A manager can earn 8% on an account over the same two years that its owner loses money, and neither number is wrong. Each one answers a different question, and the exam tests whether you know which question each answers.
Every performance measure starts with one question: how much did the investment grow, counting everything the client received? The holding period return (HPR) answers it. Subtract the beginning value from the ending value, add any income received, and divide by the beginning value. It works for a period of any length and is not annualized.
A client buys a stock at $40, collects $2 in dividends and sells at $46. The holding period return is ($46 − $40 + $2) ÷ $40 = $8 ÷ $40 = 20%.
That 20% is a total return, which combines capital appreciation and income. Total return counts both price change and income (dividends and interest, assumed reinvested), while price return and current yield each show only part...
Common mistakes
- Swapping the denominators: Sharpe divides excess return by standard deviation, and Treynor divides it by beta. With an 8% excess return, 14% standard deviation and a 1.1 beta, Sharpe is 0.57. The figure 7.27 is the Treynor ratio.
- Dividing by the years: A 33.1% gain over three years is a 10% compound rate, not 11.03%.
- Dropping or misplacing income: The $40 stock that pays $2 and rises to $46 earns 20%, not the 15% price return. Dividing a coupon by par instead of price is the same kind of slip: $50 ÷ $950 is 5.26%, not 5%.
Bottom line
- HPR = (ending value − beginning value + income) ÷ beginning value; total return counts price change plus reinvested income, while price return and current yield each show only part.
- Annualize with (1 + HPR)^(1/n) − 1; the geometric average is never above the arithmetic average (+50% then −50% = −13.4% a year); never annualize periods under a year.
- TWR links subperiod returns, removes client cash-flow timing, judges managers and is what voluntary GIPS requires for most composites; DWR is the IRR (NPV of zero) and shows the client's own experience.
- Sharpe = excess return ÷ standard deviation (whole or concentrated portfolio); Treynor = excess return ÷ beta (well-diversified); alpha = actual return − CAPM return; information ratio = return over benchmark ÷ tracking error; Sortino uses downside deviation.
Exam shortcut
Start by asking who is being judged. If the stem says "the manager" or asks you to compare managers, the answer is TWR. If it says "the investor's actual return," the answer is DWR or IRR. For risk-adjusted questions, ask whether the fund is the whole portfolio (use Sharpe) or one piece of a diversified portfolio (use Treynor or alpha). "Consistency versus a benchmark" points to the information ratio.
The full lesson (about 5,015 words, 33 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.
Learning objectives
- C29
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