Investments, tenth edition

  Expected Return and Standard Deviation 

 There is considerable uncertainty about the price of a share plus dividend income 1 year 

from now, however, so you cannot be sure about your eventual HPR. We can quantify our 

beliefs about the state of the market and the stock-index fund in terms of four possible 

scenarios with probabilities as presented in columns A through E of  Spreadsheet 5.1 . 

 How can we evaluate this probability distribution? To start, we characterize probability 

distributions of rates of return by their expected or mean return,  E ( r ), and standard devia-

tion,  s . The expected rate of return is a probability-weighted average of the rates of return 

in each scenario. Calling  p ( s ) the probability of each scenario and  r ( s ) the HPR in each 

scenario, where scenarios are labeled or “indexed” by  s,  we write the expected return as   

 

E(r) 5 a

s

p(s)r (s) 

 (5.11)   

 Applying this formula to the data in  Spreadsheet  5.1 , the expected rate of return on the 

index fund is   

 

E(r) 5 (.25 3 .31) 1 (.45 3 .14) 1

3.25 3 (2.0675)4 1 3.05 3 (2.52)4 5 .0976