Portfolio Management: Risk, Return, and Diversification
Core concepts
Portfolio management begins with the risk–return trade-off. Candidates must be fluent in expected return as a probability-weighted average, variance and standard deviation as dispersion measures, covariance and correlation as co-movement measures, and the distinction between systematic (market, non-diversifiable) and unsystematic (firm-specific, diversifiable) risk. Know the capital asset pricing model: required return = risk-free rate + beta × market risk premium, where beta = covariance(asset, market) / variance(market). Understand the security market line and what a shift in the risk-free rate or market premium does to it.
Traps
- Portfolio standard deviation is not the weighted average of component standard deviations unless correlation is exactly +1. A common distractor offers the simple weighted average.
- Beta measures systematic risk only; a low-beta stock can still be highly volatile in total terms.
- Correlation of zero is not independence in general, and negative correlation reduces but does not always eliminate risk.
- Adding a riskier asset can lower portfolio risk if its correlation with the existing portfolio is low enough-do not assume risk always rises.
- Confusing the market risk premium (Rm − Rf) with the market return (Rm).
Worked example
Two assets, equal weights. Asset A: expected return 8%, SD 10%. Asset B: expected return 14%, SD 20%. Correlation 0.25. Portfolio return = 0.5(8) + 0.5(14) = 11%. Portfolio variance = (0.5²)(10²) + (0.5²)(20²) + 2(0.5)(0.5)(0.25)(10)(20) = 25 + 100 + 25 = 150, so SD ≈ 12.25%. Note the portfolio SD (12.25%) is far below the weighted-average SD (15%)-diversification benefit from imperfect correlation.
Rule of thumb
When correlation is +1, portfolio SD equals the weighted average; when correlation is −1, risk can be driven to zero with the right weights. Everything in between lies between those bounds.