Question

Velma Vasquez, fund manager of the Vasquez Value Fund, manages a portfolio of 250 common stocks. Velma relies on various statistics, such as variance, to assess the overall risk of stocks in an economic sector. Her staff reported that for a sample 14 utility stocks the mean annualized return was 14% and that the variance was 3%. Assume that annualized returns are normally distributed. The 95% confidence interval for the population variance of annualized returns is _______.

Answer 1

Sample Size,   n=   14
Sample variance,   s²=   0.03
Confidence Level,   CL=   0.95
      
      
Degrees of Freedom,   DF=n-1 =    13
alpha,   α=1-CL=   0.05
alpha/2 ,   α/2=   0.025
Lower Chi-Square Value=   χ²_1-α/2 =   5.0088
Upper Chi-Square Value=   χ²_α/2 =   24.7356
      

95% CI for population variance is

confidence interval for variance is      
lower bound=   (n-1)s²/χ²_α/2 =   0.016
      
      
upper bound=   (n-1)s²/χ²_1-α/2 =   0.078