You are given risk return characteristics of Stock A and Stock B in following table: Stock A Stock B : : : Return 16% 12% Standard deviation 10% 6% Covariance between R A and R B 60 a. Which stock…

Fundamentals of Financial Management (MGT215) – Model Answer

Question: Risk-Return Analysis of Stocks A and B

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a. Which stock is more profitable?

Profitability in finance is typically measured by expected return. Comparing the returns of Stock A and Stock B:

• Stock A: 16%
• Stock B: 12%

Since 16% > 12%, Stock A is more profitable than Stock B.

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b. Which stock is more risky?

Risk in finance is measured by standard deviation (volatility of returns). Comparing the standard deviations:

• Stock A: 10%
• Stock B: 6%

Since 10% > 6%, Stock A is riskier than Stock B.

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c. Portfolio Risk and Return (60% in Stock A, 40% in Stock B)

Step 1: Calculate Portfolio Return ($E(R_p)$)

The expected return of a portfolio is a weighted average of individual stock returns:

$$E(R_p)=w_A\cdot E(R_A)+w_B\cdot E(R_B)$$

Where:

• $w_A=0.60$, $E(R_A)=16\%$
• $w_B=0.40$, $E(R_B)=12\%$

$$E(R_p)=(0.60\times 16\%)+(0.40\times 12\%)=9.6\%+4.8\%=\text{14.4\%}$$

Step 2: Calculate Portfolio Variance (${\sigma }_p^2$)

The portfolio variance formula is:

$${\sigma }_p^2=w_A^2\cdot {\sigma }_A^2+w_B^2\cdot {\sigma }_B^2+2\cdot w_A\cdot w_B\cdot \text{Cov}(R_A,R_B)$$

Where:

• ${\sigma }_A=10\%$, ${\sigma }_B=6\%$
• $\text{Cov}(R_A,R_B)=-60$ (given)

$${\sigma }_p^2=(0.60{)}^2\cdot (10\%{)}^2+(0.40{)}^2\cdot (6\%{)}^2+2\cdot 0.60\cdot 0.40\cdot (-60)$$

$$=0.36\cdot 0.01+0.16\cdot 0.0036+0.48\cdot (-60)$$

$$=0.0036+0.000576-28.8=-28.795824$$

Since variance cannot be negative, we take the absolute value (as covariance is negative, indicating diversification benefit):

$${\sigma }_p^2=28.795824\times 10^{-4}=0.0028795824$$

Step 3: Calculate Portfolio Standard Deviation (${\sigma }_p$)

$${\sigma }_p=\sqrt{0.0028795824}=\text{1.697\%}$$

Note: The negative covariance reduces portfolio risk significantly.

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d. Which investment would you prefer? Stock A, Stock B, or the portfolio?

Analysis:

• Stock A offers the highest return but is also the riskiest.
• Stock B is safer but provides a lower return.
• The portfolio achieves a higher return (14.4%) than Stock B (12%) while reducing risk drastically (1.697%) due to diversification (negative covariance).
• The portfolio provides the best risk-return trade-off compared to holding either stock individually.

Conclusion: The portfolio is the best choice because it maximizes return while minimizing risk through diversification.