Question 1
Consider a company A with zero earnings retention ratio and a real growth rate in earnings of γ percent. In an inflation environment, the company can only pass inflation through its earnings at a flow-through rate of λ percent. So if I is the inflation rate, its earnings will growth at a rate of g =γ+ λI . The real rate of return required for this company is ρ , so the nominal rate of return required is r= ρ+I .
Use a discounted dividend model and assume that dividends will grow indefinitely at a constant compounded annual growth rate,g =γ+ λI .
(a) Suppose earning in the current period is denoted E0 . State an expression for earnings in the next period E1 .
(b) Using an appropriate formula, show clearly with workings how you arrive at an expression for the intrinsic P/E using the prospective earnings. (Hint: Obtain an expression for P0/E1 ).
(c) Using the expression for the intrinsic P/E you obtained in part (b), explain the relationships between
(i) inflation pass through rate and the price of the company (or stock price).
(ii) the real growth rate in earnings and the P/E ratio.
(d) Calculate the P/E ratio on company A's prospective earnings given γ=2%, I= ρ= 4% and =λ100% .
(e) What is the implication on company A's P/E ratio if the inflation pass through rate is only 80%? Explain.
(f) Suppose the inflation pass through rate is 100% and the inflation rate is exactly equal to the real growth rate in earnings. What can you infer about the intrinsic P/E? Explain.
Question 2
An American investor holds a British bond portfolio worth £100 million. The portfolio has a duration of seven. She fears a temporary depreciation of the pound but wishes to retain the bonds. To cover this risk, she decides to sell pounds forward. She has observed that the British government tends to adopt a "leaning-against-the-wind" policy. When the pound depreciates, British interest rates tend to rise to defend the currency.
(a) The investor runs a regression of "variations in long-term British yields" on "percentage $/£ exchange rate movements" and found that it has a slope coefficient of - 0.2. Interpret this regression result.
(b) The investor uses only forward currency contracts to hedge this risk and not bond futures contracts. What should be the optimal hedge ratio used by the investor if she wishes to reduce the uncertainty caused by exchange risk?
(c) List 3 factors that could make this hedge imperfect if the depreciation of the pound materialises. Elaborate on these factors.
Question 3
In this question sigma (σ ) is used to denote the standard deviation of asset or portfolio returns. It is also a measure of volatility. The Japanese stock market has a sigma of 18%, when computed in yen. The U.S. stock market has a sigma of 17% in US$ and the US$/Yen exchange rate has a sigma of 6%. The correlation between the Japanese stock market and US$/Yen currency movements is -0.1. The correlation between the Japanese and U.S. stock market is equal to 0.4, measured either in local currency or in dollars.
(a) What is the sigma of the Japanese market when expressed in dollars?
(b) Using this number, calculate the sigma (in dollars) of a portfolio made up of 50% of Japanese stocks and 50% of US stocks.
(c) Suppose the dollar volatility of the Japanese stock market is 18.97%, what can you conclude about the correlation between the Japanese stock market movements and exchange rate movements?
Assume that the domestic volatility (standard deviation in yen) of the Japanese bond market is 8%. The volatility of the yen against the U.S. dollar is 6%.
(d) Suppose the dollar volatility of the bond market is 11.35%, what can you conclude about the correlation between the Japanese bond market movements and exchange rate movements?
(e) Assume that you have a portfolio made up of 50% of Japanese stocks, 20% of Japanese bonds, and 30% of U.S. stocks. Formulate an expression for the sigma (in dollars) of your portfolio in terms of σ2JS, σ2USS, σ2JB, ρUSS_JS, ρUSS_JB , ρJS_JB where the subscripts JS, USS and JB denote Japanese stocks, US stocks and Japanese bonds respectively.
Question 4
Amazon is completing construction on a new mega-warehouse outside of London, England. The final construction payment is due in three months in the amount of £525,000. The current spot rate is 1.6500 $/£, and the bid-ask quotes for the three month forward rate are 1.6600-1.6800 $/£.
(a) If Amazon hedges in the forward market, what will be its dollar cost for the construction payment three months from now? Be specific about how they would hedge? ("Buy (Sell) dollars (pounds) forward")?
b) Amazon may also choose to hedge using an option. The rates available on options to buy and sell pounds are as follows:
Type of Option Strike Price Premium Cost
Three month call on £ $1.65/£ $0.040/£
Three month put on £ $1.65/£ $0.030/£
Which option should Amazon consider? Why?
c) Suppose Amazon chose to buy the option. Three months have passed and the spot exchange rate is now 1.58$/£. What is the hedged dollar value of the payment? What is the hedged dollar value of the payment if the exchange rate is now 1.68$/£?
d) Suppose you are given prevailing interest rates in the US and UK, how would you structure a money market hedge (i.e. resorting to borrowing/lending)?