_{\text{eff}} = \frac{PV_- + PV_+ - 2\,PV_0}{(\Delta\text{Curve})^2\times PV_0} \]
Use effective measures (not analytical) for bonds with embedded options.
Fixed-Income: Credit Risk & Analysis
5 Cs of Credit Analysis
5 Cs of credit: Capacity (ability to repay), Capital (reserves), Collateral (security), Covenants (terms), Character (management integrity).
Credit Risk Measurement
Expected Credit Loss\[ E[\text{Loss}] = PD\times LGD = PD\times(1-\text{Recovery Rate})\times\text{Exposure} \]
High-Yield vs Investment-Grade Analysis
| Aspect | Investment Grade | High Yield |
|---|---|---|
| Primary risk | Interest rate risk | Default risk (credit risk) |
| Correlation with equities | Lower | Higher (behave more like equities) |
| Spreads | Narrow (basis points) | Wide (hundreds of bps) |
| Key ratios | Interest coverage, D/E | Liquidity, covenant analysis, recovery assumptions |
| Key Credit Ratio | Investment Grade (typical) | High Yield (typical) |
|---|---|---|
| Debt / EBITDA | < 3.0× | > 4.0× (LBOs can reach 7–8×) |
| EBITDA / Interest | > 5× | < 3× (near 1× = distressed) |
| FCF / Debt | > 10% | < 5% or negative |
Notching — Seniority & Recovery Critical
Different bonds from the same issuer carry different ratings based on their recovery rate in default:
| Seniority | Rating vs Issuer Rating | Why |
|---|---|---|
| Senior secured | 1–2 notches above | Collateral improves recovery in default |
| Senior unsecured | Benchmark issuer rating | Standard reference point |
| Subordinated | 1–2 notches below | Last in line; worse recovery |
Exam trap: BB-rated issuer → senior secured ≈ BB+/BBB−; subordinated ≈ B+/B. Notching difference is wider for HY issuers where recovery uncertainty is greater.
Sovereign Credit Analysis — Willingness vs Ability to Pay Critical
Unlike corporations, governments cannot be forced into bankruptcy. A sovereign may have the economic capacity to repay yet choose not to (political risk). Willingness to pay is therefore as important as ability to pay — especially for emerging market issuers.
| Factor | Key Question | Why It Matters |
|---|---|---|
| Institutional quality | Rule of law? Anti-corruption? Stability? | Stable institutions → consistent debt culture → lower default risk |
| Fiscal flexibility | Can they adjust taxes and spending? | Countries able to raise taxes in a crisis can always service debt |
| Monetary effectiveness | Is the central bank independent? | Independent CB prevents money printing → lower inflation risk |
| Economic diversification | Is GDP concentrated in one export commodity? | Diversified economy has more stable tax revenue base |
| External position | Reserve currency? Current account surplus? | Reserve currency status → cheapest possible borrowing cost |
| Quantitative Metric | Direction |
|---|---|
| Debt / GDP | Higher = worse |
| Budget deficit / GDP | Higher = worse (debt growing faster) |
| External debt / GDP | Higher = worse (FX risk — can't print foreign currency) |
| FX reserves / short-term debt | Higher = better (can meet near-term payments) |
| Current account balance | Surplus = better (earns FX) |
Fixed-Income Securitisation: ABS & MBS
Securitisation Structure
ABS structure: Originator sells loans to bankruptcy-remote SPV. SPV issues tranched securities. Senior tranches have priority; subordinate tranches absorb first losses (credit enhancement).
Non-Mortgage ABS & CDOs
| Type | Collateral | Structure |
|---|---|---|
| Auto loan ABS | Auto loans | Amortising — principal paid down over time |
| Credit card ABS | Credit card receivables | Non-amortising — revolving; reinvestment period |
| CDO | Corporate bonds, leveraged loans, CDS | Tranched by seniority |
RMBS & CMOs
Pass-through MBS: investors receive pro-rata share of principal and interest including prepayments. CMO tranches redirect prepayment risk. PAC tranches have stable cash flows; companion tranches absorb variability.
CMBS (Commercial MBS)
Debt Service Coverage Ratio\[ DSC = \frac{NOI}{\text{Debt Service}} \]
Loan-to-Value Ratio\[ LTV = \frac{\text{Loan Amount}}{\text{Appraised Value}} \]
Covered Bonds vs Securitisation Critical
| Feature | Covered Bond | ABS / MBS (Securitisation) |
|---|---|---|
| Assets on balance sheet? | Yes — stay on bank's books | No — sold to SPE (true sale) |
| Recourse to issuer? | Dual recourse: cover pool AND issuing bank | No recourse to originator — SPE only |
| Bankruptcy protection | Pool is ring-fenced on bank's balance sheet | Full bankruptcy remoteness via SPE |
| Originator risk for investor | Bank credit risk remains | Bank credit risk eliminated for investors |
Key exam distinction: Covered bonds give dual recourse — investors can claim against the cover pool first, then against the issuing bank. Securitisation transfers assets to a bankruptcy-remote SPE; investors have no claim against the originator. "Only securitisation uses an SPE" — correct; covered bonds keep assets on the bank's books.
DERIVATIVES
Derivative Instrument & Market Features
OTC vs Exchange-Traded (ETD)
| OTC Market | Exchange-Traded (ETD) | |
|---|---|---|
| Liquidity | Lower | Higher |
| Trading costs | Higher | Lower |
| Transparency | Less | Greater |
| Standardisation | Lower (customisable) | Higher (standardised) |
| Flexibility | Higher | Lower |
| Counterparty credit risk | Higher (bilateral) | Lower (CCP guarantees) |
Zero-sum game: Every gain by the long is exactly offset by a loss to the short. Derivatives redistribute wealth between parties; they do not create it in aggregate.
Derivative Underlyings
- Equities (individual stocks, indices)
- Fixed-income instruments and interest rates
- Currencies (FX forwards, FX futures)
- Commodities (oil, gold, agricultural)
- Credit (CDS, CDOs)
- Other (weather, crypto, longevity risk)
Forward Commitments vs Contingent Claims Critical
| Forward Commitments | Contingent Claims |
|---|---|
| Obligation — MUST trade at expiry | Right but NOT obligation to trade |
| Forward contracts, Futures, Swaps | Options (calls, puts), Credit derivatives |
| No premium paid at initiation | Premium paid upfront by buyer |
| Symmetric payoff profile | Asymmetric payoff profile |
Derivative Benefits & Risks
Benefits: risk transfer/hedging, price discovery, market completeness, lower transaction costs. Risks: leverage amplifies losses, counterparty risk (OTC), complexity, systemic risk.
Arbitrage, Replication & Cost of Carry
No-Arbitrage Forward Price Critical
Forward Price (no income, discrete)\[ F_0(T) = S_0\,(1+r_f)^T \]
Forward Price (continuous)\[ F_0(T) = S_0\,e^{r_f T} \]
With income/costs\[ F_0(T) = (S_0 - I + C)\,(1+r_f)^T \]
With convenience yield (commodities)\[ F_0(T) = S_0\,e^{(r_f + c - y)T} \]
Cost of Carry framework: Forward price = Spot price + Financing cost + Storage cost − Income received (dividends, coupons, convenience yield). High storage costs (commodities) → F > S (contango). High convenience yield → F < S (backwardation).
Forward Price vs Futures Price
| Correlation (Futures Price vs Interest Rates) | Relationship |
|---|---|
| None | Futures price = Forward price |
| Positive | Futures price > Forward price |
| Negative | Futures price < Forward price |
The correlation effect is because daily mark-to-market on futures means gains are invested immediately at current rates; losses are funded at current rates. When futures prices are positively correlated with interest rates, gains compound at higher rates → futures worth more.
Pricing & Valuation of Forward and Futures Contracts
Forward Contract Valuation
Forward Value at Initiation\[ V_0 = 0 \]
Forward Value During Life (long)\[ V_t = S_t - \frac{F_0(T)}{(1+r)^{T-t}} \]
Forward Value at Maturity (long)\[ V_T = S_T - F_0(T) \]
Interest Rate Forward (FRA)
FRA Settlement (received by long at settlement)\[ \text{Settlement} = \frac{(MRR - FRA\text{ rate})\times NP\times\frac{D}{360}}{1 + MRR\times\frac{D}{360}} \]
| Position | Benefits from Rising MRR | Benefits from Falling MRR |
|---|---|---|
| Long FRA (buy, fixed-rate payer) | Yes | No |
| Short FRA (sell, floating-rate payer) | No | Yes |
Futures Contract Pricing
Eurodollar / SOFR Futures Price\[ f = 100 - (100\times MRR) \]
Futures BPV (Dollar Duration)\[ BPV_f = D_{\text{mod}}\times P_f\times 0.0001 \]
Hedge Ratio\[ N^* = \frac{(D_T - D_P)\times P}{D_f\times P_f} \]
| Position | Benefits from Rising MRR | Benefits from Falling MRR |
|---|---|---|
| Short interest rate futures | Yes (price falls, short profits) | No |
| Long interest rate futures | No | Yes (price rises, long profits) |
Pricing & Valuation of Interest Rate Swaps
Swap Periodic Settlement (floating-rate payer)\[ \text{Settlement} = (MRR - r_{\text{swap}})\times NP\times\frac{D}{360} \]
Interest rate swap = series of FRAs. Fixed-rate payer benefits when rates rise.
Swap equivalence: A plain-vanilla interest rate swap (pay fixed, receive floating) is economically equivalent to: Issuing a fixed-rate bond + buying a floating-rate bond. The notional principal is NEVER exchanged in interest rate swaps (only cash flow differences). Currency swaps DO exchange principal at initiation and maturity.
Pricing & Valuation of Options
Option Moneyness & Values
| Moneyness | Call Condition | Put Condition |
|---|---|---|
| In-the-money (ITM) | S_t > X | S_t < X |
| At-the-money (ATM) | S_t = X | S_t = X |
| Out-of-the-money (OTM) | S_t < X | S_t > X |
Call Value at Expiry\[ c_T = \max(0,\; S_T - X) \]
Put Value at Expiry\[ p_T = \max(0,\; X - S_T) \]
Arbitrage Bounds
Call Lower / Upper Bounds\[ \max\!\left(0,\; S_t - \frac{X}{(1+r)^{T-t}}\right) \leq c_t \leq S_t \]
Put Lower / Upper Bounds\[ \max\!\left(0,\; \frac{X}{(1+r)^{T-t}} - S_t\right) \leq p_t \leq \frac{X}{(1+r)^{T-t}} \]
Factors Affecting Option Values
| Factor Increases | Call | Put |
|---|---|---|
| Value of underlying (S) | ↑ | ↓ |
| Exercise price (X) | ↓ | ↑ |
| Time to expiration | ↑ | ↑ (except deep ITM puts) |
| Risk-free rate (r) | ↑ | ↓ |
| Volatility of underlying (σ) | ↑ | ↑ |
| Income/Dividends on underlying | ↓ | ↑ |
| Cost of carry | ↑ | ↓ |
Volatility ALWAYS increases option value — both calls and puts. Higher volatility = more chance of large moves in either direction = more potential for the option to expire deep in the money.
Put-Call Parity & Binomial Model
Put-Call Parity
Put-Call Parity\[ c_0 + \frac{X}{(1+r)^T} = S_0 + p_0 \]
Put-Call-Forward Parity\[ c_0 + \frac{X}{(1+r)^T} = \frac{F_0(T)}{(1+r)^T} + p_0 \]
Parity allows you to create synthetic positions:
Synthetic call = Stock + Put − PV(X)
Synthetic put = Call − Stock + PV(X)
Synthetic stock = Call − Put + PV(X)
Synthetic bond = Stock + Put − Call
One-Period Binomial Model
Hedge Ratio (Delta)\[ h = \frac{c_u - c_d}{S_u - S_d} \]
Risk-Neutral Up-Probability\[ \pi_u = \frac{(1+r_f) - d}{u - d} \]
Option Value (risk-neutral)\[ c_0 = \frac{\pi_u c_u + (1-\pi_u) c_d}{1+r_f} \]
Risk-neutral pricing insight: We don't need to know actual probabilities. Risk-neutral probabilities make the expected return equal to the risk-free rate. This is the foundation of all option pricing models.
ALTERNATIVE INVESTMENTS
Alternative Investment Features, Methods & Structures
Categories of Alternatives
| Category | Sub-types |
|---|---|
| Private Capital | Private equity (LBO, VC), Private debt (direct lending, mezzanine, distressed, venture debt) |
| Real Assets | Real estate, Infrastructure, Commodities, Farmland & Timberland, Digital assets |
| Hedge Funds | Equity hedge, Event-driven, Relative value, Opportunistic (global macro) |
Defining Features
- Narrow manager specialisation
- Low correlation with traditional investments (diversification benefit)
- Large capital outlays; long investment horizons
- Illiquidity — requires patience and long-term commitment
- Incentive-based compensation (carried interest)
- Harder to appraise performance
Access Methods
| Method | Description | Best For |
|---|---|---|
| Fund investing | Indirect; pool capital with manager | No in-house expertise; want diversification |
| Co-investing | Hybrid; invest in fund PLUS directly in deals alongside manager | Building skills; reducing fees |
| Direct investing | Buy assets yourself; no manager | Large institutions with specialist team |
Limited Partnership Structure
| Party | Role | Liability |
|---|---|---|
| GP (General Partner) | Fund manager; makes all investment decisions | Unlimited |
| LP (Limited Partner) | Investor; provides capital; no management role | Limited to investment amount |
Committed Capital = total amount LPs agree to invest (called over time). Dry Powder = committed but not yet deployed capital.
Alternative Investment Performance & Returns
Fee Structures Critical
Soft hurdle: performance fee applies to ENTIRE return once hurdle is cleared. Hard hurdle: fee only on returns ABOVE the hurdle.
Catch-Up Clause\[ \text{GP share} = \text{Carry }\%\times(\text{All profits once hurdle cleared}) \]
Hard hurdle favours LPs; soft hurdle favours GPs. A catch-up clause is functionally similar to a soft hurdle — once hurdle is cleared, GP receives 100% of remaining gains until it "catches up" to its target carry percentage.
High-Water Mark & Clawback
High-Water Mark (HWM): highest NAV previously used to calculate performance fee. No performance fee until HWM is exceeded → prevents double-charging. A clawback provision allows LPs to recover carry already paid if subsequent losses reverse earlier gains — critical protection in deal-by-deal waterfalls.
Waterfall — American vs European Critical
| Structure | Also Called | How It Works | Who Benefits? |
|---|---|---|---|
| Deal-by-deal | American waterfall | Performance fee paid on each profitable exit individually — even if other deals lose money | GP — gets paid early on winners |
| Whole-of-fund | European waterfall | LPs receive 100% of invested capital + hurdle rate first; GP carry paid only after | LP — all capital returned before GP earns carry |
Worked example: Fund invests $100M each in Deal A (+$30M gain) and Deal B (−$20M loss). Net gain = $10M. Carry = 20%.
• American: Carry on A = 20% × $30M = $6M. No carry on B. LP receives $204M (2% net return).
• European: Carry = 20% × $10M = $2M. LP receives $208M (4% net return).
• With clawback (American): LP claws back $4M → same result as European.
• American: Carry on A = 20% × $30M = $6M. No carry on B. LP receives $204M (2% net return).
• European: Carry = 20% × $10M = $2M. LP receives $208M (4% net return).
• With clawback (American): LP claws back $4M → same result as European.
J-Curve Effect Critical
| Phase | What Happens | Returns |
|---|---|---|
| 1. Capital Commitment | GP makes capital calls; investments identified. Management fees charged immediately. | Negative — fees paid, no returns yet |
| 2. Capital Deployment | Capital invested; portfolio companies early-stage or being restructured. | Negative / breakeven |
| 3. Capital Distribution | Exits via IPO, trade sale, etc. Capital + profits returned to LPs. | Strongly positive — the "hockey stick" |
Intuition: The J-curve is why alternatives require patience. Positive returns come only in Phase 3. Always compare funds of the same vintage year — a fund in Year 2 and a fund in Year 8 will show wildly different reported returns even if equally well-managed. Use IRR (money-weighted) because the GP controls timing of cash flows.
MOIC & IRR
Multiple of Invested Capital\[ MOIC = \frac{\text{Realised} + \text{Unrealised Value}}{\text{Total Invested Capital}} \]
⚠ Trap: MOIC ignores timing of cash flows. A 2× MOIC in 2 years >> 2× MOIC in 10 years. Use IRR for time-adjusted performance.
Leveraged Return
Leveraged Return (Alternative)\[ R_L = R_P + \frac{V_B}{V_E}(R_P - r_B) \]
Performance Biases
| Bias | Effect on Reported Returns |
|---|---|
| Survivorship bias | Overstates returns (failed funds excluded) |
| Backfill bias | Overstates returns (only winners add historical data) |
| Stale pricing (Level 3) | Understates volatility; overstates Sharpe ratio |
Investments in Private Capital: Equity & Debt
Private Equity — Two Key Strategies Critical
| Leveraged Buyout (LBO) | Venture Capital (VC) | |
|---|---|---|
| Target company | Mature, cash-generative | Early-stage, high growth potential |
| Debt usage | 60–80% debt; heavy leverage | Primarily equity |
| Value creation | Operational improvement + deleveraging | Revenue growth; scaling the business |
| Exit timeline | 3–7 years (IPO or trade sale) | 5–10 years (IPO is common exit) |
| Return profile | Lower risk (cash flows known) | Binary — most fail, few generate huge returns |
VC Financing Stages
VC stages: Formative (angel/seed/early-stage: pre-revenue), Later-stage (post-production, pre-IPO). PE buyout strategies: LBO, growth equity, turnaround.
Private Equity Exit Strategies
- Trade sale — sell to strategic buyer (most common by number)
- IPO / Direct listing / SPAC (best price but complex and takes time)
- Secondary sale — sell to another PE firm
- Recapitalisation — take on more debt, pay special dividend to PE sponsor
- Liquidation — sell assets; last resort
Private Debt Types
| Type | Description | Risk Level |
|---|---|---|
| Direct lending | Senior secured loans to mid-market companies | Lower |
| Venture debt | Complements VC equity; early-stage companies | Medium-High |
| Mezzanine debt | Subordinated to senior; often with equity kickers | High |
| Distressed debt | Debt of companies in financial trouble; deep discount | Very high |
| Unitranche | Single combined loan blending senior and subordinated | Medium |
Real Estate, Infrastructure & Natural Resources
Real Estate Investment Structures
| Debt | Equity | |
|---|---|---|
| Private | Mortgages, Construction lending | Direct ownership, RE funds, Private REITs |
| Public | MBS, CMOs, Mortgage REITs | Shares in RE corps., Public REITs |
Open-end infinite-life funds: core/core-plus (stabilised assets, lower risk). Closed-end finite-life funds: value-add/opportunistic (higher risk, active improvement).
Commodity Investment Forms
Commodity Futures Price\[ F_0(T) = S_0\,e^{(r+c-y)T} \]
c = storage costs, y = convenience yield. Contango: F > S (storage-dominated). Backwardation: F < S (convenience yield > cost of carry).
Infrastructure Investment Features
- Greenfield (new assets built from scratch) vs Brownfield (existing assets acquired)
- Economic infrastructure: Roads, airports, ports, utilities
- Social infrastructure: Hospitals, schools, prisons
- Access: Direct ownership or indirect (MLP, ETF, listed infrastructure)
- Long-term, stable, often regulated cash flows
- Inflation hedging: Revenue often indexed to inflation
Timberland & Farmland
Returns from timberland/farmland: biological growth + commodity prices + land appreciation. Low correlation with equities and bonds.
Hedge Funds & Digital Assets
Hedge Fund Strategies
| Strategy | Description | Approach |
|---|---|---|
| Equity Hedge | Long/short equity and equity derivatives | Bottom-up stock selection |
| Event-Driven | Profit from specific corporate events (M&A, restructuring) | Bottom-up; catalyst-focused |
| Relative Value | Exploit pricing discrepancies between related securities | Market-neutral; pair trades |
| Opportunistic (Global Macro) | Top-down economic and geopolitical trends; major asset classes | Top-down; high leverage |
| Managed Futures (CTA) | Trend-following using futures across asset classes | Quantitative, systematic |
Hedge Fund Features
- Low legal and regulatory restrictions (private funds)
- Large investment universe (long, short, derivatives)
- Heavy use of leverage and derivatives
- Aggressive strategies with concentrated positions
- Limits on liquidity (lockups, gates, notice periods)
- High fees (typically "2 and 20" but declining)
Digital Assets
DLT/Blockchain: distributed, immutable, consensus-based record-keeping. Tokenisation = representing ownership rights on a ledger. NFTs are non-fungible; security tokens represent financial claims.
| Direct Access | Indirect Access |
|---|---|
| Centralised exchanges (Coinbase) | Cryptocurrency coin trusts |
| Decentralised exchanges (DEX) | Cryptocurrency futures contracts |
| Crypto ETFs | |
| Cryptocurrency stocks |
PORTFOLIO MANAGEMENT
Portfolio Risk & Return: Part I
Risk Aversion & Utility
Investor Utility Function\[ U = E(r) - \tfrac{1}{2}\,A\,\sigma^2 \]
A > 0: risk-averse (requires compensation). A = 0: risk-neutral. A < 0: risk-seeking.
Indifference curves: Risk-averse investors have upward-sloping indifference curves. More risk-averse = steeper slope (need more return to accept more risk). The optimal portfolio is where the investor's indifference curve is tangent to the CAL.
Two-Asset Portfolio Risk Critical
Two-Asset Portfolio Return\[ E(R_p) = w_A E(R_A) + w_B E(R_B) \]
Two-Asset Portfolio Variance\[ \sigma_p^2 = w_A^2\sigma_A^2 + w_B^2\sigma_B^2 + 2\,w_A w_B\,\rho_{AB}\,\sigma_A\sigma_B \]
Capital Allocation Line (CAL)
Capital Allocation Line\[ E(R_p) = R_f + \frac{E(R_i)-R_f}{\sigma_i}\,\sigma_p \]
Slope of the CAL = Sharpe ratio of the risky portfolio.
Efficient Frontier
Key points:
- Minimum-variance frontier: all portfolios with lowest risk for given return
- Global minimum-variance portfolio: leftmost point of the frontier
- Efficient frontier: UPPER portion of MVF (rational investors only choose these)
- Portfolios below the efficient frontier are suboptimal (same risk, lower return)
Roy's Safety-First Ratio
Roy's Safety-First Ratio\[ SFR = \frac{E(R_p) - R_L}{\sigma_p} \]
Portfolio Risk & Return: Part II — CAPM
Systematic vs Unsystematic Risk Critical
Total Risk = Systematic + Unsystematic. Unsystematic risk is diversified away in a large portfolio. Only systematic (market) risk is compensated.
~12–30 stocks eliminates ~90% of unsystematic risk. Since diversification is free, the market only compensates the systematic component. A biotech stock with 80% total risk but β = 0.3 has a LOWER required return than a stable stock with β = 1.2.
Beta
Beta\[ \beta_i = \frac{\text{Cov}(R_i, R_M)}{\sigma_M^2} = \rho_{i,M}\frac{\sigma_i}{\sigma_M} \]
β = 1: same risk as market. β > 1: more volatile. β < 1: less volatile. β < 0: moves inversely to market.
CAPM & Security Market Line (SML) Critical
Capital Asset Pricing Model\[ E(R_i) = R_f + \beta_i\bigl[E(R_M) - R_f\bigr] \]
Securities above the SML → expected return > CAPM required → undervalued → buy. Below SML → overvalued → sell.
Performance Measures
| Measure | Formula | Risk Used | Best Used For |
|---|---|---|---|
| Sharpe ratio | (Rₚ−Rᶠ)/σₚ | Total (σ) | Total portfolio evaluation |
| Treynor ratio | (Rₚ−Rᶠ)/βₚ | Systematic (β) | Well-diversified portfolios |
| Jensen's alpha | Rₚ − [Rᶠ + βₚ(R_M−Rᶠ)] | Systematic (β) | Absolute excess return vs SML |
| M-squared (M²) | (Rₚ−Rᶠ)(σ_M/σₚ) + Rᶠ | Total (σ) | Comparison to market with leverage |
Stocks above the SML are undervalued (positive alpha = actual return exceeds CAPM required return). Stocks below the SML are overvalued (negative alpha).
Portfolio Management: An Overview & Planning
Three-Step Portfolio Management Process
| Step | Name | Key Activities |
|---|---|---|
| 1 | Planning | Analyse objectives & constraints → produce IPS |
| 2 | Execution | Asset allocation + security analysis + portfolio construction |
| 3 | Feedback | Monitor + rebalance + performance measurement & reporting |
Investment Policy Statement (IPS) Constraints — TTLLU
| Constraint | Key Consideration |
|---|---|
| Time horizon | Longer → more risk/illiquidity tolerable |
| Tax situation | May prefer tax-advantaged instruments |
| Liquidity | High needs → more bonds/cash; avoid illiquid |
| Legal/Regulatory | Trust laws, insider trading restrictions |
| Unique circumstances | ESG, religious, ethical preferences |
Willingness vs Ability to take risk: When they conflict, the LOWER of the two prevails. You can't invest aggressively for a client whose financial situation doesn't support it, regardless of their enthusiasm.
Institutional Investor Characteristics
| Investor | Risk Tolerance | Time Horizon | Liquidity Needs |
|---|---|---|---|
| DB Pension (younger beneficiaries) | Higher | Long | Lower |
| Endowments/Foundations | High | Very long (perpetual) | Low (spending rate) |
| Banks | Very low | Short | High |
| Life insurance | Low | Long | High |
| P&C insurance | Low | Short | High |
| Investment companies (mutual funds) | Varies by mandate | Varies | High (redemptions) |
Strategic vs Tactical Asset Allocation
Strategic Asset Allocation (SAA): long-term policy weights from IPS, based on capital market expectations. Tactical Asset Allocation (TAA): short-term deviations from SAA to exploit market opportunities.
Behavioural Biases of Individuals
Cognitive Errors (can be corrected)
| Bias | What Happens | Portfolio Impact |
|---|---|---|
| Conservatism | Fail to update views with new information | Hold investments too long; miss turning points |
| Confirmation | Seek only information that confirms existing beliefs | Over-concentration; under-diversification |
| Representativeness | Classify by similarity to stereotypes; extrapolate patterns | Buy/sell based on patterns, not fundamentals |
| Illusion of control | Overestimate ability to influence uncontrollable outcomes | Excessive trading; under-diversification |
| Hindsight | "I knew it all along" after the fact | Overconfidence in future predictions |
| Anchoring & adjustment | Over-weight initial reference point | Slow to update valuations; anchored to purchase price |
| Mental accounting | Keep separate mental buckets for different money | Not considering total portfolio risk |
| Framing | Same question answered differently based on presentation | Risk perception changes with framing |
| Availability | Over-weight recent or memorable events | Overweight recently salient assets/risks |
Emotional Biases (must be accommodated)
| Bias | What Happens | Portfolio Impact |
|---|---|---|
| Loss aversion | Losses hurt ~2× more than equivalent gains | Hold losing positions too long (disposition effect) |
| Overconfidence | Overestimate own ability and precision | Excessive trading; underestimate risk |
| Self-control | Lack discipline for long-term goals | Insufficient savings; spend future money now |
| Status quo | Prefer doing nothing over making changes | Inertia; failure to rebalance |
| Endowment | Value assets more when you own them | Over-hold concentrated positions; resist selling |
| Regret aversion | Avoid decisions that could turn out badly | Herding; excessive conservatism |
Cognitive errors are caused by faulty reasoning → correct with better information and education. Emotional biases are from feelings → must be accommodated rather than eliminated. Always address cognitive component first.
Introduction to Risk Management
Risk Management Framework
- Risk governance — tone at the top; board oversight
- Risk identification and measurement
- Risk infrastructure — systems, data, processes
- Defined policies and processes — documented procedures
- Risk monitoring, mitigation, and management
- Communications — internal and external transparency
- Strategic analysis and integration
IPS constraints: TTLLU — Time horizon, Tax concerns, Liquidity needs, Legal/regulatory constraints, Unique circumstances.
Risk Categories & Measures
| Category | Types |
|---|---|
| Financial risks | Market risk, credit risk, liquidity risk |
| Non-financial risks | Operational, legal, regulatory, political, model, settlement, tail risk |
Risk measures: Standard deviation (total risk), Beta (systematic risk), VaR (max loss at confidence level), CVaR/Expected Shortfall (tail risk beyond VaR).
Sharpe Ratio\[ SR = \frac{E(R_p) - R_f}{\sigma_p} \]
Treynor Ratio\[ TR = \frac{E(R_p) - R_f}{\beta_p} \]
Jensen's Alpha\[ \alpha = R_p - \bigl[R_f + \beta_p(R_M - R_f)\bigr] \]
ETHICS & PROFESSIONAL STANDARDS
Foundation: Code of Ethics & Standards Overview
Three Layers of Obligation
| Layer | Standard | Enforced By |
|---|---|---|
| Legal / Regulatory | Minimum required by law | Government, regulators (SEC, FCA) |
| Firm / Compliance | May exceed law | Employer, CCO |
| CFA Ethics | Often exceeds both law and firm policy | Professional judgment; CFA Institute |
The CFA Standards set a FLOOR, not a ceiling. Always follow the STRICTER of local law or CFA Standards. Legal compliance is necessary but never sufficient to ensure ethical behaviour.
Map of the Seven Standards
| Standard | Theme |
|---|---|
| I — Professionalism | Knowledge of Law, Independence & Objectivity, Misrepresentation, Misconduct |
| II — Market Integrity | Material Nonpublic Information, Market Manipulation |
| III — Duties to Clients | Loyalty, Prudence & Care; Fair Dealing; Suitability; Performance; Confidentiality |
| IV — Duties to Employers | Loyalty; Additional Compensation; Supervisory Responsibilities |
| V — Investment Analysis | Diligence & Reasonable Basis; Communication with Clients; Record Retention |
| VI — Conflicts of Interest | Disclosure; Priority of Transactions; Referral Fees |
| VII — CFA Membership | Conduct as Participant/Candidate; Reference to Designation |
Why Ethics Failures Happen
- Overconfidence in own ethics: "I would never do that" → blinds to gradual drift
- Situational influences: Pressure from supervisors, bonus incentives, organisational culture
- Cognitive biases: Framing, confirmation bias, in-group loyalty distort judgment
Ethical Decision-Making Framework: (1) Identify facts, (2) Identify ethical issues, (3) Identify relevant principles/standards, (4) Identify conflicts, (5) Consider alternatives, (6) Choose and act. When an action is legal but unethical, the CFA answer is typically the more ethical choice.
Standard I — Professionalism
I(A) Knowledge of the Law
Follow the STRICTER of: local law OR CFA Standards. If CFA Standards stricter → follow CFA Standards. If local law stricter → follow local law.
Classic exam trap: CFA Standards do NOT require reporting violations to regulators. They require DISASSOCIATION. Reporting may be required by local law, but that's a separate obligation from CFA Standards.
I(B) Independence & Objectivity
Gift guidelines: modest gifts from clients are generally OK. Gifts from third parties (e.g., brokers, investment bankers) that could reasonably impair objectivity are NOT acceptable without employer disclosure.
I(C) Misrepresentation
Three forms of misrepresentation: (1) False statements, (2) Misleading omissions (technically true but creates false impression), (3) Plagiarism.
I(D) Misconduct
Does NOT apply to personal behaviour UNLESS it reflects adversely on professional reputation, integrity, or competence. Examples that DO violate I(D): fraud in personal business dealings, DUI (reflects on judgment/character), dishonesty outside of work.
Standard II — Integrity of Capital Markets
II(A) Material Nonpublic Information (MNPI)
Material: information a reasonable investor would consider important OR that would likely affect price. Nonpublic: not yet disseminated through appropriate channels. Mosaic theory: compiling public non-material information is permitted.
Classic exam trap — Mosaic Theory: An analyst who researches public filings, conducts channel checks, and speaks to customers is performing legitimate fundamental analysis. This is permitted even if the conclusion is powerful. The test is whether any SINGLE piece of information is material AND nonpublic.
II(B) Market Manipulation
Prohibited: information-based manipulation (spreading false info) and transaction-based manipulation (trades designed to distort prices or create false impressions of activity).
Key distinction: A fund manager who executes a large block trade that moves the market has NOT violated II(B) — that's a legitimate trade. A manager who executes trades WITH THE INTENT to distort prices has violated II(B).
Standard III — Duties to Clients
III(A) Loyalty, Prudence & Care
Loyalty to clients: place client interests above own and employer's. Client = actual beneficiaries (e.g., pension trustee's client = pension beneficiaries, not employer).
III(B) Fair Dealing
Fair dealing: all clients in same mandate receive same recommendation simultaneously. IPO allocations must be distributed fairly — cannot favour high-fee clients.
"Fairly" ≠ "equally". Clients paying for more personalised service can receive more customised service. But investment recommendations and changes must go to ALL clients in a mandate simultaneously, not the most profitable first.
III(C) Suitability
Suitability: determine risk tolerance (willingness AND ability), time horizon, return objective, and constraints before making recommendations.
III(D) Performance Presentation
Performance presentation: must be fair, accurate, and complete. Cannot cherry-pick periods or promise returns on risky assets.
III(E) Preservation of Confidentiality
Confidentiality: keep all client info confidential UNLESS client is engaged in illegal activity against others, OR legal/regulatory disclosure is required.
Standard IV — Duties to Employers
IV(A) Loyalty to Employer
Loyalty to employer: must obtain permission before outside work that competes with employer or uses employer's clients, information, or resources.
IV(B) Additional Compensation
Additional compensation: obtain WRITTEN permission from ALL parties before accepting compensation/benefits beyond normal salary for work performed.
IV(C) Responsibilities of Supervisors
Supervisory responsibility: adequate training, monitoring, and prompt remediation when violations are detected.
Standard V — Investment Analysis, Recommendations & Actions
V(A) Diligence & Reasonable Basis
Diligence: support all recommendations with thorough research. When relying on third-party research, investigate quality and independence.
V(B) Communication with Clients
Communications: distinguish facts from opinions clearly. Disclose investment process and methodology. Keep clients informed of material changes.
V(C) Record Retention
Record retention: maintain records supporting all investment recommendations and actions. Recommended minimum = 7 years.
Standard VI — Conflicts of Interest
VI(A) Disclosure of Conflicts
Disclosure of conflicts: disclose all material conflicts prominently and in plain language. Includes personal ownership, compensation arrangements, relationships with issuers.
VI(B) Priority of Transactions
Priority of transactions: client accounts first, employer accounts second, personal accounts last. Front-running (trading ahead of client orders) is prohibited.
VI(C) Referral Fees
Referral fees: must disclose any fees received for directing client business to third parties and any fees paid to receive client referrals.
Standard VII — Responsibilities as CFA Member/Candidate
VII(A) Conduct as Participant in CFA Program
Conduct in exam: do not share exam questions or answers. Do not misrepresent the content of the exam.
VII(B) Reference to CFA Institute / Designation
CFA designation: do not misrepresent membership (must be current, dues paid) or charter status (must have passed all 3 levels + 4,000 hours work experience).
Global Investment Performance Standards (GIPS)
GIPS: voluntary standards for fair, comparable performance presentation. Firms must present 5-year (building to 10-year) compliant records. Must use composites of similar portfolios.
GIPS error correction: If a GIPS-compliant firm discovers a significant error in historical performance, it must restate the affected period and re-present to all existing and prospective clients who received the erroneous data. Materiality of the error determines if prior client communication is needed.
Key GIPS facts for exam:
- GIPS is VOLUNTARY for investment management firms
- Compliance is claimed on FIRM-WIDE basis, not strategy-by-strategy
- Composites must include ALL fee-paying, discretionary accounts in that strategy
- Performance must be presented gross AND net of fees
- "Our composite performance was calculated in accordance with GIPS" — specific wording matters
BA II Plus Calculator Reference
TVM Worksheet
BA II Plus TVM keys: N (periods), I/Y (rate per period as %), PV (negative = outflow), PMT, FV. Use CPT to compute. Always clear TVM (2nd → CLR TVM) before each problem.
Cash Flow Worksheet (NPV/IRR)
CF worksheet: CF0 = initial cash flow; C01, C02… = subsequent distinct cash flows. F01 = frequency of C01. Press NPV then I and CPT for net present value; IRR then CPT for IRR.
CFA Level I — Expanded Revision Guide 2024 | Based on Salt Solutions Formula Sheet & CFA Curriculum
| For personal study use only