The security market line (SML) is an equation that shows the relationship between risk as measured by beta and the required rate securities. The SML equation is given below: Required return on Stock Risk-free return + (Market risk premium) (Stock’s beta) W If a stock’s expected return plots on or above the SML, then the stock’s return is -Select- expected return plots below the SML, the stock’s return is-select- to compensate the investor for r to compensate the investor for risk. The SML line can change due to expected inflation and risk aversion. If inflation changes, then the SML plotted on a graph will shi the old SML. If risk aversion changes, then the SML plotted on a graph will rotate up or down becoming more or less steep if invo less risk averse. A firm can influence market risk (hence its beta coefficient) through changes in the composition of its assets and amount of debt it uses. Quantitative Problem: You are given the following information for Wine and Cork Enterprises (WCE): TRF-4%; TM 8% ; RPM = 4%, and beta = 1.2 What is WCE’s required rate of return? Do not round intermediate calculations. Round your answer to two decimal places. % If inflation increases by 2% but there is no change in investors’ risk aversion, what is WCE’s required rate of return now? Do no calculations. Round your answer to two decimal places. % Assume now that there is no change in inflation, but risk aversion increases by 1 What is WCE’s required rate of return now? intermediate calculations. Round your answer to two decimal places
The Correct Answer and Explanation is :
Explanation:
The Security Market Line (SML) equation is given by:
[
\text{Required Return} = \text{Risk-free Rate} + (\text{Market Risk Premium} \times \text{Beta})
]
Step 1: Calculating WCE’s Required Rate of Return
Given:
- Risk-free rate (TRF) = 4%
- Market return (TM) = 8%
- Market risk premium (RPM) = 4% (since RPM = TM – TRF)
- Beta = 1.2
[
\text{Required Return} = 4\% + (4\% \times 1.2)
]
[
= 4\% + 4.8\% = 8.8\%
]
So, WCE’s required rate of return is 8.8%.
Step 2: Impact of Inflation Increase by 2%
When inflation increases by 2%, both the risk-free rate and the market return increase by 2%. The new values are:
- New risk-free rate = 4% + 2% = 6%
- New market return = 8% + 2% = 10%
- New market risk premium = 10% – 6% = 4%
Using the SML formula:
[
\text{New Required Return} = 6\% + (4\% \times 1.2)
]
[
= 6\% + 4.8\% = 10.8\%
]
Thus, WCE’s required return increases to 10.8%.
Step 3: Impact of Increase in Risk Aversion by 1%
When risk aversion increases, the market risk premium increases by 1%, making it:
- New market risk premium = 4% + 1% = 5%
Applying the SML equation:
[
\text{New Required Return} = 4\% + (5\% \times 1.2)
]
[
= 4\% + 6\% = 10.0\%
]
Thus, WCE’s required return increases to 10.0%.
Key Insights
- If a stock’s expected return plots on or above the SML, it is considered fairly or undervalued.
- If a stock’s expected return falls below the SML, it is overvalued as it does not sufficiently compensate for risk.
- An increase in inflation shifts the entire SML upward, increasing required returns.
- An increase in risk aversion makes the SML steeper, raising required returns for risky stocks.
These factors affect investment decisions, portfolio risk, and corporate finance strategies.
Final Answers
- WCE’s Required Rate of Return = 8.8%
- After 2% Inflation Increase = 10.8%
- After 1% Increase in Risk Aversion = 10.0%
Now, I’ll generate an image illustrating the changes in the SML graph.
Here is a visual representation of the Security Market Line (SML) and how it shifts due to changes in inflation and risk aversion. The key takeaways from the graph:
- Original SML (Blue Line) – Represents the initial relationship between risk (beta) and the required return.
- After a 2% Inflation Increase (Red Dashed Line) – The entire SML shifts upward, increasing the required return for all levels of beta.
- After a 1% Increase in Risk Aversion (Green Dash-Dot Line) – The SML rotates upward, making it steeper, meaning riskier stocks (higher beta) now require an even higher return.
The points marked on the graph indicate WCE’s required return under different scenarios, showing how market conditions affect investment decisions. Let me know if you need further clarifications!