Portfolio Management
Risk, return and diversification
Portfolio expected return is the weighted average of individual expected returns. Portfolio risk is not a weighted average of standard deviations - it depends on the correlation between assets. Combining assets with correlation below +1 reduces risk without proportionately reducing return; the lower the correlation, the greater the benefit. Diversification eliminates unsystematic (specific) risk but cannot remove systematic (market) risk, which is why beta matters.
Models and measures
CAPM: expected return = risk-free rate + beta × (market return − risk-free rate). Beta measures sensitivity to market movements; a beta of 1.3 means the share moves 30% more than the market. The Security Market Line plots required return against beta; a security plotting above the line is undervalued (positive alpha). Performance measures: Sharpe ratio uses total risk (standard deviation), Treynor ratio uses beta, and Jensen's alpha is the excess return over CAPM. The efficient frontier shows portfolios offering the highest return for each level of risk.
Traps
- Applying the Sharpe ratio to a fully diversified fund and expecting it to equal the Treynor ranking.
- Treating beta as a measure of total risk.
- Believing that adding many shares always cuts risk - if correlations are high, the benefit is small.
- Forgetting that the market portfolio in CAPM is fully diversified, so only systematic risk is priced.
Worked example
Risk-free rate 6%, market return 12%, beta 1.3. Required return = 6 + 1.3(12 − 6) = 13.8%. If the share is expected to return 16%, alpha = 16 − 13.8 = +2.2%, so it plots above the SML and is attractive on a risk-adjusted basis.