Question

A stock's returns have the following distribution:

Demand for the Company's Products	Probability of This Demand Occurring	Rate of Return If This Demand Occurs
Weak	0.1	(38%)
Below average	0.1	(12)
Average	0.4	13
Above average	0.3	20
Strong	0.1	47
	1.0

Assume the risk-free rate is 3%. Calculate the stock's expected return, standard deviation, coefficient of variation, and Sharpe ratio. Do not round intermediate calculations. Round your answers to two decimal places.

Stock's expected return:   %

Standard deviation:   %

Coefficient of variation:

Sharpe ratio:

Answer 1

Expected Return = Sum of (probability*Return)          
Variance formula = Sum of (Probability * (Actual return - Required return)^2)          
Standard deviation formula = √ Variance          
Coefficient of Variation = standard deviation/Expected Return          
Sharpe ratio = (Expected Return - risk free rate)/Standard deviation          

   Probability   Return of stock   Product =Prob.*Return   Return deviation    Squared deviation   Product = Sq dev * Prob.
                      
weak   0.1   -38%   -3.80%   -48.90%   23.91%   2.3912%
below average   0.1   -12%   -1.20%   -22.90%   5.24%   0.5244%
Average   0.4   13%   5.20%   2.10%   0.04%   0.0176%
Above average   0.3   20%   6.00%   9.10%   0.83%   0.2484%
Strong   0.1   47%   4.70%   36.10%   13.03%   1.3032%
                      
                      
       E(R)   10.90%       Variance =   4.4849%
                      
Standard deviation=       21.18%              

Coefficient of Variation = 21.18%/10.90%=

1.9429

Sharpe ratio = (10.90% -3%)/21.18%

=0.3730

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