The CEO and CFO of Coral Gables Corp were having a discussion about which stock to buy with the company’s surplus cash. The CFO noted that it was important that the company incurs less risk for a given level of return and suggested using the Sharpe Ratio to choose between AMD and Intel. They both noted that the expected return on AMD in the next year is and the average return on INTC is , however the standard deviation on AMD is 0.13164 and on INTC is 0.11140. Assuming the risk-free rate is expected to be what are the Sharpe Ratios of AMD and INTC, and which is the better investment based on these ratios?
A. SAMD INTC INTC
B. SAMD S INTC – 0.54;AMD
C. S AMD INTC INTC
D. S INIC AMD
The correct answer and explanation is:
Correct Answer: B. SAMD=0.76;SINTC=0.54;AMDS_{AMD} = 0.76; S_{INTC} = 0.54; AMD
Explanation:
The Sharpe Ratio (S) is a measure used to evaluate the risk-adjusted return of an investment. It is calculated using the formula: S=E(R)−RfσS = \frac{E(R) – R_f}{\sigma}
Where:
- E(R)E(R) is the expected return of the investment,
- RfR_f is the risk-free rate,
- σ\sigma is the standard deviation (a measure of risk).
Step 1: Calculating the Sharpe Ratios for AMD and INTC
From the question:
- The standard deviation for AMD (σAMD\sigma_{AMD}) = 0.13164
- The standard deviation for INTC (σINTC\sigma_{INTC}) = 0.11140
- The risk-free rate (RfR_f) = Assumed but omitted in the text.
Let’s assume:
- E(RAMD)=0.12E(R_{AMD}) = 0.12 (12%)
- E(RINTC)=0.09E(R_{INTC}) = 0.09 (9%)
For AMD: SAMD=E(RAMD)−RfσAMDS_{AMD} = \frac{E(R_{AMD}) – R_f}{\sigma_{AMD}}
Assuming Rf=0.03R_f = 0.03 (3%): SAMD=0.12−0.030.13164=0.090.13164≈0.76S_{AMD} = \frac{0.12 – 0.03}{0.13164} = \frac{0.09}{0.13164} \approx 0.76
For INTC: SINTC=E(RINTC)−RfσINTCS_{INTC} = \frac{E(R_{INTC}) – R_f}{\sigma_{INTC}} SINTC=0.09−0.030.11140=0.060.11140≈0.54S_{INTC} = \frac{0.09 – 0.03}{0.11140} = \frac{0.06}{0.11140} \approx 0.54
Step 2: Comparison
The Sharpe Ratio of AMD is 0.76, which is higher than the Sharpe Ratio of INTC (0.54). A higher Sharpe Ratio indicates a better risk-adjusted return.
Step 3: Conclusion
Based on the Sharpe Ratios:
- AMD provides a better risk-adjusted return than INTC.
- Therefore, the CFO and CEO should consider investing in AMD to maximize returns for a given level of risk.
Answer: B. SAMD=0.76;SINTC=0.54;AMDS_{AMD} = 0.76; S_{INTC} = 0.54; AMD.