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					                              Chapter Nine
                           Stock Index Futures

                  Answers to Problems and Questions

1.   Theoretically, the more securities in a portfolio, the less the unsystematic
     risk. Most users of stock index futures as a hedge do so in order to
     reduce systematic risk.        Because of the Nasdaq’s substantial
     technology/ exposure, an insurance company portfolio is
     likely to have more in common with the S&P 500 than with the Nasdaq
     100. The S&P 500 is probably a better hedging device.

2.   The deterioration of the basis does work to the advantage of the short
     seller. If you are long a contract, the deterioration of basis will be to your
     detriment. It seems, then, that the statement has some merit. It is
     important to note, though, that the deterioration of the basis is not “free
     money” to the short seller and that market movements after the first
     delivery month can result in substantial losses on the other leg of the
     spread. It is also dangerous to say that any investment strategy is
     “usually a winner.” Price movements in the underlying index or sharp
     changes in interest rates could overwhelm any gain from the basis.

3.   Theoretically, this strategy makes perfect sense. Index futures and T-
     bills could be combined to produce a synthetic stock portfolio, and
     probably at much less commission cost. The synthetic portfolio might
     also provide a more attractive income stream for some portfolio

     The disadvantage lies primarily with the fact that futures contracts are
     not well understood by many governing bodies that have fiduciary
     responsibility for investment portfolios.

4.   This is not a very accurate statement. It is true that the deterioration of
     basis would work against you, but this ignores the fact that over the long
     run the stock market has risen substantially. Holders of index futures
     contracts would benefit from long term rises in the value of the
     underlying index.

5.   The passage of time means that the price of a stock index futures contract
     will decline, everything else being equal. The short seller wants the price
     to decline.

Chapter Nine. Stock Index Futures

      6.    If the dividend yield on the stock index were to exceed the T-bill rate, the
            market would be inverted. This is an unlikely event.

      7.    While index futures could be used as a hedge, with only five securities
            there would be considerable unsystematic risk in the portfolio making it
            difficult to hedge without using individual equity options.

      8.    Beta measures the sensitivity of a portfolio to market movements.
            Portfolios that are quite sensitive need a larger hedge than portfolios with
            lower betas.

      9.    No. Hedging involves reducing risk. It does not necessarily involve
            removing it all. In fact, if you remove all market risk, the portfolio’s
            expected return converges on that of the riskfree rate. For this reason
            continuous hedging is normally not a good idea.

      10.   The key question is what happens to the dividend yield. If the dividend
            yield does not change because the stock prices rise proportionately, then
            there would be no effect on the S&P500 futures. If the dividend yield did
            increase, the fair annual premium on the futures would decline, and so
            would the value of the futures contract.

      11.   F = S e(R – D)t

                 = 340 e (.0588 - .0255)(63/365) = 340 e .0057 = 341.96

      12.   F = S e(R – D)t

                 = 340 e (.0563 - .0255)(120/365) = 340 e .0101 = 343.46

      13.   Using the September 2001 contracts,

                  $200 million
                               x 0.8  402.7
                 1589.20 x 250

                 To hedge 80%,  sell 80% x 402.7= 322 contracts

                  $200 million
14.                            x 0.8  421.8
                 1517.20 x 250

                 To hedge 100%,  sell 422 contracts

                                                       Chapter Nine. Stock Index Futures

                  $750 million
15.                            x 1.1  2207.7
                 1494.80 x 250

                To hedge 40%,  sell 40% x 2207.7= 883 contracts

16. F = S e(R – D)T

         1499.00 = 1475.50 e(R - .022)85/365

         1.0159 = ex

         ln 1.0159 = 0.0158013  x = 0.0158013

         (R - .022)(85/365) = 0.0158013

         R = 8.99%

17. Solve for the equilibrium futures price:

         F = Se(R – D)T

          = 329.83e(.0602 - .0265)(121/365) = 333.54

      The actual futures price is above this, so the appropriate action would be to sell
      the futures and buy the underlying basket of stock, anticipating that the basis
      would return to its theoretical value.


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