CFA Level 1 — Portfolio Management

Intuition-First Study Guide · Readings 83–88

Every concept explained in plain English · Likely exam questions after every topic

Reading 83

Portfolio Risk and Return: Part I

The mathematics of combining assets — why diversification is the only "free lunch" in finance.

Risk Aversion and Utility

Most investors are risk-averse — given two investments with identical expected returns, they choose the one with lower risk. This doesn't mean they avoid risk entirely; they simply demand compensation (higher expected return) for bearing it.

Think of risk aversion like paying for insurance on your phone. You'd rather pay a small certain cost (the premium) than face the uncertain large cost (replacing the phone). In investing, the "premium" you demand is a higher expected return.

A risk-seeking investor prefers more risk for the same return (rare in finance). A risk-neutral investor cares only about expected return, regardless of risk.

Indifference Curves

An indifference curve plots all risk-return combinations that give an investor equal utility (satisfaction). For risk-averse investors, these curves slope upward — to accept more risk, you need more return.

More risk-averse investors have steeper indifference curves (they demand a lot more return for a small increase in risk). Less risk-averse investors have flatter curves.

The optimal portfolio is found where the investor's indifference curve is tangent to the capital allocation line (CAL). A less risk-averse investor will hold more of the risky portfolio; a more risk-averse investor will hold more of the risk-free asset.

Variance, Covariance, and Correlation

Risk is measured by variance (or its square root, standard deviation). For a sample of T returns:

\[ s^2 = \frac{\sum_{t=1}^{T}(R_t - \bar{R})^2}{T - 1} \]

Covariance measures how two assets move together. Correlation standardises covariance between –1 and +1:

\[ \rho_{1,2} = \frac{Cov(R_1, R_2)}{\sigma_1 \times \sigma_2} \]

Correlation Value	Meaning	Diversification Benefit
ρ = +1	Move perfectly together	None — risk is just a weighted average
ρ = 0	No linear relationship	Substantial risk reduction
ρ = –1	Move perfectly opposite	Maximum — risk can be eliminated entirely

Two-Asset Portfolio Risk Critical

\[ \sigma_P = \sqrt{w_1^2\sigma_1^2 + w_2^2\sigma_2^2 + 2w_1 w_2 \rho_{1,2} \sigma_1 \sigma_2} \]

🎯 Likely Exam Question

Two assets have standard deviations of 25% and 18%, with equal weights (50/50). Calculate portfolio standard deviation when correlation is +1, 0.5, and 0.

ρ = +1: σ = 0.5(25%) + 0.5(18%) = 21.5% (just a weighted average).
ρ = 0.5: σ² = 0.25(0.0625) + 0.25(0.0324) + 2(0.5)(0.5)(0.5)(0.25)(0.18) = 0.034975 → σ = 18.70%.
ρ = 0: σ² = 0.25(0.0625) + 0.25(0.0324) = 0.023725 → σ = 15.40%.
Notice: Lower correlation → lower portfolio risk. This is the diversification benefit in action.

The Efficient Frontier

The minimum-variance frontier is the set of portfolios with the lowest risk for each level of return. The global minimum-variance portfolio sits at the leftmost point. The efficient frontier is the upper portion — no rational investor chooses a portfolio below it.

The efficient frontier is like a speed-fuel efficiency curve for cars. You can get the most speed for any fuel consumption level, but once you're on the frontier, getting more speed always costs more fuel. Portfolios below the frontier are like badly-tuned engines — they waste fuel (risk) without getting proportional speed (return).

The Capital Allocation Line (CAL)

Combining a risk-free asset with a risky portfolio produces a straight line on a risk-return graph — the CAL. This works because the risk-free asset has zero standard deviation and zero correlation with everything.

\[ \sigma_P = w_A \times \sigma_A \]

If you invest 60% in the risky portfolio (σ = 20%) and 40% in the risk-free asset, your portfolio's risk is simply 0.60 × 20% = 12%.

Two-fund separation theorem: Every investor's optimal portfolio is some mix of (1) the risk-free asset and (2) the same optimal risky portfolio. They differ only in how much they allocate to each.

🎯 Likely Exam Question

An investor puts 60% in a risky asset with E(R) = 10% and σ = 8%, and 40% in a risk-free asset at 5%. What are the portfolio's expected return and standard deviation?

E(Rp) = 0.60(10%) + 0.40(5%) = 8.0%
σp = 0.60 × 8% = 4.8%
The risk-free asset contributes zero risk, so portfolio risk is just the weight times the risky asset's risk.

Reading 84

Portfolio Risk and Return: Part II

From the CML to CAPM — the models that define how markets should price risk.

Capital Market Line (CML)

Under the assumption that all investors have homogeneous expectations (same forecasts for risk, return, correlations), there's one optimal risky portfolio everyone holds — the market portfolio. The CAL drawn from the risk-free rate through this market portfolio is the Capital Market Line.

\[ E(R_P) = R_f + \frac{E(R_M) - R_f}{\sigma_M} \times \sigma_P \]

The slope of the CML is the market price of risk: the extra return per unit of total risk. Only efficient portfolios (combinations of the risk-free asset and the market portfolio) plot on the CML.

CML uses total risk (σ) on the x-axis. Only efficient portfolios lie on it. Individual securities and poorly diversified portfolios plot below it.

Systematic vs. Unsystematic Risk Critical

Systematic (Market) Risk

Caused by macro factors (GDP, interest rates, inflation). Cannot be diversified away. Rewarded with higher expected return. Measured by beta.

Unsystematic (Firm-Specific) Risk

Caused by company-specific factors (lawsuits, management changes). Can be diversified away for free. Not rewarded — the market doesn't pay you for risk you can eliminate.

\[ \text{Total Risk} = \text{Systematic Risk} + \text{Unsystematic Risk} \]

About 12–30 stocks can eliminate ~90% of unsystematic risk. Since diversification is essentially free, the market only compensates systematic risk. A biotech stock with huge total risk but low beta may have a lower required return than a boring industrial stock with higher beta.

Beta — The Measure of Systematic Risk Formula

\[ \beta_i = \frac{Cov(R_i, R_M)}{\sigma_M^2} = \frac{\rho_{i,M} \times \sigma_i}{\sigma_M} \]

Beta Value	Interpretation
β = 1.0	Same systematic risk as the market
β > 1.0	More volatile than the market (aggressive)
β < 1.0	Less volatile than the market (defensive)
β = 0	Uncorrelated with the market (e.g., risk-free asset)

🎯 Likely Exam Question

The market's standard deviation is 20%. Stock A has σ = 30% and ρ with the market = 0.8. What is Stock A's beta?

β = (ρ × σ_A) / σ_M = (0.8 × 0.30) / 0.20 = 1.2
Alternatively: if Cov(A,M) = 0.048, then β = 0.048 / 0.04 = 1.2. Know both methods.

The CAPM and Security Market Line (SML) Critical

\[ E(R_i) = R_f + \beta_i \times [E(R_M) - R_f] \]

This is the Capital Asset Pricing Model. It says every security's required return equals the risk-free rate plus a beta-adjusted market risk premium. The SML plots this relationship with beta on the x-axis.

CML

X-axis = Total risk (σ). Only efficient portfolios plot on it. Shows combinations of the risk-free asset + market portfolio.

SML

X-axis = Systematic risk (β). All securities and portfolios (efficient or not) plot on it in equilibrium.

🎯 Likely Exam Question

Rf = 6%, E(Rm) = 15%, Stock X has β = 1.2 and is priced at $25. It will pay a $1 dividend and be worth $30 at year-end. Is it under- or overvalued?

Required return (CAPM): 6% + 1.2(15% – 6%) = 16.8%
Expected return: (30 – 25 + 1)/25 = 24%
Since 24% > 16.8%, the stock plots above the SML → it is undervalued → buy it. Positive alpha = expected return exceeds required return.

Performance Measures

Measure	Formula	Risk Type Used	When to Use
Sharpe Ratio	$\frac{R_P - R_f}{\sigma_P}$	Total risk (σ)	Single manager / total portfolio
Treynor Measure	$\frac{R_P - R_f}{\beta_P}$	Systematic risk (β)	Well-diversified portfolio / multi-manager
Jensen's Alpha	$R_P - [R_f + \beta_P(R_M - R_f)]$	Systematic risk (β)	Excess return above SML
M-squared	$R_f + \frac{\sigma_M}{\sigma_P}(R_P - R_f)$	Total risk (σ)	Leveraged comparison to market

🎯 Likely Exam Question

Which return metric measures excess return per unit of systematic risk?

The Treynor measure. The Sharpe ratio uses total risk. Jensen's alpha measures the difference between actual return and SML-predicted return (not a ratio). M-squared adjusts for total risk.

Reading 85

Portfolio Management: An Overview

The big picture — why portfolios exist, who manages them, and the three-step process.

The Portfolio Perspective

The portfolio perspective means evaluating every investment by its contribution to the portfolio's risk and return — not in isolation. An investor who holds all wealth in one stock is not taking the portfolio perspective, because they bear unsystematic risk that is not compensated.

Owning 50 mediocre stocks is often better than owning 1 "great" stock. The portfolio of 50 stocks eliminates most firm-specific risk, so your return comes almost entirely from compensated market risk. The single stock might have incredible returns — or devastating losses.

The diversification ratio = portfolio σ ÷ average individual σ. A ratio of 0.72 means the portfolio captures only 72% of the average stock's risk — a 28% risk reduction from diversification. A ratio of 1.0 means no diversification benefit.

Diversification works best during normal markets. During crises (e.g., 2008), correlations spike toward 1.0, reducing diversification benefits precisely when you need them most.

The Three-Step Portfolio Management Process

Step	Name	Key Activities
1	Planning	Analyse client objectives, constraints, risk tolerance → produce the Investment Policy Statement (IPS)
2	Execution	Top-down (macro → asset allocation) and bottom-up (security analysis → individual picks)
3	Feedback	Monitor, rebalance, measure performance vs. the IPS benchmark

Types of Investors

Investor Type	Risk Tolerance	Time Horizon	Liquidity Needs	Income Needs
Individuals	Varies	Varies	Varies	Varies
Banks	Low	Short	High	Pay interest
Endowments	High	Long	Low	Spending level
Insurance (Life)	Low	Long	High	Low
Insurance (P&C)	Low	Short	High	Low
DB Pension	High	Long	Low	Depends on age

Defined Benefit vs. Defined Contribution

Defined Benefit (DB)

Employer promises a specific retirement income → employer bears investment risk. Must manage assets vs. liabilities.

Defined Contribution (DC)

Employer contributes a set amount each period → employee bears investment risk. No promise about final value.

🎯 Likely Exam Question

In a defined contribution pension plan, who assumes the investment risk?

The employee. The employer only promises contributions, not outcomes. In a DB plan, the employer bears the risk because they've promised a specific benefit.

Pooled Investments

Open-end mutual funds issue/redeem shares at NAV. Closed-end funds trade on exchanges at market-determined prices (can trade at premium or discount to NAV). ETFs trade like stocks with low fees but incur brokerage costs. Hedge funds are for accredited investors, use leverage and derivatives, and typically charge "2 and 20" (2% management + 20% of profits).

Reading 86

Basics of Portfolio Planning and Construction

The IPS is the GPS for investing — without it, you're driving blind.

The Investment Policy Statement (IPS)

The IPS is the starting point of portfolio management. It's a written plan documenting the investor's objectives and constraints, ensuring discipline and realistic expectations.

🧠 The Big Picture

The IPS forces the conversation: "What do you want, what can you handle, and what are your limits?" Without this document, managers make assumptions, investors have unrealistic expectations, and nobody has a benchmark to measure success against.

Major IPS Components

Description of client · Statement of purpose · Duties & responsibilities · Procedures for updates · Investment objectives (risk & return) · Investment constraints · Investment guidelines · Performance evaluation · Appendices (strategic asset allocation, rebalancing policy).

Risk and Return Objectives

Type	Absolute Example	Relative Example
Risk	"No loss greater than 10% in any year"	"Returns within 2% of FTSE return"
Return	"At least 6% per annum nominal"	"Exceed S&P 500 by 2% per year"

Risk and return objectives must be compatible. A client who wants 15% returns with no chance of loss is setting contradictory goals — the adviser must reconcile this.

Willingness vs. Ability to Take Risk Exam Favorite

Willingness = psychological (personality, beliefs, comfort). Ability = financial (wealth, time horizon, income stability, liabilities).

When willingness and ability conflict, the lower of the two typically prevails. High willingness + low ability → low overall tolerance. High ability + low willingness → adviser may educate, but ultimately defers to lower willingness.

🎯 Likely Exam Question

A client has above-average willingness to take risk but below-average ability. What is the overall risk tolerance?

Below average. The prudent approach is to use the lower of ability and willingness. You can't invest aggressively when the client's financial situation doesn't support it, regardless of their enthusiasm.

The Five Investment Constraints — "TTLLU" Critical

Constraint	Description	Impact on Portfolio
Time horizon	Period until funds are needed	Longer → more risk/illiquidity tolerable
Tax situation	Tax rates, tax-deferred accounts	May prefer tax-free bonds, capital gains over income
Liquidity	Need for spendable cash	High needs → more bonds/cash, avoid illiquid assets
Legal/Regulatory	Trust laws, insider trading rules	May restrict certain asset types or concentrations
Unique circumstances	Ethical, religious, ESG preferences	May exclude sectors (tobacco, gambling) or countries

Think of constraints as guardrails on a highway. Your return objectives set the destination and speed, but the guardrails (liquidity, taxes, time, laws, preferences) keep you on a safe path. Without guardrails, you might reach the destination faster — or drive off a cliff.

Strategic vs. Tactical Asset Allocation

Strategic asset allocation is the long-term baseline mix (e.g., 60% equity, 30% bonds, 10% alternatives) derived from the IPS objectives and asset class characteristics. Tactical asset allocation involves short-term deviations to exploit perceived opportunities.

A core-satellite approach puts the majority (core) in passive index funds and a smaller portion (satellite) in active strategies. This reduces excessive trading, offsetting positions, and unintended tax consequences.

ESG Considerations

Approaches include negative screening (exclude certain companies), positive screening (invest in ESG leaders), thematic investing, impact investing, and active ownership. ESG constraints may decrease returns (smaller universe) but may also increase returns (avoiding ESG-related risks). Benchmark choice must reflect the constrained universe.

Reading 87

The Behavioral Biases of Individuals

Humans are not rational calculators — understanding your biases is the first step to managing them.

Cognitive Errors vs. Emotional Biases

Cognitive Errors

From faulty reasoning or information processing. Can be corrected with better information, education, or training. Think of these as "bugs in the software."

Emotional Biases

From feelings, impulses, or intuition. Difficult to correct — often must be accommodated rather than eliminated. Think of these as "features of the hardware."

When a bias has both cognitive and emotional elements, focus on correcting the cognitive component first — you'll have more success there.

Cognitive Errors: Belief Perseverance

Bias	What Happens	Example	Portfolio Impact
Conservatism	Fail to update views with new info	Ignoring a central bank tightening signal	Hold investments too long; miss opportunities
Confirmation	Seek info that confirms existing beliefs	Only reading bullish analyst reports on a stock you own	Over-concentration; under-diversification
Representativeness	Classify based on similarity to a stereotype	"This stock was a growth stock last year, so it must still be"	Buy/sell based on patterns, not fundamentals
Illusion of control	Believe you can influence uncontrollable outcomes	Over-trading in your employer's stock	Inadequate diversification
Hindsight	"I knew it all along" after the fact	Claiming you predicted a market crash — after it happened	Overconfidence in predictive ability

Cognitive Errors: Information Processing

Bias	What Happens	Example
Anchoring	Over-rely on an initial number	Estimating EPS based on last quarter's figure, adjusting insufficiently
Mental accounting	Treat money differently based on source/account	Gambling with "found money" (bonus) but being conservative with savings
Framing	Decision changes depending on how info is presented	Choosing risk when losses are framed, choosing certainty when gains are framed
Availability	Overweight easily recalled information	Buying stocks advertised heavily; ignoring historical data

Emotional Biases Critical

Bias	What Happens	Portfolio Consequence
Loss aversion	Feel losses more than equivalent gains	Sell winners too early (lock in gains); hold losers too long (avoid realising losses). Take excessive risk after losses to "get back to even."
Overconfidence	Overestimate own ability	Under-diversify, trade too much, underestimate risk
Self-control	Favour short-term gratification	Insufficient savings; take too much risk to compensate
Status quo	Resist change; stick with current allocation	Hold inappropriate portfolios; miss better alternatives
Endowment	Value assets more because you own them	Refuse to sell inherited stocks; fail to diversify
Regret aversion	Fear of making wrong decision causes inaction	Excess conservatism; herding (follow the crowd to avoid blame)

🎯 Likely Exam Question

A spouse holds on to the deceased partner's stock portfolio for sentimental reasons, despite it being inappropriate for their needs. Which bias?

Endowment bias (emotional) — valuing assets more simply because you own them. The test: "Would you buy this same portfolio with new money today?" If no, it's endowment bias. Note: this is emotional (hard to correct), not cognitive.

🎯 Likely Exam Question

An investor is given $10 and chooses the certain $5 gain over a 50/50 gamble for $10. Given $20, they choose the 50/50 gamble to lose $0 or $10 over a certain $5 loss. Both scenarios have identical expected values of $15. What bias?

Loss aversion. People are risk-averse with gains (prefer certainty) but risk-seeking with losses (prefer the gamble to avoid a sure loss). This asymmetry is the hallmark of loss aversion, distinct from simple risk aversion.

Behavioral Biases in Markets

The value/growth anomaly may partly reflect behavioral factors like the halo effect (a form of representativeness where good company characteristics are extended to "good stock" conclusions, overvaluing growth stocks). Home bias reflects investors over-weighting domestic stocks, possibly from familiarity or availability bias. Herding during bubbles amplifies overconfidence and regret aversion. Behavioral finance has not fully explained bubbles and crashes but identifies contributing biases.

Reading 88

Introduction to Risk Management

Risk management isn't about eliminating risk — it's about choosing the right risks to take.

What Risk Management Actually Is

Risk management is the process of: (1) identifying the organisation's risk tolerance, (2) identifying and measuring its risks, and (3) modifying and monitoring those risks. The goal is not to minimise or eliminate all risks. The goal is to select the optimal bundle of risks that maximises expected returns given the organisation's tolerance.

An investor controls risk — not returns. You can't force the market to give you 15% returns, but you can choose to allocate 60% to equities vs. 40% to bonds. Risk management is about making that choice deliberately rather than accidentally.

Risk Management Framework

A comprehensive framework includes: identifying and measuring existing risks → determining overall risk tolerance → establishing risk governance processes → managing/mitigating risks to achieve the optimal bundle → monitoring exposures over time → communicating across the organisation → performing strategic risk analysis.

Risk Governance

Risk governance is determined at the enterprise level by senior management. It sets risk tolerance, the optimal risk exposure strategy, and oversight of the risk management function. A risk management committee integrates risks across business units.

Risk governance must be enterprise-wide, not siloed by department. A risk that looks manageable at the business unit level may be catastrophic when combined with risks from other units.

Risk Tolerance and Risk Budgeting

Risk tolerance is the overall amount of risk the organisation will accept. Risk budgeting allocates that total risk across assets/investments based on their risk characteristics and how they combine. The budget can use metrics like portfolio beta, VaR, duration, or returns variance.

Risk budgeting is like a household budget. Your total monthly budget (risk tolerance) is $5,000. You allocate $1,500 to housing, $500 to food, $300 to entertainment, etc. Similarly, your total portfolio risk budget might be allocated across domestic equities, international equities, bonds, and alternatives.

Financial vs. Non-Financial Risks

Category	Risk Type	Description
Financial	Credit risk	Counterparty fails to honour obligations
	Liquidity risk	Forced to sell at below fair value
	Market risk	Adverse moves in prices, rates, currencies
Non-Financial	Operational risk	Human error, systems failures, cyber risk
	Solvency risk	Running out of cash to continue operating
	Regulatory risk	Changes in regulations impose new costs
	Legal risk	Exposure to lawsuits or contract disputes
	Model / Tail risk	Models are wrong; extreme events more likely than assumed

Risks interact — especially during crises. Market decline → counterparty can't pay (credit risk) → must sell to raise cash (liquidity risk) → selling in a down market amplifies losses → potential solvency risk. These cascading interactions are why enterprise-wide risk management matters.

Risk Measures

Measure	What It Measures	Used For
Standard deviation	Volatility of returns	General asset risk (may miss tail risk)
Beta	Systematic risk relative to market	Equity portfolios
Duration	Sensitivity to interest rate changes	Bond portfolios
Delta, Gamma, Vega, Rho	Sensitivity to various factors	Derivatives positions
VaR	Maximum loss at a given confidence level	Tail risk estimation
Conditional VaR	Expected loss beyond the VaR threshold	Worst-case tail risk

Methods of Risk Modification Exam Favorite

Method	How It Works	Example
Avoid/Prevent	Don't engage in the risky activity	Not investing in a politically unstable country
Accept (Self-insure)	Bear the risk; possibly set up reserves	Accepting currency risk on small foreign positions
Transfer	Pay someone else to bear the risk	Buying insurance, surety bonds, fidelity bonds
Shift	Change the distribution of outcomes with derivatives	Buying puts (floor), selling calls (give up upside), forwards, swaps

🎯 Likely Exam Question

A firm uses forward currency contracts to eliminate foreign exchange risk on its international bond holdings. This is best described as:

Risk shifting. Derivatives change the distribution of possible outcomes. Risk transfer is paying someone to bear the risk (insurance). Risk shifting uses derivatives to change the payoff profile. This is a commonly tested distinction.

Individual Risk Management

Individuals face mortality risk (dying before providing for dependents — addressed with life insurance), longevity risk (outliving assets — addressed with lifetime annuities), and health expense risk (addressed with health insurance). The framework is the same: identify risks, determine tolerance, choose which to bear, transfer, or shift.

Reference

Master Formula Sheet — All 6 Readings

Every formula you need for Portfolio Management, in one place.

Formula	Description	Reading
$s^2 = \frac{\sum(R_t - \bar{R})^2}{T-1}$	Sample variance of returns	83
$\rho_{1,2} = \frac{Cov(R_1,R_2)}{\sigma_1 \sigma_2}$	Correlation from covariance	83
$\sigma_P = \sqrt{w_1^2\sigma_1^2 + w_2^2\sigma_2^2 + 2w_1w_2\rho_{12}\sigma_1\sigma_2}$	Two-asset portfolio std dev	83
$\sigma_P = w_A \sigma_A$ (with risk-free)	Risk of portfolio with risk-free asset	83
$E(R_P) = R_f + \frac{E(R_M)-R_f}{\sigma_M}\sigma_P$	Capital Market Line (CML)	84
$\beta_i = \frac{Cov(R_i,R_M)}{\sigma_M^2} = \frac{\rho_{i,M}\sigma_i}{\sigma_M}$	Beta (systematic risk measure)	84
$E(R_i) = R_f + \beta_i[E(R_M) - R_f]$	CAPM / Security Market Line	84
$\text{Sharpe} = \frac{R_P - R_f}{\sigma_P}$	Excess return per unit of total risk	84
$\text{Treynor} = \frac{R_P - R_f}{\beta_P}$	Excess return per unit of systematic risk	84
$\alpha_P = R_P - [R_f + \beta_P(R_M - R_f)]$	Jensen's alpha	84
$M^2 = R_f + \frac{\sigma_M}{\sigma_P}(R_P - R_f)$	M-squared measure	84
$\text{Diversification Ratio} = \frac{\sigma_\text{portfolio}}{\bar\sigma_\text{individual}}$	Measure of diversification benefit	85

Measure	Formula	Risk Type Used	When to Use
Sharpe Ratio	\(\frac{R_P - R_f}{\sigma_P}\)	Total risk (σ)	Single manager / total portfolio
Treynor Measure	\(\frac{R_P - R_f}{\beta_P}\)	Systematic risk (β)	Well-diversified portfolio / multi-manager
Jensen's Alpha	\(R_P - [R_f + \beta_P(R_M - R_f)]\)	Systematic risk (β)	Excess return above SML
M-squared	\(R_f + \frac{\sigma_M}{\sigma_P}(R_P - R_f)\)	Total risk (σ)	Leveraged comparison to market

Formula	Description	Reading
\(s^2 = \frac{\sum(R_t - \bar{R})^2}{T-1}\)	Sample variance of returns	83
\(\rho_{1,2} = \frac{Cov(R_1,R_2)}{\sigma_1 \sigma_2}\)	Correlation from covariance	83
\(\sigma_P = \sqrt{w_1^2\sigma_1^2 + w_2^2\sigma_2^2 + 2w_1w_2\rho_{12}\sigma_1\sigma_2}\)	Two-asset portfolio std dev	83
\(\sigma_P = w_A \sigma_A\) (with risk-free)	Risk of portfolio with risk-free asset	83
\(E(R_P) = R_f + \frac{E(R_M)-R_f}{\sigma_M}\sigma_P\)	Capital Market Line (CML)	84
\(\beta_i = \frac{Cov(R_i,R_M)}{\sigma_M^2} = \frac{\rho_{i,M}\sigma_i}{\sigma_M}\)	Beta (systematic risk measure)	84
\(E(R_i) = R_f + \beta_i[E(R_M) - R_f]\)	CAPM / Security Market Line	84
\(\text{Sharpe} = \frac{R_P - R_f}{\sigma_P}\)	Excess return per unit of total risk	84
\(\text{Treynor} = \frac{R_P - R_f}{\beta_P}\)	Excess return per unit of systematic risk	84
\(\alpha_P = R_P - [R_f + \beta_P(R_M - R_f)]\)	Jensen's alpha	84
\(M^2 = R_f + \frac{\sigma_M}{\sigma_P}(R_P - R_f)\)	M-squared measure	84
\(\text{Diversification Ratio} = \frac{\sigma_\text{portfolio}}{\bar\sigma_\text{individual}}\)	Measure of diversification benefit	85