Risk and Return Measurement for Research Recommendations
What is tested
Return measurement, risk measurement, and the models that convert risk into a required return - the arithmetic behind every target price and rating.
Return
- Holding period return: HPR = (P1 − P0 + D) / P0.
- Multi-period: use CAGR or the geometric mean for realised performance.
- The arithmetic mean exceeds the geometric mean when returns vary; the gap widens with volatility.
Risk
- Variance and standard deviation measure dispersion of returns around the mean.
- Covariance and correlation drive diversification; a correlation of +1 gives no diversification benefit.
- Beta measures sensitivity to the market: β = Cov(Ri, Rm) / Var(Rm). β above 1 is aggressive, below 1 defensive.
- Unsystematic risk is diversifiable; systematic risk is not.
Risk-adjusted measures
- CAPM: E(R) = Rf + β(E(Rm) − Rf).
- Sharpe = (Rp − Rf) / σp; Treynor = (Rp − Rf) / βp.
- Jensen's alpha = Rp − [Rf + βp(Rm − Rf)]; positive alpha means outperformance after adjusting for beta.
Worked example
A stock is bought at ₹480, sold a year later at ₹540, and paid a ₹12 dividend. HPR = (540 − 480 + 12)/480 = 15%. The risk-free rate is 6.5%, the market return is 12%, and the stock's beta is 1.3. Required return = 6.5 + 1.3 × (12 − 6.5) = 13.65%. Alpha = 15 − 13.65 = +1.35 percentage points. The position beat its CAPM requirement, but if the stock's standard deviation was 30% against the market's 14%, the Sharpe ratio still has to be checked before calling it a good risk-adjusted bet.
Traps
Forgetting dividends in HPR; using an arithmetic average where a five-year CAGR is needed; mixing standard deviation (total risk) with beta (systematic risk); quoting alpha without stating the benchmark and the period.