Question

You have a portfolio which is composed by a risky asset with an expected rate of return of 15% and a standard deviation of 20% and a risk free asset with a rate of return of 10%. What portion of your portfolio should be invested in the risky asset if you want your portfolio to have a standard deviation of 8%?

Answer 1

Weight of risky asset = 0.4 or 40%

Step-by-step explanation:

The standard deviation(SD) of a portfolio with one risky asset and one risk free asset can be calculated by multiplying the weightage of investment in the risky asset by the standard deviation of the risky asset as the risk free asset's standard deviation is zero. The formula to calculate the standard deviation of such a portfolio is,

Portfolio SD = weight of risky asset * Standard deviation of risky asset

Plugging in the values for portfolio SD and standard deviation of risky asset, we can calculate the weight of risky asset in the portfolio to be,

0.08 = weight of risky asset * 0.2

0.08 / 0.2 = weight of risky asset

Weight of risky asset = 0.4 or 40%