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Ch. 25 PORTFOLIO RETURN MEASURES I. Single period A. Holding period return (over period t) r t = Dividend yield

Ch. 25 PORTFOLIO RETURN MEASURES I. Single period A. Holding period return (over period t) r t = Dividend yield + capital gains yield = D t /P 0 + (P t - P 0 )/P 0 = (P t + D t - P 0 ) / P 0 where r t = return earned during period t

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Ch. 25 PORTFOLIO RETURN MEASURES I. Single period A. Holding period return (over period t) r t = Dividend yield

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  1. Ch. 25 PORTFOLIO RETURN MEASURES I. Single period A. Holding period return (over period t) rt = Dividend yield + capital gains yield = Dt/P0 + (Pt - P0)/P0 = (Pt + Dt - P0) / P0 where rt = return earned during period t Dt = period cash flows (dividends or interest) Pt = price at end of period t P0 = price at beginning of period t II. Multiperiod A. Annualized return rann = (1 + rt)1/T - 1 where T = number of years in evaluation period

  2. PORTFOLIO PERFORMANCE I. Risk unadjusted performance A. Dollar-weighted rate of return (DWROR) MV0 = S CFt / (1 + rdw)t + CFT + MVT / (1 + rdw)T where MV0 = beginning market value CFt = cash flows during time t MVT = ending market value rdw = DWROR = IRR = YTM 1. Return actually earned by investor B. Time-weighted return (TWROR) rtw = [P(1 + rit)1/T ] - 1 1. Return assessed to investment manager 2. Required by Global Investment Performance Standards (GIPS) II. Relationship between DWROR & TWROR

  3. ABSOLUTE PORTFOLIO PERFORMANCE EVALUATION • Jensen (1968) measure (alpha) • A. Single-index model • (rpt - RFt) = aP+ bP (Rmt - Rft)+ ePt • 1.Statistically significant pos. (neg.) aP • indicates superior (inferior) performance • B. Four-factormodel(p. 284) • (Rpt–RFt) = ai0 + bi1(Rmt–RFt)+ bi2SMBt + bi3HMLt + bi4UMDt + e. • 1. Fama-French (1992) factors • a. SMB (small minus big) = size • b. HML (high minus low) = valuation • 2. Carhart (1997) factor • a. UMD (up minus down) = momentum

  4. RELATIVE PORTFOLIO PERFORMANCE EVALUATION I. Ratios A. Sharpe (1966) 1. Avg. excess return / per unit of total risk B. Treynor (1965) 1. Avg. excess return / per unit of systematic risk C. Information 1. Avg. return / per unit of unsystematic risk

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