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Topic 27: Investment Returns
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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
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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
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Topic 27: Investment Returns
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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
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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
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Topic 27: Investment Returns
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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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