1. Lecture 10
Return and Risk

2. Rates of Return
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 = (P1-Po + Cash Dividend)/Po
This definition assumes end of period returns and ignores re-investment of income

3. Rates of Return
Dividend Yield = Percentage return from dividends i.e. (Dividend x100)/Po
To calculate HPR over a period of time, we can use:
Arithmetic average
Geometric average
Dollar weighted return

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

5. Geometric Average nth root of the product of returns for n years
Geometric mean = (1+R1)x(1+R2)x(1+R3)1/n – 1
= [(1+10%) x (1+ 25%) x(1+(-20%))] 1/3 – 1
[(1.1) x (1.25) x (.8)] 1/3 – 1
(1.1) 1/3 – 1
1.03-1
.03 or 3%

6. Problem with Arithmetic average
Suppose the following:
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%
Year
Begin value
Ending value
HPR
2007 50
100
100%
2008
-50%

7. Geometric Vs Arithmetic
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