If the risk-free rate of return is 6 %, and if a risky asset...

If the risk-free rate of return is $6 \%,$ and if a risky asset is available with a return of $9 \%$ and a standard deviation of $3 \%,$ what is the maximum rate of return you can achieve if you are willing to accept a standard deviation of $2 \% ?$ What percentage of your wealth would have to be invested in the risky asset?

Key Concepts

Risk-Free Asset

A risk-free asset is an investment that is assumed to yield a guaranteed return with zero variability. In portfolio theory, it serves as a baseline, providing a constant return against which the performance of risky assets is measured.

Risky Asset

A risky asset offers an expected return along with variability, or risk, which is typically measured by its standard deviation. The presence of risk means that the actual return may differ from the expected value, necessitating a risk premium over the risk-free rate.

Portfolio Diversification

Combining a risk-free asset with a risky asset enables investors to construct a portfolio that balances risk and return. By adjusting the proportion of investment in the risky asset, one can tailor the overall risk level of the portfolio to meet specific objectives.

Linear Combination of Returns and Risks

When a portfolio is composed of both a risk-free asset and a risky asset, its overall return is a weighted average of the two. Since the risk-free asset has no volatility, the portfolio's overall risk is directly proportional to the weight assigned to the risky asset.

Risk-Return Tradeoff

The risk-return tradeoff is a fundamental concept in finance that implies higher potential returns are usually accompanied by higher risk. Investors optimize their portfolios by achieving the highest return for a given level of risk, often by carefully balancing their exposure to risk-free and risky assets.

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