pag. 229 - Corporate Finance book. There are 5 stocks (exhibit 4) with all the quarterly returns from Q3 - 2004 to Q2 - 2006- At pag. 229 the book says “When we randomly select one security each quarter, we found an average annualized return of 15,1% and an average annualized standard deviation of 24,9% …” How can you calculate the variance when you randomly select securities (every security should have its own distribution)? Is it an empirical calculation? I did also a test. Let’s consider the following 2 stocks: Returns A = 10; 12 Returns B = 11; 11 If I select randomly I can have the following results: P1 = 10; 12 --> Var = 2 P2 = 10; 11 --> Var = 0.5 P3 = 11; 12 --> Var = 0.5 P4 = 11; 11 --> Var = 0 The average is 0.75 However if I consider the probabilities… I would say that the average return, picking up stocks randomly is: 1/4*10+1/4*11+1/4*12+1/4*11=11 So computing variance with probabilities is: Var=(10-11)^2*1/4 + (11-11)^2*1/4 + (12-11)^2*1/4 + (11-11)^2*1/4 = 0.5 However 0.5 is different from 0.75. Which is the correct one? What did they use to compute 24.9%? Thanks
Sorry… I think the correct one is the following:
P1 = 10; 12 –> Total = 22; Prob = 0.25 P2 = 10; 11 –> Total = 21; Prob = 0.25 P3 = 11; 12 –> Total = 23; Prob = 0.25 P4 = 11; 11 –> Total = 22; Prob = 0.25
Average = 22
Var = (22-22)^2 * 0.25 + (21-22)^2 * 0.25 + (23-22)^2 * 0.25 + (22-22)^2 * 0.25 = 0.5
… or as it was done above …
So in order to compute the average annualized std on the quarterly returns Exhibit 4 pag 228/229 - Corporate Finance book, considering that:
Number of returns = 80
Quarterly average return = 3.765%
the corret calculus should be:
Std = ((1/80 * sum (return - 3.765)^2) * 4) ^ 0.5 = 25.07%
That is slightly different from 24.9% but maybe there are some rounding involved (?) …
Let me know