Final answer:
The calculation of a portfolio's standard deviation requires the standard deviation of the risky assets and their proportions in the portfolio. Since the risk-free asset's standard deviation is zero, only the proportion of the investment in stock A affects the portfolio's standard deviation.
Step-by-step explanation:
To find the standard deviation of a portfolio that has invested $10 in stock A and $60 in a risk-free asset, we need to know the standard deviation of stock A and assume that the risk-free asset has a standard deviation of zero since it does not carry any risk (therefore it does not contribute volatility to the portfolio). When combining the weights of the assets in a portfolio to determine its overall standard deviation, we only consider the assets which carry risk, in this case, only stock A.
Let's denote the standard deviation of stock A as σ_A. Since a risk-free asset has a standard deviation of 0 (no risk), and stock A is $10 out of a total $70 investment, the proportion of stock A in the portfolio is 10/70 or about 0.143. To calculate the portfolio standard deviation, we multiply the standard deviation of stock A by this proportion.
Portfolio Standard Deviation (PSD) = σ_A × (Investment in Stock A / Total Investment)
If σ_A is unknown and cannot be derived from the information given, the exact numerical value for the portfolio standard deviation cannot be calculated. However, if the standard deviation for stock A, σ_A, was provided, then you would simply calculate the portfolio standard deviation using the formula given above.