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1 Topic 27: Investment Returns Arithmetic average: sum/n Geometric mean: Less than arithmetic as it factors in compounding As standard deviation increases, geometric becomes larger than arithmetic If no standard deviation, they are same Steps Multiply all returns +/-1, calculate PV of result Time weighted: evaluate portfolio manager Ignores cash flows in/out of portfolio by investors Includes capital gains, and dividends received by portfolio Same calculation as geometric mean 2 Topic 27: Investment Returns Dollar weighted: evaluate investor’s performance Factors cash flows in/out of portfolio IRR calculation Underperformance by mutual fund investors More frequent/pronounced in volatile funds Holding period: (capital gain/loss)+dividend or interest/original investment Can also factor in taxes and transaction costs 3 Topic 27: Investment Returns Real return= Nominal return – Inflation rate Nominal 13% Inflation 3% I = ((1+Nominal)/(1+Inflation))-1 Also referred to as serial Assumes nominal rate not compouded If it is, real return = nominal – inflation Internal Rate of Return, NPV Present value of -0 If IRR>required return, present value positive Assumes cash flows reinvested at IRR Favors projects generating cash flows early 4 Topic 27: Investment Returns Total return:(capital gain + dividend)/investment YTM: return on bonds Compute using semi-annual periods for zero coupon bonds Yield to call: assumes bond is called in YTM calculation Current yield: annual income/current price After-tax: dividends currently taxed at 15% Taxable equivalent yield (munis): tax-free yield/(1- tax rate) After-tax rate of return: Taxable return x (1 – tax rate)

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