A client of Investment Advisor Associates (IAA), Gillian Bissett, has recently won $5 million in the lottery and has asked for investment advice. She has indicated that she would like to have $5 million available for her retirement in 15 years and has therefore decided to invest $2 million in a secure account that is expected to provide an effective annual return of 4% over this period. She would then like to supplement her current income and add to the balance in the secure account by investing the remaining $3 million that she has won. Here, she has initially indicated that she would like to invest a part of the remaining amount in government bonds and the remainder in an equity fund highly recommended by IAA. As a part of their advice, she has asked IAA to provide her with details on the return and risk profiles of these two investments.
a. Assume that Gillian deposits $2 million into the secure account at 4%. How much must she additionally deposit into the account at the end of each year for the next 15 years to have the required $5 million at the end of the 15 years, assuming that she intends to deposit an equal amount each year?
b. The government bonds that Gillian is interested in investing in have a 12-year maturity and a coupon rate of 6% paid semi-annually. These bonds are currently selling at $108 for each $100 face value bond. What is the yield to maturity on these bonds? What is their expected effective annual return?
c. The equity fund recommended by IAA has provided a dividend (current) yield of 4% over the past decade as well as providing a consistent capital gain. Gillian would like to know what the required return on the equity fund is. To determine this, the following information is available:
• Expected return on the market = 10%
• Standard deviation of the market return = 12%
• Risk-free rate = 3.5%
• Standard deviation of return on the equity fund = 20%
• Correlation between the return on the equity fund and the market = 0.75
Based on this information, what is the required return on the equity fund?
d. If the standard deviation of return for the bonds in part (b) is 8% and the correlation between their return and the return on equity fund in part (c) is 0.55, what is the standard deviation of return for a portfolio comprised of 35% bonds and 65% the equity fund?
e. Estimate the beta of this portfolio (35% bonds and 65% equity) and determine its required return according to the security market line (SML) based on the information supplied in parts (b), (c), and (d) above if the correlation coefficient between the bond returns and the market returns is 0.3.
f. Ignore your answers for parts (b) and (c), and alternatively assume that the expected effective annual return on the bond is 7% and the expected return on the equity fund is 12%. Also assume portfolio weights of 60% debt and 40% equity. Does the portfolio lie above or below the SML?
g. Independent of parts (a) to (f) above, Gillian is considering investing in a relatively new company whose profitability has been growing at a compound rate of 25% per year. Using the constant growth DDM (dividend discount model), she calculates that the share price should be $75; this is substantially more than the actual market price of the shares ($50). What is the most likely reason for the wide disparity between the observed price and that which Gillian estimates?