# The following usual parity value except for the

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the following usual parity value (except for the factor p): S 0 (l + r f p) – D The dividend (D) equals: 0.012 × 1,350 = \$16.20 The factor p arises because only this fraction of the proceeds from the short sale can be invested in the risk-free asset. We can solve for p as follows: 1,350 × (1 + 0.022p) – 16.20 = 1,351 p = 0.579 b. With p = 0.9, the no-arbitrage lower bound on the futures price is: 1,350 × [1 + (0.022 × 0.9)] – 16.20 = 1,360.53 The actual futures price is 1,351. The departure from the bound is therefore 9.53. This departure also equals the potential profit from an arbitrage strategy. The strategy is to short the stock, which currently sells at 1,350. The investor receives 90% of the proceeds (1,215) and the remainder (135) remains in the margin account until the short position is covered in 6 months. The investor buys futures and lends 1,215: CF Now CF in 6 months Buy futures 0 S T - 1,351 Sell shares 1350 - 135 135 - S T - 16.20 Lend - 1,215 1,215 × 1.022 = 1,241.73 Total 0 9.53 The profit is: 9.53 × \$250 per contract = \$2,382.50 CFA PROBLEMS 1. a.By spot-futures parity: F 0 = S 0 × (l + r f ) = 185 × [1 + (0.06/2)] = 190.55 b. The lower bound is based on the reverse cash-and-carry strategy. Action Now CF in \$ Action at period-end CF in \$ Buy one TOBEC index futures contract 0 Sell one TOBEC index futures contract \$100 × (F 1 F 0 ) Sell spot TOBEC index +\$18,500 Buy spot TOBEC index \$100 × S 1 Lend \$18,500 \$18,500 Collect loan repayment \$18,500 × 1.03 = +\$19,055 Pay transaction costs \$15.00 Total 0 Total \$100F 0 + \$19,040 (Note that F 1 = S 1 at expiration.) The lower bound for F 0 is: 19,040/100 = 190.40 23-9

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Chapter 23 - Futures, Swaps, and Risk Management 2. a.The strategy would be to sell Japanese stock index futures to hedge the market risk of Japanese stocks, and to sell yen futures to hedge the currency exposure. b. Some possible practical difficulties with this strategy include: Contract size on futures may not match size of portfolio. Stock portfolio may not closely track index portfolios on which futures trade. Cash flow management issues from marking to market. Potential mispricing of futures contracts (violations of parity). 3. a.The hedged investment involves converting the \$1 million to foreign currency, investing in that country, and selling forward the foreign currency in order to lock in the dollar value of the investment. Because the interest rates are for 90-day periods, we assume they are quoted as bond equivalent yields, annualized using simple interest. Therefore, to express rates on a per quarter basis, we divide these rates by 4: Japanese government Swiss government Convert \$1 million to local currency \$1,000,000 × 133.05 = ¥133,050,000 \$1,000,000 × 1.5260 = SF1,526,000 Invest in local currency for 90 days ¥133,050,000 × [1 + (0.076/4)] = ¥135,577,950 SF1,526,000 × [1 + (0.086/4)] = SF1,558,809 Convert to \$ at 90-day forward rate 135,577,950/133.47 = \$1,015,793 1,558,809/1.5348 = \$1,015,643 b. The results in the two currencies are nearly identical. This near-equality reflects the interest rate parity theorem. This theory asserts that the pricing relationships between interest rates and spot and forward exchange rates must make covered (that is, fully hedged and riskless) investments in any currency equally attractive.
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