Question

Now suppose the investor in Problem 5 also sells forward £5,000 at a forward exchange rate of $2.10/£.

a. Recalculate the dollar-denominated returns for each scenario.

b. What happens to the standard deviation of the dollar-denominated return? Compare it to both its old value and the standard deviation of the pound-denominated return.

Short answer

a. As below

b. 10.24%

Step-by-step solution

Calculation of dollar value of 125 shares of stock

Price per share (￡)	Exchange rate	Dollar-value of stock at given Exchange Rate
		1.80/￡	2.00/￡	2.20/￡
￡35		7,875	8,750	9,625
￡40		9000	10,000	11,000
￡45		10,125	11,250	12,375
Profits on forward exchange = ￡5,000 x (2.10 – E1)		1,500	500	-500

Now let’s add profits from the forward contract:

Price per share (￡)	Exchange rate	Dollar-value of stock at given Exchange Rate
		1.80/￡	2.00/￡	2.20/￡
￡35		9,375	9,250	9,125
￡40		10500	10,500	10,500
￡45		11,625	11,750	11,875

Now let’s calculate the dollar dominated rate of return with initial investment of $10,000

Price per share (￡)	Exchange rate	Rate of return % at given Exchange Rate
		1.80/￡	2.00/￡	2.20/￡
￡35		-6.25%	-7.5%	-8.75%
￡40		5%	5%	5%
￡45		16.25%	17.50%	18.75%

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

Formula σ = √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. This is also slightly higher than the standard deviation of pound denominated return.