NO.PZ2022123002000008
问题如下：
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.
Calculate the contribution of
foreign currency to the Bhatt account’s total return. Show your calculations.
选项：
解释：
Correct Answer:
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
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, and ωi
is the weight of the asset as a percentage of the aggregate domestic-currency
value of the portfolio. This equation can be rearranged as
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%.
Total return in USD(domestic currency) equals to weighted average return on asset return puls weighted average turen on currency return, plus weighted cross product of asset retrun and currency return.
The latter 2 items explain foregin currency contribution to total account.
weighted average return on asset return is .05*10%+0.25 5% +0.25*(-3%)=5.5%
So contribution of foreign currency to the total return is 7%-5.5%=1.5%
