A
Aradhana Saha
Consider the following two-factor model for the returns of three stocks:. Assume that the factors and $e_{j}$ have a zero mean, that all the factors have a variance of 0.01 and are uncorrelated, and that var [$e_{a}$] = 0.01, var [$e_{b}$] = 0.04, and var [$e_{c}$] = 0.02.
$r_{a}$ = 0.13 + 6$F_{1}$ + 4$F_{2}$ + $e_{a}$
$r_{b}$ = 0.15 + 2$F_{1}$ + 2$F_{2}$ + $r_{b}$
$r_{c}$ = 0.07 + 5$F_{1}$ - $F_{2}$ + $r_{c}$
Construct one portfolio with $\beta_{1}$ = 0, $\beta_{2}$ = 1, and compute the expected return and risk premia of the portfolio.
I want to confirm if we have to use the formulas $\sum_{a}^{c}w_{i}\beta_{1i}$ = 1, $\sum_{a}^{c}w_{i}\beta_{2i}$ = 0 and $\sum_{a}^{c}w_{i}$ =1 to get the weights. To calculate the risk premia of this particular portfolio do I have to calculate the zero beta portfolio ie $\sum_{a}^{c}w_{i}\beta_{ji}$ = 0 for all betas and compare the return of this with the former?
$r_{a}$ = 0.13 + 6$F_{1}$ + 4$F_{2}$ + $e_{a}$
$r_{b}$ = 0.15 + 2$F_{1}$ + 2$F_{2}$ + $r_{b}$
$r_{c}$ = 0.07 + 5$F_{1}$ - $F_{2}$ + $r_{c}$
Construct one portfolio with $\beta_{1}$ = 0, $\beta_{2}$ = 1, and compute the expected return and risk premia of the portfolio.
I want to confirm if we have to use the formulas $\sum_{a}^{c}w_{i}\beta_{1i}$ = 1, $\sum_{a}^{c}w_{i}\beta_{2i}$ = 0 and $\sum_{a}^{c}w_{i}$ =1 to get the weights. To calculate the risk premia of this particular portfolio do I have to calculate the zero beta portfolio ie $\sum_{a}^{c}w_{i}\beta_{ji}$ = 0 for all betas and compare the return of this with the former?