M05_MCDO8122_01_ISM_C05

M05_MCDO8122_01_ISM_C05 - Chapter 5 Financial Forwards and...

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Chapter 5 Financial Forwards and Futures n Question 5.1 Four different ways to sell a share of stock that has a price 0 S at time 0. Description Get Paid at Time Lose Ownership of Security at Time Receive Payment of Outright Sale 0 0 0 S at time 0 Security Sale and T 0 0 rT S e at time T Loan Sale Short Prepaid Forward 0 T ? Contract Short Forward T T ? rT e × Contract n Question 5.2 1. 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: 3 12 4 0.06 0, 1 $50 $1 $50 $0.985 $0.970 $0.956 $0.942 $50 $3.853 $46.147 i P T i F e - × = = - = - - - - = - = 2. The forward price is equivalent to the future value of the prepaid forward. With an interest rate of 6% and an expiration of the forward in one year, we have: 0.06 1 0.06 1 0, 0, $46.147 $46.147 1.0618 $49.00 P T T F F e e × × = × = × = × = Note that this is equivalent to taking the future value of the initial stock price and subtracting the future value (at 6%) of the dividends received, as in Equation (5.6) of the text.
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60 McDonald • Fundamentals of Derivatives Markets n Question 5.3 1. 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: 0.08 1 0, $50 $50 0.9231 $46.1558 P T F e - × = = × = We see that the value is very similar to the value of the prepaid forward contract with discrete dividends that 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 implies a total annual dividend yield of approximately$4 $50 0.08. ÷ = 2. The forward price is equivalent to the future value of the prepaid forward. With an interest rate of 6% and an expiration of the forward in one year we thus have: 0.06 1 0.06 1 0, 0, $46.1558 $46.1558 1.0618 $49.01 P T T F F e e × × = × = × = × = We could also use Equation (5.7) of the text, i.e., (.06 .08) 0, $50 $49.01. T F e - = = n Question 5.4 1. We use the continuously compounded interest rate and the time to expiration in years (6 months is 0.5 year) in Equation (5.7). We have: 0.05 0.5 0, 0 $35 $35 1.0253 $35.886. r T T F S e e × × = × = × = × = 2. The annualized forward premium is calculated as: 0, 0 1 1 $35.50 annualized forward premium ln ln 0.0284 0.5 $35 T F T S = = = Notice this is less than the interest rate, hence the index must pay a dividend. 3. We could use ( ) 0, 0 r T T F S e δ - = and solve for δ . However, it is easier to use the previous result concerning the annualized forward premium. The forward premium is simply the difference between the risk-free rate and the dividend yield: ( ) 0, 0 0 0 ( ) 1 1 annualized forward premium ln ln 1 1 ln ( ) ( ) r T T r T F S e T T S S e r T T T r δ δ δ δ - - × = = = = - = - Therefore, we can solve: 0 0284 0 05 0 0216 δ δ . = . - = .
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