CHAPTER 15 EQUITY PORTFOLIOS

Transcription

1 CHAPTER 15 EQUITY PORTFOLIOS Answers to end-of-chapter exercises CROSS SHAREHOLDING 1. Suppose Firm A has 1,000 shares outstanding and Firm B has 500 shares outstanding. Firm A and B each issue 100 new shares. Firm A purchases the shares from Firm B and Firm B purchases the shares from Firm A. a. What is the net effect on the market capitalization of Firm A and B? On the overall market capitalization? b. What is the net effect on each firm s balance sheet? c. If Firm A and B are part of the overall market index, what will happen to their respective weights in the index? d. How is the debt-to-equity ratio affected? e. What is the number of shares now available for trading in the open market? a. Market capitalization of Firm A increases by 10% and that of B increases by 20%. Overall market capitalization increases by the net amount of the newly issued shares. b. Each firm has its equity account increased by the amount raised in the new issue. On the asset side, the "securities held" account increases by the amount of shares purchased. c. The weights for firms A and B increase in the overall index because of the increased number of shares outstanding. d. The debt-to-equity ratio decreases as equity has increased. Debt capacity for each firm is increased. e. The number of shares available for trading is unchanged as the new shares are not traded publicly. They are held by the two firms. 1

2 INTERNATIONAL EQUITY INVESTMENT 2. Suppose you have $100,000 to invest in the Swiss Equity market. Nestlé is a major blue-chip firm and is trading at SFr 666. The current exchange rate is 1.50 SFr/$. a. How many shares of Nestlé can you buy? b. Suppose the share price rises to SFr 800 over 1 year. Calculate the percentage return on your investment in SFr terms. Calculate the dollar return in the following cases: the spot rate stays the same, the US$ appreciates to 1.70 SFr/$, the US$ depreciates to 1.35 SFr/$. c. Make the same calculation as in b but assume that the end-of-year share price is SFr 666. d. Make the same calculation as in b but assume that the end-of-year share price is SFr 600. e. Suppose that at the beginning of the period, you could sell SFr 150,000 forward (your initial SFr investment) for one year delivery. Would this offer you a perfect hedge, an under-hedge or an over-hedge? f. Determine the dollar return in each scenario for questions b and c assuming that you sell SFr 150,000 forward at a one-year forward rate of 1.60 SFr/$. g. Has currency hedging (in f) affected the exposure of US$ returns to foreign exchange changes? a. Initial wealth $100,000 x 1.50 SFr/$ = SFr 150,000. SFr 150,000 / 666 SFr/share = 225 shares b. ( ) / 666 = 134 / 666 = 20% in SFr terms. With 1.50 SFr/$; SFr 180,000 / 1.50 SFr/$ = $120,000 ==> Return: 20% in US$ terms With 1.70 SFr/$ SFr 180,000 / 1.70 SFr/$ = $105,882 ==> Return: 5.88% in US$ terms With 1.35 SFr/$ SFr 180,000 / 1.35 SFr/$ = $133,333 ==> Return: 33.33% in US$ terms 2

3 c. ( ) / 666 = 0% in SFr terms With SFr 1.50/$; SFr 150,000 / 1.50 SFr/$ = $100,000 ==> Return: 0% in US$ terms With SFr 1.70/$ SFr 150,000 / 1.70 SFr/$ = $88,235 ==> Return: % in US$ terms With SFr 1.35/$ SFr 150,000 / 1.35 SFr/$ = $111,111 ==> Return: 11.11% in US$ terms d. ( ) / 666 = -9.91% in SFr terms With SFr 1.50/$; 225 shares x 600 SFr/share = SFr 135,000; SFr 135,000 / 1.50 SFr/$ = $90,000 ==> Return: -10.0% in US$ terms With SFr 1.70/$ 225 shares x 600 SFr/share = SFr 135,000; SFr 135,000 / 1.70 SFr/$ = $79,412 ==> Return: % in US$ terms With SFr 1.35/$ 225 shares x 600 SFr/share = SFr 135,000; SFr 135,000 / 1.35 SFr/$ = $100,000 ==> Return: 0% in US$ terms e. Selling SFr 150,000 forward is a perfect hedge only if the value of the Nestlé shares in one year is SFr 150,000. This is only the case when the share price is unchanged at SFr 666. If the share price rises to SFr 800, our shares are worth SFr 180,000, so SFr 150,000 is an under-hedge. If the share price falls to SFr 600, our shares are worth only SFr 135,000, so SFr 150,000 is an overhedge. f. ANSWERS TO B WITH A SFr 150,000 FORWARD HEDGE AT SFr 1.60/$. With 1.50 SFr/$; 3

4 SFr 30,000 / 1.50 SFr/$ = $ 20,000; $113,750 total ==> Return: 13.75% in US$ terms With 1.70 SFr/$ SFr 30,000 / 1.70 SFr/$ = $ 17,647; $111,397 total ==> Return: 11.40% in US$ terms With 1.35 SFr/$ SFr 30,000 / 1.35 SFr/$ = $ 22,222; $115,972 total ==> Return: 15.97% in US$ terms ANSWERS TO C WITH A 150,000 SFr FORWARD HEDGE AT 1.60 SFr/$. With 1.50 SFr/$; SFr 0/ 1.50 SFr/$ = $ 0; $ 93,750 total ==> Return: -6.25% in US$ terms With 1.70 SFr/$ SFr 0 / 1.70 SFr/$ = $ 0; $ 93,750 total ==> Return: -6.25% in US$ terms With 1.35 SFr/$ SFr 0 / 1.70 SFr/$ = $ 0; $ 93,750 total ==> Return: -6.25% in US$ terms g. If exchange rate (SFr/$) turns out to be higher than the one-year forward of 1.60 SFr/$, forward hedging increases the return in US$ terms. 4

5 3. Consider the case of a British investor. Suppose that the US$ is at a recent low against the Pound, at $ 1.62/. a. What factors should the British investor take into consideration when assessing the opportunity to invest in US$-denominated equities? b. If the British investor forecasts that the fall of the US$ is over and a rebound is likely, should he hedge his exposure to US equities? c. Suppose the investor buys 1,000 shares of IBM at $80 per share. What is the cost of these shares in Pound terms? d. Suppose the price of IBM shares stay at $80 and the dollar subsequently rebounds to $ 1.55/. What is the net gain for the British investor? e. At $ 1.55/, how far could IBM share prices fall before the British investor starts to lose money? a. A forecast of an increase in prices in the US equity market as well as a forecast of an appreciation in the US$ would provide the British investor with the opportunity to invest profitably in the US. b. The British investor is long US$ by virtue of holding US equities. Hedging protects the investor from a declining dollar. A rebounding dollar is a positive event for the British investor. Therefore, he should not hedge if he believes in that scenario. c. $80/share x 1,000 shares / $1.62/ = 49, d. $80/share x 1,000 shares / $1.55/ = 51, Gain: (51, ,382.72) / 49, = % e. Break-even point: X / ($1.55/ ) = 49.38; => X = $76.54/IBM share. 4. In the first quarter of 1995, the Mexican crisis resulted in the devaluation of the Peso from MP 3.40/$ to MP 7/$. Stock prices on the Mexican Bolsa plummeted by 40% in peso terms. a. Calculate the loss during the quarter for a US investor in the Mexican stock market? 5

6 b. Shares of Telmex, traded in the US market in the form of ADRs, plunged from $60 to $26. How much did Telmex lose in Peso terms? c. In the absence of an active futures market in Peso prior to the crisis, how would you hedge your Telmex shares? a. An investment of MP 100 (or 100 / 3.40 = $29.41) is now worth MP 60 (or 60 / 7 = $8.57). Loss is ($ $29.41) / $29.41 = % in US$ terms. b. In MP terms at the start of the quarter: $60 / Telmex share x 3.40 MP/$ = MP 204 / Telmex share. In MP terms at the end of the quarter: $26 / Telmex share x 7.0 MP/$ = MP 182 / Telmex share. Loss in MP: ( ) / 204 = % Loss in US$: (26-60) / 60 = % c. Could hedge the Telmex position directly by buying put options on Telmex ADRs traded in New York. Or by selling call options on Telmex. Alternatively, could hedge the MP exchange rate risk by borrowing Mexican Pesos to buy the Telmex shares. This amounts to a synthetic MP forward contract. 5. A large investment fund has invested in international equity markets using the following weights: 20% UK, 20% Germany, 15% France, 5% Italy, 5% Switzerland, 20% Japan, 10% Honk Kong, and 5% Mexico. The percentage returns (measured in logarithmic, continuous terms) for each country and for each currency gauged against the dollar are shown in the table below: Market Currency UK + 10% - 2% Germany + 7% + 5% France + 6% + 4% Italy + 10% - 5% Switzerland + 6% + 5% Japan - 15% + 10% Honk Kong - 25% + 0% Mexico - 40% - 50% a. Calculate the overall return for the portfolio in US dollar terms. 6

7 b. Calculate the proportion of the overall returns on the portfolio that were the result of rising share prices. c. Calculate the proportion of the overall returns on the portfolio that were the result of currency price changes. Using equation 13.1, the US$-denominated returns are the sum of the local currency returns in the market plus the returns on the currency. Market Currency Performance Weight UK + 10% - 2% + 8.0% 20% Germany + 7% + 5% % 20% France + 6% + 4% % 15% Italy + 10% - 5% + 5.0% 5% Switzerland + 6% + 5% % 5% Japan - 15% + 10% - 5.0% 20% Honk Kong - 25% + 0% % 10% Mexico - 40% - 50% % 5% a. Overall portfolio performance is -1.70%. b. The performance that can be attributed to share prices is -2.40%. c. The performance that can be attributed to currency price changes is +0.70%. 7