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25 the required rate of return on an asset with the

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25. The required rate of return on an asset with the same risk as corn is: 1% + 0.5(1.8% – 1%) = 1.4% per month Thus, in the absence of storage costs, three months from now corn would sell for: $2.75 × 1.014 3 = $2.867 The future value of 3 month’s storage costs is: $0.03 × FA(1%, 3) = $0.091 where FA stands for the future value factor for a level annuity with a given interest rate and number of payments. Thus, in order to induce storage, the expected price would have to be: $2.867 + $0.091 = $2.958 Because the expected spot price is only $2.94, you would not store corn. 23-9
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26. a. Delsing should sell stock index futures contracts and buy bond futures contracts. This strategy is justified because buying the bond futures and selling the stock index futures provides the same exposure as buying the bonds and selling the stocks. This strategy assumes high correlation between the bond futures and the bond portfolio, as well as high correlation between the stock index futures and the stock portfolio. b. The number of contracts in each case is: i. 5 × $200,000,000 × 0.0001 = $100,000 $100,000/97.85 = 1022 contracts ii. $200,000,000/($1,378 × 250) = 581 contracts 27. Situation A. The market value of the portfolio to be hedged is $20 million. The market value of the bonds controlled by one futures contract is $63,330. If we were to equate the market values of the portfolio and the futures contract, we would sell: $20,000,000/$63,330 = 315.806 contracts However, we must adjust this “naive” hedge for the price volatility of the bond portfolio relative to the futures contract. Price volatilities differ according to both the duration and the yield volatility of the bonds. In this case, the yield volatilities may be assumed equal, because any yield spread between the Treasury portfolio and the Treasury bond underlying the futures contract is likely to be stable. However, the duration of the Treasury portfolio is less than that of the futures contract. Adjusting the naive hedge for relative duration and relative yield volatility, we obtain the adjusted hedge position: 300 0 . 1 0 . 8 6 . 7 806 . 315 = × × contracts Situation B . Here, the treasurer seeks to hedge the purchase price of the bonds; this requires a long hedge. The market value of the bonds to be purchased is: $20 million × 0.93 = $18.6 million The duration ratio is 7.2/8.0, and the relative yield volatility is 1.25. Therefore, the hedge requires the treasurer to take a long position in: 330 25 . 1 0 . 8 2 . 7 330 , 63 000 , 600 , 18 = × × contracts 23-10
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28. a. % change in T-bond price = modified duration × change in YTM = 7.0 × 0.50% = 3.5% b. When the YTM of the T-bond changes by 50 basis points, the predicted change in the yield on the KC bond is 1.22 × 50 = 61 basis points. Therefore: % change in KC price = modified duration × change in YTM = 6.93 × 0.61% = 4.23% 29. If the exchange of currencies were structured as three separate forward contracts, the forward prices would be determined as follows:
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25 The required rate of return on an asset with the same...

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