Mock 2017 AM, Question 10A

CFA Level III
#1

In the 2017 Mock question 10A they calculate the standard deviation with the following formula: ((weight1)^2 * (stdev1)^2 + (weight2)^2 * (stdev2)^2 + 2 * (weight1 * weight 2 * stdev1 * stdev2 * Correlation))^0.5.

Why do I get a different solution for the standard deviation if I calculate it the following way:

beta = Cov / variance --> beta is given 0.78; Cov = weight1 * weight 2 * Correlation -> solve for variance -> stdev = variance^0.5

Can someone shed some light on this?

Many thanks

#2

In your beta calculation the covariance is the covariance of the portfolio returns with the market returns and hence you also need the correlation of the portfolio returns to the market returns. The correlation given is the correlation between the returns of the two asset classes in your portfolio, which is not what you need for your calculation.