McDonald ISM3e Chapter 5
Chapter 5
Financial Forwards and Futures
Question 5.1
Four different ways to sell a share of stock that has a price S(0) at time 0.
Description
Get paid at time
Lose ownership of security at time
Receive payment of
Outright sale
0
0
S0 at time 0
Security sale and loan sale
T
0
S0erT at time T
Short prepaid forward contract
0
T
?
Short forward contract
T
T
? × erT
Question 5.2
a) The owner of the stock is entitled to receive dividends. As we will get the stock only in one year, the value of the prepaid forward contract is today’s stock price, less the present value of the four dividend payments: = $50 − = $50 − $0.985 − $0.970 − $0.956 − $0.942
= $50 − $3.853 = $46.147
b) The forward price is equivalent to the future value of the prepaid forward. With an interest rate of 6 percent and an expiration of the forward in one year, we thus have:
F0,T = × e0.06×1 = $46.147 × e0.06×1 = $46.147 × 1.0618 = $49.00
Question 5.3
a) The owner of the stock is entitled to receive dividends. We have to offset the effect of the continuous income stream in form of the dividend yield by tailing the position: = $50e−0.08×1 = $50 × 0.9231 = $46.1558 We see that the value is very similar to the value of the prepaid forward contract with discrete dividends we have calculated in question 5.2. In question 5.2, we received four cash dividends, with payments spread out through the entire year, totaling $4. This yields a total annual dividend yield of approximately $4 ÷ $50 = 0.08.
b) The forward price is equivalent to the future value of the prepaid forward. With an interest rate of 6 percent and an expiration of the forward in one year we thus have:
F0,T = × e0.06×1 = $46.1558 × e0.06×1 = $46.1558 × 1.0618 = $49.01
Question 5.4
This question asks us to familiarize ourselves with the forward valuation equation.
a) We plug the continuously compounded interest rate and the time to expiration in years into the valuation formula and notice that the time to expiration is six months, or 0.5
Financial Forwards and Futures
Question 5.1
Four different ways to sell a share of stock that has a price S(0) at time 0.
Description
Get paid at time
Lose ownership of security at time
Receive payment of
Outright sale
0
0
S0 at time 0
Security sale and loan sale
T
0
S0erT at time T
Short prepaid forward contract
0
T
?
Short forward contract
T
T
? × erT
Question 5.2
a) The owner of the stock is entitled to receive dividends. As we will get the stock only in one year, the value of the prepaid forward contract is today’s stock price, less the present value of the four dividend payments: = $50 − = $50 − $0.985 − $0.970 − $0.956 − $0.942
= $50 − $3.853 = $46.147
b) The forward price is equivalent to the future value of the prepaid forward. With an interest rate of 6 percent and an expiration of the forward in one year, we thus have:
F0,T = × e0.06×1 = $46.147 × e0.06×1 = $46.147 × 1.0618 = $49.00
Question 5.3
a) The owner of the stock is entitled to receive dividends. We have to offset the effect of the continuous income stream in form of the dividend yield by tailing the position: = $50e−0.08×1 = $50 × 0.9231 = $46.1558 We see that the value is very similar to the value of the prepaid forward contract with discrete dividends we have calculated in question 5.2. In question 5.2, we received four cash dividends, with payments spread out through the entire year, totaling $4. This yields a total annual dividend yield of approximately $4 ÷ $50 = 0.08.
b) The forward price is equivalent to the future value of the prepaid forward. With an interest rate of 6 percent and an expiration of the forward in one year we thus have:
F0,T = × e0.06×1 = $46.1558 × e0.06×1 = $46.1558 × 1.0618 = $49.01
Question 5.4
This question asks us to familiarize ourselves with the forward valuation equation.
a) We plug the continuously compounded interest rate and the time to expiration in years into the valuation formula and notice that the time to expiration is six months, or 0.5