Portfolio Management
Portfolio Management tests how risk and return combine, how diversification works, what the CAPM implies about expected returns, and how to judge a manager's performance against the right benchmark. Items mix conceptual questions about risk aversion with short calculations.
Risk, return and diversification
- Expected portfolio return is the weighted average of asset expected returns; portfolio risk is not, because covariance drives the result.
- When correlation is below +1, portfolio standard deviation falls below the weighted average of the components. At -1, a zero-variance combination may exist.
- Total risk = systematic + unsystematic risk; diversification removes unsystematic risk, so only systematic risk is priced.
CAPM and the two lines
- CAPM: expected return = r_f + beta x (market return - r_f), where beta = covariance with the market / market variance.
- The capital market line plots expected return against total risk for efficient portfolios combining the risk-free asset and the market. The security market line plots expected return against beta for any asset.
Worked example
A portfolio returns 12%, the risk-free rate is 4%, the portfolio standard deviation is 16% and beta is 1.2. Sharpe ratio = (12 - 4) / 16 = 0.50. Treynor ratio = 8 / 1.2 = 6.67. If the market return is 10%, the CAPM required return is 4 + 1.2 x 6 = 11.2%, so Jensen's alpha is 12 - 11.2 = 0.8%, a superior result on a risk-adjusted basis.
Traps that cost marks
- Using beta in the Sharpe ratio or standard deviation in the Treynor ratio; each measure pairs with its own risk definition.
- Forgetting that a portfolio's beta is the weighted average of betas, while its standard deviation is not a weighted average.
- Treating a low correlation as eliminating risk entirely; only the right weights and correlations can do that.
- Judging performance without considering the benchmark, the investment mandate and the risk taken.