Problem Set 3 - asm PDF

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Problem Set 3 - FINA 2322 Thomas Andreas Maurer

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1. Suppose the current stock price of the Walt Disney Company is $50 and you can enter a forward contract (long or short position) to buy 50’000 stocks in 9 months for $51 each. The Walt Disney stock is expected to increase to $53 in 9 months. The 9-month (risk free) spot rate is 3% (c.c.). (a) Is there an arbitrage if Walt Disney does not pay dividends? If so, carefully describe a possible arbitrage strategy. What should the forward price be in a world without arbitrage? (b) Suppose the 3-month (risk free) spot rate is 2.75%. Is there an arbitrage if Walt Disney pays a dividend of $0.75 in 3 months? If so, carefully describe a possible arbitrage strategy. What should the forward price be in a world without arbitrage? 2. The current exchange rate between the Japanese Yen (Y en) and US dollar (U SD) is . Suppose the 9-month spot rate in the USA (invest U SD) is 3% (monthly 0.0128 UYSD en compounded) and the 9-month spot rate in Japan (invest Y en) is 1% (quarterly compounded). (a) Assuming markets are arbitrage free, calculate the forward exchange rate to exchange U SD and Y en in 9 months. (b) Is there an arbitrage opportunity if the forward price to buy Y en in 9 months is )? If so, describe an arbitrage the same as the current exchange rate (0.0128 UYSD en strategy. How much money can you make if you own $1’000 which you can invest (assume your trades do not have a price impact, e.g. exchanging Y en for U SD does not affect the current exchange rate)? (c) The real interest rate is defined as the difference between the nominal interest rate and the expected inflation, i.e. if in Japan the nominal interest rate is 1% and the expected inflation is 0.75% then the real interest rate is 0.25%. The real interest rate measures by how much money grows in real terms or adjusted for increases in prices, i.e. how much more consumption a dollar buys after investing it in the risk free asset. How does your result in question a) change, if there was inflation

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in Japan. The nominal 9-month spot rate stays at 1% (quarterly compounded) but there is an expected inflation over the next 9 months of 0.75%? 3. The current spot price of one lb of copper is $3.75, the 3.5-year spot rate is 2% (semiannual compounding), the (continuous flow of) storage costs of copper is 3% per year. (a) In absence of arbitrage, what should be the forward price to trade copper in 3.5 years if copper was an investment asset? (b) Since copper is a consumption asset, it might be impossible or undesirable to short sell it in the spot market. Does the result/ formula in question a) still hold? Explain carefully. (c) Assume copper is a consumption asset. Is there an arbitrage if the forward price to trade copper in 3.5 years is $5? If so, describe an arbitrage strategy. (d) What is the convenience yield if the true forward price to trade copper in 3.5 years is $3.78? 4. The expected return of the Dow Jones Industrial Average index is 5.5% per year, its dividend yield is 0%, the yield curve is flat and the risk free interest rate is constant and equals 2% (c.c.). (a) In general, do you expect speculators to take long or short positions in DJIA forwards and futures? Explain. (b) There is a forward contract with 9 months to maturity written on $1’000 times the DJIA index points at maturity. Given there is no arbitrage, what is the forward price of the contract if the DJIA is currently at a level of 13000 index points? (c) Consider you have entered a short position in the forward contract in question b). What is the value of your position 3 months later if the DJIA has increased to 13001 index points? What if the DJIA has increased to 14500 index points? 5. The current spot price of one bushel of corn is $5, the 1.5-year spot rate is 3% (c.c.), the (continuous flow of) storage costs of corn is 5% per year. 3

(a) In absence of arbitrage, what should be the forward price to trade corn in 1.5 years if corn was an investment asset? (b) Assume corn is a consumption asset. Is there an arbitrage if the forward price to trade corn in 1.5 years is $10? If so, describe an arbitrage strategy. (c) What is the convenience yield if the true forward price to trade corn in 1.5 years is $2.5?

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