Question

The average monthly return of a bond portfolio is 1% with a standard deviation of 4%. On the other hand the average monthly return of a stock portfolio is 2% with standard deviation of 6%. Each portfolio is measured on a period of 24 months. Test if the variance of the stock portfolio is higher at 5% significance level.

Answer 1

Data:       

n1 = 24      

n2 = 24      

s1^2 = 6^2 = 36      

s2^2 = 4^2 = 16      

Hypotheses:      

Ho: σ1^2 = σ2^2      

Ha: σ1^2 > σ2^2      

Decision Rule:      

α = 0.05      

Numerator DOF = 24 - 1 = 23    

Denominator DOF = 24 - 1 = 23    

Critical F- score = 2.014425     

Reject Ho if F > 2.014425     

Test Statistic:      

F = s1^2 / s2^2 = 36/16 = 2.25    

p- value = 0.028823      

Decision (in terms of the hypotheses):    

Since 2.25 > 2.0144 we reject Ho and accept Ha

Conclusion (in terms of the problem):

There is sufficient evidence that the variance of the stock portfolio is higher.