Chapter 22

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1. Award: 10.00 points Problems? Adjust credit for all students. Are the following statements true or false? Required: a. All else equal, the futures price on a stock index with a high dividend yield should be higher than the futures price on an index with a low dividend yield. False b. All else equal, the futures price on a high-beta stock should be higher than the futures price on a low-beta stock. False c. The beta of a short position in the S&P 500 futures contract is negative. True Explanation: a. False. For any given level of the stock index, the futures price will be lower when the dividend yield is higher. This follows from spot-futures parity: F 0 = S 0 (1 + r f d ) T b. False. The parity relationship tells us that the futures price is determined by the stock price, the interest rate, and the dividend yield; it is not a function of beta. c. True. The short futures position will profit when the S&P 500 Index falls. This is a negative beta position. Worksheet Difficulty: 1 Basic Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 22: Futures Markets > Chapter 22 Problems - Algorithmic & Static References
2. Award: 10.00 points Problems? Adjust credit for all students. Refer to the Mini-S&P contract in Figure 22.1 . Assume the closing price for this day. Required: a. If the margin requirement is 10% of the futures price times the contract multiplier of $50, how much must you deposit with your broker to trade the December maturity contract? b. If the December futures price increases to $4,400, what percentage return will you earn on your investment if you entered the long side of the contract at the price shown in the figure? c. If the December futures price falls by 1%, what is your percentage return? Required A Required B Complete this question by entering your answers in the tabs below. If the margin requirement is 10% of the futures price times the contract multiplier of $50, how much must you deposit with your broker to trade the December maturity contract? Note: Do not round intermediate calculations. Round your answer to 2 decimal places. Required A Required B Required C $ Required margin deposit 21,718.75 Explanation: a. The closing futures price for the December contract was $4,343.75, which has a dollar value of: $50 × $4,343.75 = $217,187.50 Therefore, the required margin deposit is: $217,187.50 × 0.10 = $21,718.75 b. The futures price increases by: $4,400.00 − $4,343.75 = 56.25 The credit to your margin account would be: $56.25 × $50 = $2,812.50 This is a percent gain of: $2,812.50 ÷ $21,718.75 = 0.1295 = 12.95% Note that the futures price itself increased by only $56.25 ÷ $4,343.75 = 1.29%. c. Following the reasoning in part (b), any change in F is magnified by a ratio of (l ÷ margin requirement). This is the leverage effect. The return will be −10%. Worksheet Difficulty: 2 Intermediate Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 22: Futures Markets > Chapter 22 Problems - Algorithmic & Static References
2. Award: 10.00 points Problems? Adjust credit for all students. Refer to the Mini-S&P contract in Figure 22.1 . Assume the closing price for this day. Required: a. If the margin requirement is 10% of the futures price times the contract multiplier of $50, how much must you deposit with your broker to trade the December maturity contract? b. If the December futures price increases to $4,400, what percentage return will you earn on your investment if you entered the long side of the contract at the price shown in the figure? c. If the December futures price falls by 1%, what is your percentage return? Required A Required C Complete this question by entering your answers in the tabs below. If the December futures price increases to 4,400, what percentage return will you earn on your investment if you entered the long side of the contract at the price shown in the figure? Note: Do not round intermediate calculations. Round your answer to 2 decimal places. Required A Required B Required C Percentage return on net investment 12.95 % Explanation: a. The closing futures price for the December contract was $4,343.75, which has a dollar value of: $50 × $4,343.75 = $217,187.50 Therefore, the required margin deposit is: $217,187.50 × 0.10 = $21,718.75 b. The futures price increases by: $4,400.00 − $4,343.75 = 56.25 The credit to your margin account would be: $56.25 × $50 = $2,812.50 This is a percent gain of: $2,812.50 ÷ $21,718.75 = 0.1295 = 12.95% Note that the futures price itself increased by only $56.25 ÷ $4,343.75 = 1.29%. c. Following the reasoning in part (b), any change in F is magnified by a ratio of (l ÷ margin requirement). This is the leverage effect. The return will be −10%. Worksheet Difficulty: 2 Intermediate Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 22: Futures Markets > Chapter 22 Problems - Algorithmic & Static References
2. Award: 10.00 points Problems? Adjust credit for all students. Refer to the Mini-S&P contract in Figure 22.1 . Assume the closing price for this day. Required: a. If the margin requirement is 10% of the futures price times the contract multiplier of $50, how much must you deposit with your broker to trade the December maturity contract? b. If the December futures price increases to $4,400, what percentage return will you earn on your investment if you entered the long side of the contract at the price shown in the figure? c. If the December futures price falls by 1%, what is your percentage return? Required B Required C Complete this question by entering your answers in the tabs below. If the December futures price falls by 1%, what is your percentage return? Note: Negative value should be indicated by a minus sign. Required A Required B Required C Percentage return on net investment (10) % Explanation: a. The closing futures price for the December contract was $4,343.75, which has a dollar value of: $50 × $4,343.75 = $217,187.50 Therefore, the required margin deposit is: $217,187.50 × 0.10 = $21,718.75 b. The futures price increases by: $4,400.00 − $4,343.75 = 56.25 The credit to your margin account would be: $56.25 × $50 = $2,812.50 This is a percent gain of: $2,812.50 ÷ $21,718.75 = 0.1295 = 12.95% Note that the futures price itself increased by only $56.25 ÷ $4,343.75 = 1.29%. c. Following the reasoning in part (b), any change in F is magnified by a ratio of (l ÷ margin requirement). This is the leverage effect. The return will be −10%. Worksheet Difficulty: 2 Intermediate Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 22: Futures Markets > Chapter 22 Problems - Algorithmic & Static References
3. Award: 10.00 points Problems? Adjust credit for all students. Required: a. A futures contract on a non-dividend-paying stock index with current value $150 has a maturity of one year. If the T-bill rate is 3%, what should the futures price be? b. What should the futures price be if the maturity of the contract is three years? c. What if the interest rate is 6% and the maturity of the contract is three years? Required A Required B Complete this question by entering your answers in the tabs below. A futures contract on a non-dividend-paying stock index with current value $150 has a maturity of one year. If the T-bill rate is 3%, what should the futures price be? Note: Round your answer to 2 decimal places. Required A Required B Required C $ Futures price 154.50 Explanation: a. F 0 = S 0 × (1 + r f ) = $150 × 1.03 = $154.50 b. F 0 = S 0 × (1 + r f ) 3 = $150 × 1.03 3 = $163.91 c. F 0 = $150 × 1.06 3 = $178.65 Worksheet Difficulty: 2 Intermediate Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 22: Futures Markets > Chapter 22 Problems - Algorithmic & Static References
3. Award: 10.00 points Problems? Adjust credit for all students. Required: a. A futures contract on a non-dividend-paying stock index with current value $150 has a maturity of one year. If the T-bill rate is 3%, what should the futures price be? b. What should the futures price be if the maturity of the contract is three years? c. What if the interest rate is 6% and the maturity of the contract is three years? Required A Required C Complete this question by entering your answers in the tabs below. What should the futures price be if the maturity of the contract is three years? Note: Do not round intermediate calculations. Round your answer to 2 decimal places. Required A Required B Required C $ Futures price 163.91 Explanation: a. F 0 = S 0 × (1 + r f ) = $150 × 1.03 = $154.50 b. F 0 = S 0 × (1 + r f ) 3 = $150 × 1.03 3 = $163.91 c. F 0 = $150 × 1.06 3 = $178.65 Worksheet Difficulty: 2 Intermediate Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 22: Futures Markets > Chapter 22 Problems - Algorithmic & Static References
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