Lecture 10 Return and Risk Rates of Return

Lecture 10 Return and Risk

Rates of Return l l A key measure of investors’ success is the rate at which their funds have grown Holding-period return (HPR) of shares is composed of capital gain and dividend HPR = (P 1 -Po + Cash Dividend)/Po This definition assumes end of period returns and ignores re-investment of income

Rates of Return l l Dividend Yield = Percentage return from dividends i. e. (Dividend x 100)/Po To calculate HPR over a period of time, we can use: l l l Arithmetic average Geometric average Dollar weighted return

Arithmetic Average l l It is the sum of periodic return divided by number of periods Period 1 10% Period 2 25% Period 3 -20% Sum 15% Arithmetic Average = 15/3 = 5%

Geometric Average nth root of the product of returns for n years Geometric mean = (1+R 1)x(1+R 2)x(1+R 3)1/n – 1 l = [(1+10%) x (1+ 25%) x(1+(-20%))] 1/3 – 1 l [(1. 1) x (1. 25) x (. 8)] 1/3 – 1 l (1. 1) 1/3 – 1 l 1. 03 -1 l. 03 or 3%

Problem with Arithmetic average l Suppose the following: Year l l l Ending value 100 HPR 2007 Begin value 50 2008 100 50 -50% 100% Calculating arithmetic mean gives false value of 25% return = (100%-50%)/2 And geometric = (1+1)x(1 -. 5)1/2 - 1 =1 -1 = 0%

Geometric Vs Arithmetic l l In highly volatile security prices, arithmetic mean is biased upward and we should use geometric mean If rates of returns are the same for all years, geometric and arithmetic averages gives same results