Reading 60: Forward Markets and Contracts-LOS b 习题精选 interpret, class, contract, forward, div

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Session 16: Derivative Investments: Forwards and Futures
Reading 60: Forward Markets and Contracts

LOS b: Calculate and interpret the price and the value of an equity forward contract, assuming dividends are paid either discretely or continuously.

 

 

Calculate the no-arbitrage forward price for a 90-day forward on a stock that is currently priced at $50.00 and is expected to pay a dividend of $0.50 in 30 days and a $0.60 in 75 days.  The annual risk free rate is 5% and the yield curve is flat.

A) $50.31.

B) $49.49.

C) $48.51.

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The present value of expected dividends is: $0.50 / (1.05^{30 / 365}) + $0.60 / (1.05^{75 / 365}) = $1.092

Future price = ($50.00 ? 1.092) × 1.05^{90 / 365} = $49.49

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An index is currently 965 and the continuously compounded dividend yield on the index is 2.3%. What is the no-arbitrage price on a one-year index forward contract if the continuously compounded risk-free rate is 5%.

A) 991.1.

B) 991.4.

C) 987.2.

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FP = S₀ e^-δT (e^RT) = S₀ e^(R-δ)T = 965e^(.05-.023) = 991.4

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Jim Trent, CFA has been asked to price a three month forward contract on 10,000 shares of Global Industries stock. The stock is currently trading at $58 and will pay a dividend of $2 today. If the effective annual risk-free rate is 6%, what price should the forward contract have? Assume the stock price will change value after the dividend is paid.

A) $56.85.

B) $58.85.

C) $56.82.

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One method is to subtract the future value of the dividend from the future value of the asset calculated at the risk free rate (i.e. the no-arbitrage forward price with no dividend).

FP = 58(1.06)^1/4 – 2(1.06)^1/4 = $56.82

This is equivalent to subtracting the present value of the dividend from the current price of the asset and then calculating the no-arbitrage forward price based on that value.

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The value of the S& 500 Index is 1,260.  The continuously compounded risk-free rate is 5.4% and the continuous dividend yield is 3.5%.  Calculate the no-arbitrage price of a 160-day forward contract on the index.

A) $1,270.54.

B) $562.91.

C) $1,310.13.

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FP = 1,260 × e^{(0.054 ? 0.035) × (160 / 365)} = 1,270.54

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A stock is currently priced at $110 and will pay a $2 dividend in 85 days and is expected to pay a $2.20 dividend in 176 days. The no arbitrage price of a six-month (182-day) forward contract when the effective annual interest rate is 8% is closest to:

A) $110.00.

B) $110.20.

C) $110.06.

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In the formulation below, the present value of the dividends is subtracted from the spot price, and then the future value of this amount at the expiration date is calculated.

(110 – 2/1.08^85/365 – 2.20/1.08^176/365) 1.08^182/365 = $110.06

Alternatively, the future value of the dividends could be subtracted from the future value of the stock price based on the risk-free rate over the contract term.