Learning Module 1
Portfolio Risk and Return: Part I

Expected return vs. Historical return — Historical return is what was actually earned; expected return is what an investor anticipates. Historical mean return is often used as a proxy for expected return.

Risk-return trade-off — Higher risk is associated with higher expected returns over long periods. Small company stocks have historically had higher risk and higher returns than large company stocks.

Real returns — Adjusting for inflation provides more meaningful comparisons across time periods. Real geometric mean return for US equities (1900–2017) was 6.5% vs. 2.0% for bonds.

Risk of major asset classes — Small company stocks have the highest risk (31.7% SD), followed by large company stocks (19.8%), corporate bonds (8.3%), government bonds (9.9%), and T-bills (3.1%).

Skewness — Asymmetry of the return distribution. Negative skew means most returns are concentrated to the right with a long left tail (more extreme losses).

Kurtosis — Fat tails or higher probability of extreme events than a normal distribution would suggest. Increases risk not captured by mean-variance framework.

Liquidity — Affects bid-ask spreads and price impact. Less liquid assets have higher trading costs and may require a liquidity premium.

Market characteristics — Analyst coverage, information availability, and firm size affect investment decisions and costs.

Risk averse — Prefers a guaranteed outcome to a gamble with the same expected value. Requires compensation (risk premium) to accept risk.

Risk neutral — Cares only about return, not risk. Risk aversion coefficient A = 0.

Risk seeking — Prefers risk; accepts lower expected return for the thrill of uncertainty. A < 0.

Utility function — U = E(r) − ½Aσ². Higher A means more risk-averse. Utility increases with return, decreases with variance.

Indifference curves — Plot combinations of risk and return that provide the same utility. More risk-averse investors have steeper curves.

Perfect positive correlation (ρ = +1) — Portfolio risk is a weighted average of individual risks. No diversification benefit.

Perfect negative correlation (ρ = −1) — Portfolio can be made risk-free with appropriate weights.

Zero correlation (ρ = 0) — Diversification benefit exists; portfolio risk is less than weighted average.

Covariance — Cov(R₁,R₂) = ρ₁₂σ₁σ₂. Measures how two assets move together.

Equal-weight portfolio — σ_p² = σ̄²/N + (N−1)/N × Cov̄. As N increases, average covariance dominates portfolio risk.

Systematic vs. Nonsystematic risk — Nonsystematic (idiosyncratic) risk can be diversified away; systematic (market) risk cannot.

Diversification benefit — Combining assets with low or negative correlations reduces portfolio risk without necessarily reducing return.

Correlation and risk — Lower correlations among assets provide greater diversification benefits.

Investment opportunity set — All possible portfolios of risky assets.

Minimum-variance frontier — Portfolios with the lowest risk for each level of return.

Global minimum-variance portfolio — The portfolio with the lowest risk among all risky portfolios.

Markowitz efficient frontier — The upper portion of the minimum-variance frontier; contains portfolios that maximize return for each level of risk.

Capital Allocation Line (CAL) — Combines the risk-free asset with a risky portfolio. The slope is the Sharpe ratio [E(R_i) − R_f] / σ_i.

Two-fund separation theorem — All investors hold a combination of the risk-free asset and the optimal risky portfolio (the market portfolio).

Optimal investor portfolio — The tangency point between the CAL and the investor's highest attainable indifference curve.