You are given: (i) The current price of a stock is 1,000. (ii) The stock pays di
ID: 2818430 • Letter: Y
Question
You are given:
(i) The current price of a stock is 1,000.
(ii) The stock pays dividends continuously at a rate proportional to its price.
(iii) The continuously compounded risk-free interest rate is 5%.
(iv) a 6-month forward price of 1,020 is observed in the market.
Describe actious you could take to exploit an arbitrage opportunity and calculate the resulting profit (per stock unit) in each of the following cases:
(a) The dividend yield of the stock is 0.5%
(b) The dividend yield of the stock is 2%
Explanation / Answer
Current stock price =1000
Contineous risk free rate = 5%
Time (t)= 6 months (1/2) years
Forward Price = 1020
a) Dividend yield (D)= 0.5%
Ideally, Forward Price = Spot price * e^(Rf - D)*t
Forward Price = 1000 * e^(0.045)/2 = 1046.02
Since expected forward price is more than the observed forward price, this contract is under priced so we should buy it
Short sell share and get the money = 1000
Invest the money at risk free rate
Buy the forward contract = 1020
Money you will have after 6 months = 1046.02
buy the share at = 1020
Profit = 26.02
b) Dividend yield (D)= 2%
Ideally, Forward Price = Spot price * e^(Rf - D)*t
Forward Price = 1000 * e^(0.03)/2 = 1030.45
Since expected forward price is more than the observed forward price, this contract is under priced so we should buy it
Short sell share and get the money = 1000
Invest the money at risk free rate
Buy the forward contract = 1020
Money you will have after 6 months = 1030.45
buy the share at = 1020
Profit = 10.45
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