The betas and variances of three assets are beta_1 = 0.5, beta_2 = 1, beta_3 = 1.5, and
sigma^2_1 = 20%, sigma^2_2 = 10%, sigam^2_3 of = 30%, respectively. The market variance is
sigam^2_m = 10%. Compute the covariance matrix implied from the single index model.
Solution
The covariance matrix implied by this model is:
= 2 001 +
where 2 00 is the variance of market returns,
is the vector of slopes,
and is the diagonal matrix containing residual variances ii. Call ij the (i, j)-th entry of ..
The betas and variances of three assets are beta_1 = 0.5, beta_2 = 1,.pdf
1. The betas and variances of three assets are beta_1 = 0.5, beta_2 = 1, beta_3 = 1.5, and
sigma^2_1 = 20%, sigma^2_2 = 10%, sigam^2_3 of = 30%, respectively. The market variance is
sigam^2_m = 10%. Compute the covariance matrix implied from the single index model.
Solution
The covariance matrix implied by this model is:
= 2 001 +
where 2 00 is the variance of market returns,
is the vector of slopes,
and is the diagonal matrix containing residual variances ii. Call ij the (i, j)-th entry of .
