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%.
总收益为6.995%
USD(本币)资产的收益为5%
那(6.995%-5%)/6.995%是否可以求得由于foreign currency对于总收益的contibution?