22 4 chapter 22 futures markets 19 a cash flows

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Chapter 22 - Futures Markets 19. a. Cash Flows Action Now T 1 T 2 Long futures with maturity T 1 0 P 1 – F( T 1 ) 0 Short futures with maturity T 2 0 0 F( T 2 ) – P 2 Buy asset at T 1 , sell at T 2 0 –P 1 +P 2 At T 1 , borrow F( T 1 ) 0 F( T 1 ) –F( T 1 ) × (1+ r f ) ( T 2 –T 1 ) Total 0 0 F( T 2 ) – F( T 1 ) × (1+ r f ) ( T 2 –T 1 ) b. Since the T 2 cash flow is riskless and the net investment was zero, then any profits represent an arbitrage opportunity. c.The zero-profit no-arbitrage restriction implies that F( T 2 ) = F( T 1 ) × (1+ r f ) ( T 2 – T 1 ) CFA PROBLEMS 1. a.The strategy that would take advantage of the arbitrage opportunity is a “reverse cash and carry.” A reverse cash and carry opportunity results when the following relationship does not hold true: F 0 S 0 (1+ C) If the futures price is less than the spot price plus the cost of carrying the goods to the futures delivery date, then an arbitrage opportunity exists. A trader would be able to sell the asset short, use the proceeds to lend at the prevailing interest rate, and then buy the asset for future delivery. At the future delivery, the trader would then collect the proceeds of the loan with interest, accept delivery of the asset, and cover the short position in the commodity. b. Cash Flows Action Now One year from now Sell the spot commodity short +$120.00 $125.00 Buy the commodity futures expiring in 1 year $0.00 $0.00 Contract to lend $120 at 8% for 1 year $120 .00 +$129.60 Total cash flow $0.00 +$4.60 22-5
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Chapter 22 - Futures Markets 2. a.The call option is distinguished by its asymmetric payoff. If the Swiss franc rises in value, then the company can buy francs for a given number of dollars to service its debt, and thereby put a cap on the dollar cost of its financing. If the franc falls, the company will benefit from the change in the exchange rate. The futures and forward contracts have symmetric payoffs. The dollar cost of the financing is locked in regardless of whether the franc appreciates or depreciates. The major difference from the firm’s perspective between futures and forwards is in the mark-to-market feature of futures. The consequence of this is that the firm must be ready for the cash management issues surrounding cash inflows or outflows as the currency values and futures prices fluctuate. b. The call option gives the company the ability to benefit from depreciation in the franc, but at a cost equal to the option premium. Unless the firm has some special expertise in currency speculation, it seems that the futures or forward strategy, which locks in a dollar cost of financing without an option premium, may be the better strategy. 3. The important distinction between a futures contract and an options contract is that the futures contract is an obligation. When an investor purchases or sells a futures contract, the investor has an obligation to either accept or deliver, respectively, the underlying commodity on the expiration date. In contrast, the buyer of an option contract is not obligated to accept
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