You are currently only invested in the Natasha Fund (aside from risk-free securities). It has an expected return of 14% with a volatility of 20%. Currently, the risk-free rate of interest of 3.8%. Your broker suggests that you add Hannah Corporation to your portfolio. Hannah Corporation has an expected return of 20%, a volatility of 60%, and a correlation of 0 with the Natasha fund.
a. Is your broker right?
b. You follow your broker’s advice and make a substantial investment in Hannah stock so that, considering only your risky investments, 60% is in the Natasha Fund and 40% is in Hannah stock. When you tell your finance professor about your investment, he says that you made a mistake and should reduce your investment in Hannah. Is your finance professor right?
c. You decide to follow your finance professor’s advice and reduce your exposure to Hannah. Now Hannah represents 15% of your risky portfolio, with the rest in the Natasha Fund. Is this correct amout of Hannah stock to hold?
a. Your broker is right in the sense that adding Hannah Corporation to your portfolio will improve your diversification, given that it has a correlation of 0 with the Natasha fund. Diversification can help lower the overall volatility of your portfolio without sacrificing expected returns.
b. Your finance professor might have concerns about the degree of investment in Hannah because of its relatively high volatility (60%) compared to the Natasha Fund (20%). While diversification can be beneficial, a 40% allocation in a high-volatility stock like Hannah may increase overall portfolio risk. It would be essential to assess the portfolio's risk and return profile after the investment adjustment to determine if the new allocations align with your risk tolerance and investment goals.
c. The correct amount of Hannah stock to hold in your portfolio depends on your risk tolerance and investment objective. By reducing the exposure to Hannah to 15% of your risky portfolio, you are decreasing the overall portfolio risk due to its high volatility. Still, it would be best to evaluate the resulting portfolio risk and return characteristics to ensure it meets your requirements. You might also consider other investments or optimizing your portfolio further to reach a balance between return and risk that suits your preferences.
a. To determine if the broker is right, we need to calculate the expected return and volatility of the portfolio. Since the correlation between the Natasha Fund and Hannah Corporation is 0, the portfolio expected return and volatility can be calculated as follows:
Portfolio Expected Return = (Weight of Natasha Fund * Expected Return of Natasha Fund) + (Weight of Hannah Corporation * Expected Return of Hannah Corporation)
= (0.6 * 0.14) + (0.4 * 0.20)
= 0.084 + 0.08
= 0.164 or 16.4%
Portfolio Volatility = (Weight of Natasha Fund^2 * Volatility of Natasha Fund^2) + (Weight of Hannah Corporation^2 * Volatility of Hannah Corporation^2)
= (0.6^2 * 0.2^2) + (0.4^2 * 0.6^2)
= (0.36 * 0.04) + (0.16 * 0.36)
= 0.0144 + 0.0576
= 0.072 or 7.2%
The broker is right if the return on the portfolio exceeds the risk-free rate by a sufficient margin, considering the added risk. Let's calculate this:
Excess Return = Portfolio Expected Return - Risk-Free Rate
= 0.164 - 0.038
= 0.126 or 12.6%
Since the excess return (12.6%) is greater than the risk-free rate (3.8%), it suggests that the broker's suggestion to add Hannah Corporation to the portfolio may be a good decision.
b. To determine if the finance professor is right, we need to consider whether further adjustments to the portfolio weightings are necessary.
However, without specific information provided by the professor, we cannot assess their reasoning or determine whether their suggestion is valid. We require additional information to evaluate the professor's recommendation accurately.
c. The professor suggests reducing the exposure to Hannah to 15% of the risky portfolio, with the rest in the Natasha Fund. Let's calculate the updated portfolio weightings:
Weight of Natasha Fund = 1 - Weight of Hannah Corporation
= 1 - 0.15
= 0.85 or 85%
Weight of Hannah Corporation = 0.15 or 15%
The professor's suggestion of allocating 15% of the portfolio to Hannah Corporation may be suitable based on their desired risk-reward trade-off. However, this decision relies on the investor's risk tolerance and investment goals, which may vary.
a. To determine whether your broker is right, you need to assess the impact of adding Hannah Corporation to your portfolio. One way to evaluate this is by calculating the expected return and volatility of the combined portfolio.
The expected return of a portfolio with weights W1 and W2 in two assets A and B respectively can be calculated as:
(Expected return of portfolio) = (W1 * Expected return of A) + (W2 * Expected return of B)
The volatility of a portfolio with weights W1 and W2 in two assets A and B respectively can be calculated as:
(Volatility of portfolio) = sqrt[(W1^2 * Volatility of A^2) + (W2^2 * Volatility of B^2) + (2 * W1 * W2 * Correlation between A and B * Volatility of A * Volatility of B)]
In this case, the weights for the Natasha Fund and Hannah Corporation are 60% and 40% respectively, as mentioned in the question. The correlation between the two assets is given as 0.
Now, plug in the values:
(Expected return of portfolio) = (0.6 * 14%) + (0.4 * 20%)
Volatility of portfolio = sqrt[(0.6^2 * 20%^2) + (0.4^2 * 60%^2) + (2 * 0.6 * 0.4 * 0 * 20% * 60%)]
Calculate these values to see if the expected return is higher and the volatility is lower than the current portfolio. If both conditions hold, then your broker's suggestion of adding Hannah Corporation would be deemed correct.
b. Your finance professor suggests reducing your investment in Hannah Corporation. To evaluate this advice, compare the new portfolio's expected return and volatility to the previous scenario.
Given that the current portfolio consists of 60% Natasha Fund and 40% Hannah Corporation, if you reduce your investment in Hannah, the proportions will change. Let's say you now allocate 15% to Hannah Corporation and the rest to the Natasha Fund.
Re-calculate the expected return and volatility for the new portfolio using the formula mentioned in part a, replacing the weights with 15% and 85% respectively for Hannah Corporation and the Natasha Fund.
Compare the new expected return and volatility with the previous scenario. If the expected return is higher and the volatility is lower, your finance professor's advice would be considered correct.
c. The finance professor suggests that you reduce your exposure to Hannah Corporation so that it represents 15% of your risky portfolio, with the rest in the Natasha Fund.
To evaluate whether this allocation is correct, you need to analyze the new expected return and volatility of the revised portfolio. Use the formula mentioned in part a, replacing the weights with 15% for Hannah Corporation and 85% for the Natasha Fund.
Compare the new expected return and volatility with the previous portfolio scenarios. If the new allocation provides a higher expected return and lower volatility than the previous scenarios, then the professor's advice would be considered correct.