JoeyDVivre

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) $48.51.

C) $49.49.

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The present value of expected dividends is: $0.50 / (1.0530 / 365) + $0.60 / (1.0575 / 365) = $1.092
Future price = ($50.00 − 1.092) × 1.0590 / 365 = $49.49

JoeyDVivre

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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The futures price FP = S0 e-δT (eRT)
= S0 e(R-δ)T
= 965e(.05-.023)
= 991.4

JoeyDVivre

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.

JoeyDVivre

The value of the S&P 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) $562.91.

B) $1,310.13.

C) $1,270.54.

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FP = 1,260 × e(0.054 − 0.035) × (160 / 365) = 1,270.54

JoeyDVivre

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) $110.06.

B) $110.00.

C) $110.20.

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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 – 2/1.0885/365 – 2.20/1.08176/365) 1.08182/365 = $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.

JoeyDVivre

Consider a 9-month forward contract on a 10-year 7% Treasury note just issued at par. The effective annual risk-free rate is 5% over the near term and the first coupon is to be paid in 182 days. The price of the forward is closest to:

A) 1,037.27.

B) 1,001.84.

C) 965.84.

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The forward price is calculated as the bond price minus the present value of the coupon, times one plus the risk-free rate for the term of the forward.
   

    (1,000 – 35/1.05182/365) 1.059/12 = $1,001.84

JoeyDVivre

The U.S. risk-free rate is 2.96%, the Japanese yen risk-free rate is 1.00%, and the spot exchange rate between the United States and Japan is $0.00757 per yen. Both rates are continuously compounded. The price of a 180-day forward contract on the yen and the value of the forward position 90 days into the contract when the spot rate is $0.00797 are closest to:

Forward Price

Value After 90 Days

A) $0.00764 $0.00212

B) $0.00750 $0.00212

C) $0.00764 $0.00037

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The no-arbitrage price of the 180-day forward contract is:
FT = $0.00757 × e(0.0296 − 0.0100) × (180 / 365) = $0.00764
The value of the contract in 90 days with 180 – 90 = 90 days remaining is: