Suppose a U.S. investor wishes to invest in a British firm currently selling for

Question

Suppose a U.S. investor wishes to invest in a British firm currently selling for £34 per share. The investor has $6,800 to invest, and the current exchange rate is $2/E. Consider three possible prices per share at £30, £35, and £40 after 1 year Also, consider three possible exchange rates at $1.7/S, $2/E, and $2.3/E after 1 year. Calculate the standard deviation of both the pound- and dollar-denominated rates of return if each of the nine outcomes (three possible prices per share in pounds times three possible exchange rates) is equally likely. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Standard deviation of pound-denominated return Standard deviation of dollar-denominated return

Explanation / Answer

Current dollars=6800

Current pounds=6800/2=3400

Number of shares bought=3400/34=100

As each price and exhcnge rate is equally likely and pound denomniated returns would not depend on exchange rates, so for each price pound denominated returns would have equal probability of 1/3

Price Probability Pound denominated return

30 1/3 (30*100-3400)/3400=-11.765%

35 1/3 (35*100-3400)/3400=2.9412%

40 1/3 (40*100-3400)/3400=17.6471%

Mean=-11.765%/3+2.9412%/3+17.6471%/3=2.9411%

Standard deviation =sqrt(1/3*(-11.765-2.9411)^2+1/3*(2.9412-2.9411)^2+1/3*(17.6471-2.9411)^2)=12.0744%

Dollar denominated returns

Exchange rate Price Probability Dollar denominated returns

1.7 30 1/9 =(100*30*1.7-6800)/6800=-25%   

2 30 1/9 =(100*30*2-6800)/6800=-11.765%    

2.3 30 1/9 =(100*30*2.3-6800)/6800=1.4706%   

1.7 35 1/9 =(100*35*1.7-6800)/6800=-12.5%   

2 35 1/9 =(100*35*2-6800)/6800=2.9412%   

2.3 35 1/9 =(100*35*2.3-6800)/6800=18.3824%   

1.7 40 1/9   =(100*40*1.7-6800)/6800=0   

2 40 1/9 =(100*40*2-6800)/6800=17.6471%   

2.3 40 1/9 =(100*40*2.3-6800)/6800=35.2941%

Mean=1/9*-25%+1/9*-11.765%+1/9*1.4706%+1/9*-12.5%+1/9*2.9412%+1/9*18.3824%+1/9*0+1/9*17.6471%+1/9*35.2941%=2.9412%

Standard deviation=sqrt(1/9*(-25%-2.9412%)^2+1/9*(-11.765%-2.9412%)^2+1/9*(1.4706%-2.9412%)^2+1/9*(-12.5%-2.9412%)^2+1/9*(2.9412%-2.9412%)^2+1/9*(18.3824%-2.9412%)^2+1/9*(0-2.9412%)^2+1/9*(17.6471%-2.9412%)^2+1/9*(35.2941%-2.9412%)^2)=17.4726%

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