The market risk premium for next period is 5.44% and the risk-free rate is 1%. Stock Z has a beta of 1.39 and an expected return of 11.72%. What is the market’s reward-to-risk ratio? (For this problem, please list your answer in decimal format to 3 places. For example, if your answer is 12.3%, then enter it as 0.123).
The correct answer and explanation is :
To calculate the market’s reward-to-risk ratio, we use the following formula:
[
\text{Market Reward-to-Risk Ratio} = \frac{\text{Market Risk Premium}}{\text{Beta of the Market}}
]
However, since the market’s reward-to-risk ratio is essentially the ratio between the market risk premium and the beta of the market, and the beta of the market is always 1 (since the market’s return corresponds to itself), we can simplify this to:
[
\text{Market Reward-to-Risk Ratio} = \text{Market Risk Premium}
]
Given:
- Market Risk Premium = 5.44% or 0.0544 (in decimal form)
- The market’s beta is 1.
So, the market’s reward-to-risk ratio is simply:
[
\text{Market Reward-to-Risk Ratio} = 0.0544 \text{ (in decimal form)}
]
Thus, the market’s reward-to-risk ratio is 0.054 (rounded to 3 decimal places).
Explanation:
The market risk premium is the difference between the expected return of the market and the risk-free rate. In this problem, it is given as 5.44% or 0.0544 in decimal form. This represents the additional return that an investor can expect from the market for taking on the extra risk of investing in the market compared to a risk-free investment.
The market’s reward-to-risk ratio compares the return an investor receives for taking on risk (the market risk premium) to the amount of risk being taken (which, in this case, is represented by the beta of the market). Since the market’s beta is always 1, the formula simplifies to the market risk premium itself.
In practice, this ratio is an important measure for evaluating how much return an investor can expect per unit of risk in the market. A higher reward-to-risk ratio indicates that the market is providing higher expected returns for each unit of risk taken.
This ratio is useful for asset pricing models like the Capital Asset Pricing Model (CAPM), which helps investors understand the relationship between expected return, risk, and the market as a whole.