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)