Question

Scenario Modeler’s prospective stock has a 15% chance of producing a 65% return, a 25% chance of producing a 22% return, a 40% chance of producing a 9% return, and a 20% chance of producing a –24% return. What is the firm’s coefficient of variation of return?

Deep Value, Inc.’s annual stock returns for the last ten years are: –5%, 15%, 11%, 18%, –8%, 9%, 16%, –3%, 3%, and 35%. The Market Index’s annual returns for the same ten years are: 10%, 22%, 9%, 13%, –7%, 8%, 15%, –13%, –12%, and 18%. What is Deep Value’s beta coefficient?  

Answer 1

Average Return formula in case of Probability = sum of (Probability*Return)          
Standard deviation = ((∑ (actual return-Average Return)^2*Probability))^(1/2)          
Probability   Return   RR*Prob.   (R-AR)^2 * probaility
          
15%   65%   9.75%   0.0389385375
25%   22%   5.50%   0.0015800625
40%   9%   3.60%   0.0010201
20%   -24%   -4.80%   0.02895605
Total=       14.05%   0.07049475
Standard deviation = (0.07049475)^(1/2)          
0.2655084744          
          
standard deviation is 26.55%          
          
Coefficient of Variation = Standard deviation/Average Return          
26.55%/14.05%          
1.889740032          
So coefficient of variation is 1.90