Can someone help understanding this? Is one of the examples in the CFA Practice Review Website.
Mason Darden is an adviser at Colgate & McIntire (C&M), managing large-cap global equity separate accounts. C&M’s investment process restricts portfolio positions to companies based in the United States, Japan, and the eurozone. All C&M clients are US-domiciled, with client reporting in US dollars.
Darden manages Ravi Bhatt’s account, which had a total (US dollar) return of 7.0% last year. Darden must assess the contribution of foreign currency to the account’s total return. Exhibit 1 summarizes the account’s geographic portfolio weights, asset returns, and currency returns for last year.
Exhibit 1.
Performance Data for Bhatt’s Portfolio Last Year
| Geography | Portfolio Weight | Asset Return | Currency Return |
|---|---|---|---|
| United States | 50% | 10.0% | NA |
| Eurozone | 25% | 5.0% | 2.0% |
| Japan | 25% | –3.0% | 4.0% |
| Total | 100% |
Calculate the contribution of foreign currency to the Bhatt account’s total return.**
Solution
Currency movements contributed 1.5% to the account’s 7.0% total (US dollar) return, calculated as follows:
The domestic-currency return (RDC) on a portfolio of multiple foreign assets is
RDC=∑i=1nωi(1+RFC,i)(1+RFX,i)−1
Where RFC,i is the foreign-currency return on the ith foreign asset, RFX,i is the appreciation of the ith foreign currency against the domestic currency, andωiωi is the weight of the asset as a percentage of the aggregate domestic-currency value of the portfolio. This equation can be rearranged as
RDC=∑i=1nωi[RFC,i+RFX,i+(RFC,i×RFX,i)]
Therefore, the domestic-currency return is equal to the sum of the weighted asset return, the weighted currency return, and the weighted cross-product of the asset return and the currency return. The latter two terms explain the effects of foreign-currency movements on the Bhatt account’s total (US dollar) return of 7.0%.
The weighted asset return is equal to 5.5%, calculated as follows:(0.50 × 10.0%) + (0.25 × 5.0%) + [0.25 × (–3.0%)] = 5.5%.
The weighted currency return is equal to 1.5% calculated as follows:(0.50 × 0.0%) + (0.25 × 2.0%) + (0.25 × 4.0%) = 1.5%.
The weighted cross-product is equal to –0.005%, calculated as follows:[0.50 × (10.0% × 0.0%)] + [0.25 × (5.0% × 2.0%)] + [0.25 × (–3.0% × 4.0%)] = –0.005%.
Therefore, the contribution of foreign currency equals 1.5%, calculated as the 7.0% total (US dollar) return less the 5.5% weighted asset return. Alternatively, the contribution of foreign currency to the total return can be calculated as the sum of the weighted currency return of 1.5% and the weighted cross-product of –0.005%:1.5% + (–0.005%) = 1.495%, which rounds to 1.5%.