One year ago, an American investor bought 1000 shares of London Bridges at a pri
ID: 2670848 • Letter: O
Question
One year ago, an American investor bought 1000 shares of London Bridges at a price of £8 (or 8 UK pounds) per share when the exchange rate was $1.40/1£ (or $1.40 dollars = 1 pound). The investor also invested 6,000,000 Japanese Yen in a money market fund in Japan last year when the exchange rate was 75 Yen = $ 1 US.(a) Using current exchange rates (Today’s exchange rate: ¥77.7330 = $1, $1.5620 = £1) what is today’s value of the investor’s portfolio in U.S. dollars if the UK investment increased 6% (in local currency) and the Japan investment increased 2% (in local currency)?
(b) What is the overall rate of return on the portfolio over the last year?
Explanation / Answer
(a) If the UK investment increased by 6% in GBP terms then, the price of one share of London Bridges would be: GBP8 x (1.06) = GBP8.48
Multiply this by 1,000 shares, you get GBP 8,480.
We then convert this to USD by multiplying by 1.5620, we get: $13,245.76.
If the Japan investment increased by 2% in JPY terms then, the value of his JPY6,000,000 would now be JPY6,000,000 x (1.02) or JPY6,120,000.
We then convert this to USD by dividing by 77.7330, we get: $78,731.04.
Add them together we get: $13,245.76 + $78,731.04 = $91,976.80.
(b) We now know that the current value of the portfolio is $91,976.80. We then have to solve for the investor's cost (i.e. the value of the portfolio when he bought it).
UK investment costs GBP8 x 1,000 shares = GBP8,000. Converted to USD at 1.40 (note that we used historical rate as this was the rate that he used to exchange to GBP). We get $11,200.
Japan investment has value of JPY6,000,000. Converted to USD at 75, we get $80,000
Add them together we get the cost to be: $91,200.
We now solve for the rate of return. Note that the formula is earnings (or loss) / cost.
Earnings is equal to the change in portfolio value or $91,976.80 - $91,200 = $776.8
Divide this by the cost (which is $91,200), we get 0.0085 or 0.85%.
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