# 007 - 7 Stock Index Futures Introduction Answers to...

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44 Answers to Questions and Problems 1. Assume that the DJIA stands at 8340.00 and the current divisor is 0.25. One of the stocks in the index is priced at \$100.00 and it splits 2:1. Based on this information, answer the following questions: a. What is the sum of the prices of all the shares in the index before the stock split? The equation for computing the index is: If the index value is 8340.00 and the divisor is 0.25, the sum of the prices must be 8,340.00(0.25) 5 \$2,085.00. b. What is the value of the index after the split? Explain. After the split, the index value is still 8,340.00. The whole purpose of the divisor technique is to keep the index value unchanged for events such as stock splits. c. What is the sum of the prices of all the shares in the index after the split? The stock that was \$100 is now \$50, so the sum of the share prices is now \$2,035.00. d. What is the divisor after the split? With the new sum of share prices at \$2,035.00, the divisor must be 0.244005 to maintain the index value at 8340.00. 2. What is the main difference in the calculation of the DJIA and the S&P 500 index? Explain. The S&P 500 index gives a weight to each represented share that is proportional to the market value of the outstanding shares. The DJIA simply adds the prices of all of the individual shares, so the DJIA effectively weights each stock by its price level. 3. For the S&P 500 index, assume that the company with the highest market value has a 1 percent increase in stock prices. Also, assume that the company with the smallest market value has a 1 percent decrease in the price of its shares. Does the index change? If so, in what direction? Index 5 o N i 5 1 P i Divisor 7 Stock Index Futures: Introduction

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ANSWERS TO QUESTIONS AND PROBLEMS 45 The index value increases. The share with the higher market value has a greater weight in the index than the share with the smallest market value. Therefore, the 1 percent increase on the high market value share more than offsets the 1 percent decrease on the low market value share. 4. The S&P 500 futures is scheduled to expire in half a year, and the interest rate for carrying stocks over that period is 11 percent. The expected dividend rate on the underlying stocks for the same period is 2 percent of the value of the stocks. (The 2 percent is the half-year rate, not an annual rate.) Ignoring the interest that it might be possible to earn on the dividend payments, find the fair value for the futures if the current value of the index is 945.00. Assuming the half-year rate is 0.11/2, the fair value is: Assuming semiannual compounding, the interest factor would be 1.0536 and the fair value would be: 5. Consider a very simple index like the DJIA, except assume that it has only two shares, A and B. The price of A is \$100.00, and B trades for \$75.00. The current index value is 175.00. The futures contract based on this index expires in three months, and the cost of carrying the stocks forward is 0.75 percent per month. This is also the interest rate that you can earn on invested funds. You expect Stock A to pay a \$3 dividend in one month and Stock B to pay a \$1 dividend in two months. Find the fair value of the futures. Assume monthly
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007 - 7 Stock Index Futures Introduction Answers to...

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