Learning objectives: Calculate, using the cost-of-carry model, forward prices where the underlying asset either does or does not have interim cash flows. Describe the various delivery options available in the futures markets and how they can influence futures prices. Explain the relationship between current futures prices and expected future spot prices, including the impact of systematic and nonsystematic risk. Define and interpret contango and backwardation, and explain how they relate to the cost-of-carry model.
Questions:
718.1. Assume that the risk-free rate is 3.0% per annum with continuous compounding and that the dividend yield on a stock index varies throughout the year. In January, April, July, and October, dividends are paid at a rate of 7.0% per annum. In other months, dividends are paid at a rate of 4.0% per annum. Suppose that the value of the index on June 30th is 2,500. Which is nearest to the theoretical futures price for a contract deliverable on December 31st? (this question is inspired by Hull's EOC Problem 5.11)
a. $2,450.50
b. $2,475.12
c. $2,602.03
d. $2,708.22
718.2. The six-month interest rates in Mexico and the United States are 7.0% and 1.0% per annum, respectively, with continuous compounding. The spot price of the Mexican peso is MXN/USD $0.05650, that is, about 17.70 pesos per one US dolllar. If the futures price for a contract deliverable in six months is $0.0610 (i.e., about 16.39 pesos per one US dollar), then which of the following best exploits the arbitrage opportunity (this question is inspired by Hull's EOC Problem 5.14)?
a. There is no arbitrage because the futures contract is fairly priced
b. Borrow dollars and invest USD for six months at 1.0%; and enter into (long) futures contract to buy pesos
c. Borrow dollars, convert immediately to pesos and invest in MXN for six months at 7.0%; and enter into (short) futures contract to sell pesos
d. Borrow pesos, convert immediately to dollars and invest in USD for six months at 1.0%; and enter into (long) futures contract to buy pesos
718.3. The current price of a technology index is 3,000 and its yield, q, is 2.0% per annum with continuous compounding; i.e., about 2.010% per annum with semi-annual compounding. The riskfree rate is 3.0% per annum with continuous compounding. The discount rate for the index can be determined by the capital asset pricing model (CAPM) where its beta is 1.80 and the market's expected return is 9.0%; i.e., the market's expected excess return is 6.0%. Which is nearest to the index's expected future spot price in 10 months, E[S(+0.833)]?
a. $3,025.10
b. $3,127.64
c. $3,309.99
d. $4,005.05
Answers here:
Questions:
718.1. Assume that the risk-free rate is 3.0% per annum with continuous compounding and that the dividend yield on a stock index varies throughout the year. In January, April, July, and October, dividends are paid at a rate of 7.0% per annum. In other months, dividends are paid at a rate of 4.0% per annum. Suppose that the value of the index on June 30th is 2,500. Which is nearest to the theoretical futures price for a contract deliverable on December 31st? (this question is inspired by Hull's EOC Problem 5.11)
a. $2,450.50
b. $2,475.12
c. $2,602.03
d. $2,708.22
718.2. The six-month interest rates in Mexico and the United States are 7.0% and 1.0% per annum, respectively, with continuous compounding. The spot price of the Mexican peso is MXN/USD $0.05650, that is, about 17.70 pesos per one US dolllar. If the futures price for a contract deliverable in six months is $0.0610 (i.e., about 16.39 pesos per one US dollar), then which of the following best exploits the arbitrage opportunity (this question is inspired by Hull's EOC Problem 5.14)?
a. There is no arbitrage because the futures contract is fairly priced
b. Borrow dollars and invest USD for six months at 1.0%; and enter into (long) futures contract to buy pesos
c. Borrow dollars, convert immediately to pesos and invest in MXN for six months at 7.0%; and enter into (short) futures contract to sell pesos
d. Borrow pesos, convert immediately to dollars and invest in USD for six months at 1.0%; and enter into (long) futures contract to buy pesos
718.3. The current price of a technology index is 3,000 and its yield, q, is 2.0% per annum with continuous compounding; i.e., about 2.010% per annum with semi-annual compounding. The riskfree rate is 3.0% per annum with continuous compounding. The discount rate for the index can be determined by the capital asset pricing model (CAPM) where its beta is 1.80 and the market's expected return is 9.0%; i.e., the market's expected excess return is 6.0%. Which is nearest to the index's expected future spot price in 10 months, E[S(+0.833)]?
a. $3,025.10
b. $3,127.64
c. $3,309.99
d. $4,005.05
Answers here:
