A portfolio manager is managing a $10 million portfolio. Currently the portfolio is invested in the following manner: Investment Dollar Amount Invested Beta Electric Utility $2 million 0.6 Cable Company $3 million 0.8 Real Estate Development $3 million 1.2 International Projects $2 million 1.4 Required: a) What is the portfolio’s beta? b) If the risk free-rate is 5% and the market risk premium is 5.5 %, what is the portfolio’s required rate of return? c) If the expected return on the portfolio for the upcoming year is 9.5% with a standard deviation of 4.5%, what is the probability that the portfolio will have a return greater than its required return? What is the probability the portfolio would have a negative return? The portfolio manager is considering a change in the strategic focus of the portfolio; it will reduce its reliance on the electric utility investment, reducing the investment to $1 million and at the same time increasing the investment in international projects to $3 million. Explain what will happen to the portfolio’s beta, as well as the required rate of return for the portfolio. What you do expect to happen to the portfolio’s expected rate of return and its standard deviation?
To calculate various measures related to the portfolio described, we need to use the following formulas:
a) Portfolio Beta:
The formula to calculate the portfolio beta is the weighted sum of the individual betas of the investments in the portfolio. Mathematically, it can be represented as:
Portfolio Beta = (Weight of Investment A * Beta of Investment A) + (Weight of Investment B * Beta of Investment B) + ...
b) Required Rate of Return:
The required rate of return of a portfolio can be calculated using the Capital Asset Pricing Model (CAPM):
Required Rate of Return = Risk-Free Rate + (Beta of Portfolio * Market Risk Premium)
c) Probability of Portfolio Return:
To calculate the probability of the portfolio return being greater than the required return, as well as the probability of a negative return, we need to use the concept of the normal distribution and z-scores. By calculating the z-score, we can look up the corresponding probabilities from a standard normal distribution table.
Now, let's calculate the answers:
a) Portfolio Beta:
Given the dollar amounts and individual betas of the investments, we can calculate the portfolio beta by using the formula mentioned earlier:
Portfolio Beta = (0.6 * $2 million) + (0.8 * $3 million) + (1.2 * $3 million) + (1.4 * $2 million) / $10 million
Portfolio Beta = 0.6 + 2.4 + 3.6 + 2.8 / 10
Portfolio Beta = 9.4 / 10
Portfolio Beta = 0.94
b) Required Rate of Return:
Using the given risk-free rate (5%) and market risk premium (5.5%), we can calculate the required rate of return using CAPM:
Required Rate of Return = 5% + (0.94 * 5.5%)
Required Rate of Return = 5% + 5.17%
Required Rate of Return = 10.17%
c) Probability of Portfolio Return:
To calculate the probabilities, we need additional information about the distribution of portfolio returns. Assumptions about the distribution shape and other parameters are necessary. Without this additional information, it's not possible to calculate the probabilities accurately.
Regarding the change in the portfolio's strategic focus:
Reducing the investment in electric utility and increasing the investment in international projects will impact the portfolio's beta, required rate of return, expected rate of return, and standard deviation.
- Portfolio Beta: As beta is a measure of systematic risk, the change in investment allocation will affect the portfolio's beta. Investments with different betas will lead to a different portfolio beta. In this case, with the reduction in the electric utility investment (which had a lower beta) and the increase in the international projects investment (which had a higher beta), the portfolio beta is likely to change.
- Required Rate of Return: As the risk profile of the portfolio changes due to the altered investment allocation, the required rate of return is also likely to change. A higher beta generally leads to a higher required rate of return.
- Expected Rate of Return: The change in investment allocation may lead to a change in the expected rate of return. However, without specific information on the expected returns of the investments being added or subtracted, it is not possible to determine the exact impact.
- Standard Deviation: The change in investment allocation could potentially impact the portfolio's overall risk and standard deviation. Investments with different variances and covariances will contribute differently to the overall portfolio risk. Without specific information about the variances and covariances of the investments, it is difficult to determine the exact impact on the portfolio's standard deviation.