Contribution Foreign Currency - CFA Mock

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%.

They want you to calculate R_{FX} + R_{FX} \times R_{FC}

R_{DC} = (1 + R_{FC})(1 + R_{FX}) - 1

R_{DC} = 1 + R_{FC} + R_{FC} \times R_{FX} + R_{FX} - 1

R_{DC} - R_{FC} = R_{FC} \times R_{FX} + R_{FX} = Contribution of foreign currency to account’s return