Question

Calculate the nominal U.S. dollar rates of return to a Los Angeles-based investor on the following asset purchases. Assume that all of the LA investor’s consumption takes place in the United States.

a.  A US$100,000 deposit in Banco Santander during a one-year period in which the €/US$ exchange rate moved from 1.100 to 1.111 and the interest rate on euro deposits was 2.5 percent

b.  A Seattle office building that was purchased for US$100 million and sold for US$102 million during a year in which the U.S. dollar appreciated by 3 percent against the Hong Kong dollar.

c.  A South Sea pearl necklace purchased in Hong Kong for HK$7,500 when the US$/HK$ exchange rate was 1.0 and sold for HK$7,450 a year later when one Hong Kong dollar sold for 1.02 U.S. dollars.

d. Suppose that the U.S. Consumer Price Index (CPI) increased by 2 percent, the Spanish CPI increased by 1 percent, and the Hong Kong CPI increased by 3 percent over the year in which each asset was owned. What was the real rate of return to the SB investor on the asset from part (a)?

Answer 1

a. (1+id) =S/F*(1+if) where id =?, S =1.10, E =1.111 and if = 0.025

(1+id) = 1.10/1.111*(1+0.025)

1+id =1.01485

id = 0.01485 = 1.485%

Nominal US dollar return = 1.485%

b. Here the transaction is in US and there is no affect of dollar movement against the HK dollar. So, nominal united states dollar rate of return = (102-100)/100 = 0.02 = 2%

c. Rate of return in HK$ = (7450-7500)/7500 = -0.00666 = -0.66%

(1+id) = 1.0/1.02*(1-0.00666)

id = -0.026 = -2.61%

Nominal US dollar return = -2.6%

d. Average increase in CPI = (1+2 +3)/3 = 2%

The nominal US rate of return = 1.485%

Real return = 1.485 -2 = -0.515%