Answer:
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%