If you invest half your money in a risk-free asset and half your money in a risky asset such that the standard deviation of the return on the risky asset is s, then the standard deviation of the return on your investment portfolio is s/2.

Question

Quizplus · Accepted Answer

When you diversify your investments between a risk-free asset and a risky asset, the overall risk of the portfolio is averaged out. Since the risk-free asset has a standard deviation of zero, investing half in it and half in a risky asset with standard deviation s, effectively spreads the risk over the entire investment, resulting in a portfolio standard deviation of s/2. This is because the risk (volatility) of the risk-free asset does not contribute to the portfolio's volatility, thus the portfolio's standard deviation is only coming from the risky asset, but diluted by the 50% investment in the risk-free asset.

If You Invest Half Your Money in a Risk-Free Asset