Portfolio Performance Measures

The whole unit on one sheet: the return formulas, risk-adjusted measures, benchmarks, and the manager-versus-investor return distinction the exam loves.

The One-Liners That Win Points

• Current yield = annual income over current market price; it ignores capital gains, losses, and time value.
• Bond yield hierarchy: at par, coupon = current yield = yield to maturity (YTM); at a premium, coupon > current yield > YTM; at a discount, coupon < current yield < YTM.
• Total return is the most comprehensive measure because current yield ignores price changes.
• Time-weighted return (TWR) evaluates the manager (strips out client cash flows); the Global Investment Performance Standards (GIPS) require it.
• Dollar-weighted return (DWR) measures the investor's actual experience and equals the internal rate of return (IRR).
• Sharpe ratio uses total risk (standard deviation); alpha uses systematic risk (beta via the capital asset pricing model, CAPM).
• Alpha is NOT return minus market return; compute the CAPM-expected return with beta first, then subtract.
• Dow Jones Industrial Average (DJIA) is price-weighted; the S&P 500 is market-cap weighted.
• Match the benchmark to the style: small-cap to Russell 2000, international to MSCI EAFE, bonds to the Bloomberg U.S. Aggregate.

Numbers to Lock In

• Holding period return (HPR) = (Ending Value - Beginning Value + Income) / Beginning Value
• Total Return = (Ending Value - Beginning Value + Income) / Beginning Value (same formula, HPR just covers any span)
• Annualized Return = (1 + HPR)^(1/n) - 1, where n = number of years
• Sharpe Ratio = (Rp - Rf) / σp (excess return per unit of total risk; higher is better, negative means it lagged the risk-free rate)
• Alpha = Actual Return - CAPM Expected Return, where CAPM Expected Return = Rf + β(Rm - Rf)
• Time-Weighted Return = [(1 + R1)(1 + R2) ... (1 + Rn)] - 1
• Expected Return = Σ [Probability x Outcome]
• Real Return (exact) = [(1 + Nominal) / (1 + Inflation)] - 1; approximate = Nominal - Inflation
• After-Tax Return = Pre-Tax Return x (1 - Tax Rate)
• Tax-Equivalent Yield (TEY) = Tax-Exempt Yield / (1 - Tax Rate) (divide, never multiply)

Top Gotchas

• TWR vs. DWR: time-weighted removes client cash flows (manager skill); dollar-weighted includes them (investor experience). A large deposit before poor returns makes TWR greater than DWR; a large deposit before strong returns makes DWR greater than TWR; with no external cash flows the two are identical.
• Real vs. nominal return: subtract inflation to get real (purchasing-power) return. A 6% nominal return against 5% inflation is only about 1% real, barely growing purchasing power.
• Do not divide a multi-year return by the number of years. That ignores compounding; use the geometric formula (1 + HPR)^(1/n) - 1.
• Sharpe for an undiversified, standalone portfolio (unsystematic risk still present); alpha for manager skill against a CAPM expectation.
• The TEY formula divides the tax-exempt yield by (1 - tax rate); a higher bracket makes municipals more attractive.

One-Breath Recap

Total return and holding period return use one formula, ending minus beginning plus income over beginning, and multi-year returns annualize geometrically, (1 + HPR)^(1/n) - 1, never by dividing by the years. The Sharpe ratio rewards excess return per unit of total risk (standard deviation), while alpha measures skill against the CAPM-expected return built on beta. Time-weighted return grades the manager and is required by GIPS; dollar-weighted return equals the internal rate of return and grades the investor's actual, cash-flow-timed experience. Subtract inflation for real return, apply (1 - tax rate) for after-tax, and divide by (1 - tax rate) for tax-equivalent yield. Match the benchmark to the portfolio, remembering the Dow is price-weighted, and this two-percent unit answers itself.

Need more than the recap? This is a condensed summary. If it is not enough, read the full Portfolio Performance Measures unit for the complete lesson.