Question

If each of the nine outcomes in Problem 5 is equally likely, find the standard deviation of both the pound- and dollar-denominated rates of return.

Question: Suppose a U.S. investor wishes to invest in a British firm currently selling for £40 per share.

The investor has \(10,000 to invest, and the current exchange rate is \)2/£

a. How many shares can the investor purchase?

b. Fill in the table below for rates of return after one year in each of the nine scenarios (three possible prices per share in pounds times three possible exchange rates).

Price per share (￡)	Price denominated return (%)	Dollar-Denominated Return (%) for Year-End Exchange Rate
		1.80/￡	2.00/￡	2.20/￡
￡35
￡40
￡45

c. When is the dollar-denominated return equal to the pound-denominated return?

Short answer

10.24%

Step-by-step solution

Given information

Price per share (￡)	Price denominated return (%)	Dollar-Denominated Return (%) for Year-End Exchange Rate
		1.80/￡	2.00/￡	2.20/￡
￡35	-12.5%	-21.25%	-12.5%	-3.75%
￡40	0.0%	-10.00%	0.0%	10.00%
￡45	12.5%	1.25%	12.5%	23.75%

Calculation of the standard deviation of dollar dominated return and pound dominated return

Formulaσ=√Σ(x_i –μ)² / N

Hence the standard deviation is now 10.24%.

This is lower than the un-hedged dollar-denominated standard deviation.