Final answer:
To achieve a portfolio standard deviation of 13% when the risky asset has a standard deviation of 25%, you should invest 52% of your portfolio in the risky asset. The calculation is based on the desired standard deviation divided by the standard deviation of the risky asset.
Step-by-step explanation:
The question pertains to the allocation of an investment between a risky asset and a risk-free asset (Treasury bill) to achieve a particular portfolio standard deviation. To determine what percentage of the portfolio should be invested in the risky asset to achieve a portfolio standard deviation of 13%, you need to understand the concept of investment diversification and its relation to risk and return.
Since the Treasury bill is risk-free, it has a standard deviation of 0%. Therefore, the entire standard deviation of the complete portfolio comes from the risky asset. If the risky asset has a standard deviation of 25% and you want a complete portfolio with a standard deviation of 13%, you calculate the percentage invested in the risky asset by the formula:
Weight of risky asset = desired standard deviation / standard deviation of risky asset
Weight of risky asset = 13% / 25% = 0.52 or 52%
Therefore, the correct answer is A. 52% of your complete portfolio should be invested in the risky asset to have a standard deviation of 13%.