You are given the following information: • Spot price of an asset today = 1,500

Question

You are given the following information: • Spot price of an asset today = 1,500 • Spot price of the asset nine months from today = 1,560 • A $1000 face value nine-month zero-coupon bond is selling for $963.39. • The nine-month forward price of the asset is F. Questions: (a) Compute F so that the payoff of the long forward strategy is equal to the payoff of the long asset strategy. Does it depend on the spot price nine months from today? 1 (b) Suppose that the forward price is the one computed in part (a) plus $10. Explain how to make a sure profit in this situation. Write a detailed explanation: when and what to buy or sell, and when and how much to borrow/repay. (Hint: think about a short forward strategy and a long asset strategy, together.)

Explanation / Answer

Answer (a)

Forward Price(F) = Spot rate today (1+ i) where i is 3.8%. which is 9 month interest rate(see working note.)

= 1500* 1.038 = 1557

No this forward price does not depend upon the spot asset price of the asset at nine months.

Working note:

calculation of nine month interest rate from zero coupon bond = (1000-963.39)/963.39*100 = 3.8%

Please note all calculatons are based on interest rate of nine month i.e. 3.8% (or 3.8*12/9 i.e. 5.067% annually)

Answer (b)

Now forward price = 1557 + 10 = 1567

So in this situation both strategy i.e. long asset and short forward will result in profit.

Borrow $1500 today and invest in buying a asset at spot price today at 1500. Simultaneously sell a 9 month forward i.e. short forward at 1567.

So at end of nine month Relaized gain = (1567-1500) - interest cost on 1500

= 67 - 3.8%*1500 = 67-57 = $10

Repay 1500 at the end of nine month.

combined strategy will result in a net arbitrage profit of $10.

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.