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.

Which One-Liners Win Points?

• Current yield = annual income over current market price; it ignores capital gains and losses.
• 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.
• Yield to call (YTC) uses the call date and call price instead of maturity date and par value; it applies only to callable bonds.
• Total return is the most comprehensive measure because current yield ignores price changes.
• Benchmark types: market index, peer group, absolute return (a fixed target like CPI plus 3%), and custom blend (weighted to match a portfolio's actual allocation).
• 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.

Which Numbers Matter Most?

• 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)

Which Gotchas Trip Students Up?

• 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 expected return built on beta. Time-weighted return grades the manager and is required by the Global Investment Performance Standards; 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 one minus the tax rate for after-tax, and divide by one minus the tax rate for tax-equivalent yield. Match the benchmark to the portfolio and its type, remembering the Dow is price-weighted.

Need more than the recap? Read the full Portfolio Performance Measures unit.