Investments: Efficient Diversification, CAPM, APT, and Market Efficiency

Comprehensive vocabulary flashcards covering Chapter 6 (Efficient Diversification, Portfolio Mathematics, Optimization, Separation Theorem) and Chapters 7 & 8 (CAPM, APT, Factor Models, and the Efficient Market Hypothesis).

Diversification

The practice of allocating capital across multiple investments to reduce overall risk without sacrificing expected return, often called the only 'free lunch' in finance.

Market (Systematic) Risk

Risk that is common to the entire economy—driven by macro factors such as interest rates, GDP, inflation, and geopolitics—and cannot be eliminated through diversification.

Unique (Firm-Specific) Risk

Risk that affects individual companies or specific assets—such as CEO departures, lawsuits, or product failures—and can be diversified away.

20-30 Stock Rule

The empirical observation that approximately $80\%$ of diversification benefits are achieved within the first $20$ stocks, after which portfolio standard deviation asymptotically approaches the non-diversifiable market risk floor of roughly $20\%$.

Total Portfolio Variance Equation

The breakdown of total risk into systematic and nonsystematic components, expressed as $\sigma^2_{\text{total}} = \sigma^2_{\text{market}} + \sigma^2_{\text{firm}}$.

Two-Asset Portfolio Expected Return

The weighted average of individual expected returns, given by the linear formula $E(r_P) = w_D E(r_D) + w_E E(r_E)$, where weights satisfy $w_D + w_E = 1$.

Two-Asset Portfolio Variance

The measure of portfolio risk defined as $\sigma^2_P = w_D^2 \sigma_D^2 + w_E^2 \sigma_E^2 + 2 w_D w_E \text{Cov}(r_D, r_E)$, where diversification benefits occur through the covariance cross-term.

Covariance Cross-Term

The component $2 w_D w_E \text{Cov}(r_D, r_E)$ within the portfolio variance formula; when covariance is negative, this term subtracts directly from total portfolio variance.

Mean-Variance Criterion

The selection rule stating that Portfolio A dominates Portfolio B if $E(r_A) \ge E(r_B)$ and $\sigma_A \le \sigma_B$, with at least one strict inequality.

Minimum Variance Portfolio (MVP)

The specific portfolio on the investment opportunity set that has the lowest possible risk ($\sigma$), which depends exclusively on risk parameters (variances and covariances) rather than expected returns.

Efficient Frontier

The upward-sloping portion of the investment opportunity set located at and above the Minimum Variance Portfolio, offering the highest expected return for any given level of standard deviation.

Sharpe Ratio

A measure of excess return per unit of total risk, defined as $S = \frac{E(r) - r_f}{\sigma}$.

Capital Allocation Line (CAL)

A straight line showing the risk-return profiles available from combining a risk-free asset with a specific risky portfolio, with intercept at $r_f$ and slope equal to that portfolio's Sharpe ratio.

Tangency Portfolio

The optimal risky portfolio located at the point where the Capital Allocation Line is tangent to the efficient frontier, maximizing the Sharpe ratio.

Capital Market Line (CML)

The optimal Capital Allocation Line formed by combining the risk-free asset ($r_f$) with the optimal market tangency portfolio ($M$).

Separation Theorem

The principle stating that portfolio choice splits into two distinct stages: (1) the technical investment decision of finding the optimal risky portfolio, which is identical for all investors, and (2) the financing decision of allocating wealth between that risky portfolio and the risk-free asset based on individual risk aversion.

Complete Portfolio Allocation ($y^*$)

The optimal proportion of wealth allocated to the risky portfolio based on mean-variance utility ($U = E(r) - \frac{1}{2} A \sigma^2$), calculated as $y^* = \frac{E(r_P) - r_f}{A \sigma_P^2}$, where $A$ is the investor's risk aversion coefficient.

Target-Date Funds

Investment funds that operationalize the Separation Theorem by holding a diversified optimal risky portfolio and automatically adjusting the allocation toward lower-risk bonds as the investor ages.

Curse of Dimensionality (Portfolio Theory)

The exponential growth in the number of pairwise covariances required for an $N$-asset portfolio, given by $\frac{N(N - 1)}{2}$, meaning covariance estimates dominate individual asset variances as $N$ expands.

Capital Asset Pricing Model (CAPM)

An equilibrium model developed by Treynor, Sharpe, Lintner, and Mossin asserting that an asset's expected risk premium is strictly proportional to its systematic risk ($\beta$): $E(r_i) - r_f = \beta_i [E(r_M) - r_f]$.

Beta ($\beta$)

A quantitative measure of an individual asset's sensitivity to systematic market movements, serving as the relevant risk metric rewarded in CAPM.

Security Market Line (SML)

The graphical benchmark of the CAPM that plots the expected return of individual assets against their systematic risk measured by beta ($\beta$).

Alpha ($\alpha$)

The abnormal rate of return on a security relative to the return predicted by the CAPM benchmark; positive values indicate an underpriced asset, while negative values indicate an overpriced asset.

Security Characteristic Line (SCL)

The linear regression of an individual security's excess return against the market index excess return, represented as $r_{it} - r_{ft} = \alpha_i + \beta_i (r_{Mt} - r_{ft}) + e_{it}$.

Mutual Fund Theorem

A CAPM result establishing that a single passive mutual fund containing the market portfolio satisfies the optimal risky asset demand for all investors.

Roll's Critique

A 1977 critique by Richard Roll stating that empirical tests of the CAPM are invalid because the true market portfolio is unobservable, as it encompasses non-traded assets such as real estate and human capital.

Arbitrage Pricing Theory (APT)

A multi-asset equilibrium model proposed by Stephen Ross in 1976 relying on factor models, well-diversified portfolios, and the Law of One Price to state that persistent riskless profits cannot exist in equilibrium.

Arbitrage

The practice of earning a riskless profit without making a net capital investment by simultaneously exploiting relative price discrepancies across markets.

Law of One Price

The economic rule stating that identical assets or cash flows must trade at the same price across competitive markets, enforced by arbitrageurs bidding prices into alignment.

Efficient Market Hypothesis (EMH)

The proposition that security prices fully and rapidly reflect all available information, preventing investors from consistently earning abnormal, risk-adjusted returns.

Weak-Form EMH

The hypothesis stating that stock prices fully reflect all historical trading information and past price trends, implying that technical analysis cannot generate excess returns.

Semistrong-Form EMH

The hypothesis asserting that stock prices rapidly incorporate all publicly available information, such as financial statements and economic reports, implying fundamental analysis cannot consistently yield abnormal returns.

Strong-Form EMH

The hypothesis stating that stock prices reflect all information, including private insider information.

Random Walk

The statistical property asserting that changes in stock prices are unpredictable and random from day to day because they respond only to newly arriving, unpredictable news.

Technical Analysis

An investment strategy seeking to identify mispriced securities by detecting recurring and predictable patterns in charts, past price trends, and trading volume.

Fundamental Analysis

The valuation approach that analyzes earnings prospects, management quality, economic conditions, and dividend forecasts to determine an asset's discounted cash flow value and locate mispricings.

Size Effect (SMB)

An empirical market anomaly demonstrating that shares of small-market-capitalization firms historically achieve higher average returns than large-market-capitalization firms.

Value Premium (HML)

An empirical market anomaly wherein high book-to-market (value) stocks historically outperform low book-to-market (growth) stocks.

Momentum Effect

The empirical tendency of stocks with strong returns over the past 12 months to continue outperforming stocks with low past returns over short-to-intermediate horizons.

Reversal Effect

The empirical tendency of well-performing and poorly performing stocks over long investment horizons to experience subsequent performance reversals.

January Effect

A calendar anomaly characterized by abnormally high stock returns in the month of January, observed primarily among small-cap securities.