m48-ch05 shrunk v02

m48-ch05 shrunk v02 - Chapter 5 Financial Forwards and...

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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 Lose Ownership of Receive Payment Time Security at Time of Outright Sale 0 0 S 0 at time o Security Sale and T 0 S 0 e rT at time T Loan Sale Short Prepaid Forward 0 T ? Contract Short Forward T T ? × e rT Contract 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: F P 0 ,T = $50 4 i = 1 $1 e 0 . 06 × 3 12 i = $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: F 0 ,T = F P 0 ,T × e 0 . 06 × 1 = $46 . 147 × e 0 . 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: F P 0 ,T = $50 e 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, 66
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Chapter 5 Financial Forwards and Futures 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: F 0 ,T = F P 0 ,T × e 0 . 06 × 1 = $46 . 1558 × e 0 . 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 6 months, or 0.5 years. We have: F 0 ,T = S 0 × e r × T = $35 × e 0 . 05 × 0 . 5 = $35 × 1 . 0253 = $35 . 886 b) The annualized forward premium is calculated as: annualized forward premium = 1 T ln µ F 0 ,T S 0 = 1 0 . 5 ln µ $35 . 50 $35 = 0 . 0284 c) For the case of continuous dividends, the forward premium is simply the difference between the risk-free rate and the dividend yield: annualized forward premium = 1 T ln µ F 0 ,T S 0 = 1 T ln à S 0 × e (r δ)T S 0 ! = 1 T ln ³ e (r δ)T ´ = 1 T (r δ) T = r δ Therefore, we can solve: 0 . 0284 = 0 . 05 δ δ = 0 . 0216 The annualized dividend yield is 2.16 percent. Question 5.5.
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m48-ch05 shrunk v02 - Chapter 5 Financial Forwards and...

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