NO.PZ201601050100001201
问题如下：
Calculate the contribution of foreign currency to the Bhatt account’s total
return. Show your calculations.
选项：
解释：
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 Éi
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%.
中文解析：
本题考察的是外汇投资中return的计算。
表格中给到的currency return是对应单个资产的，而本题中是投资了三个外币资产，因此是一个资产组合，所以涉及到加权平均的过程。
另外需要注意的是“the contribution of foreign currency”是包含了交叉项部分的return的。
老师，如果我们老老实实算，
EURO这个资产用USD计算的收益应该是：(1+5%)*(1+2%)-1=7.1%，因为他的比例是25%，所以最后应该是7.1%*25%=1.775%计算入总portfolio对吧？
同理，Japan资产，用USD计算的收益应该是：(1-3%)*(1+4%)=0.88%，按比例25%计算，最后是0.22%计算入总portfolio return
答案里虽然给了展开式，但是我用最基础的ΣwiR(dc)算并没有省略任何的部分呀,为什么1.775%+0.022%+50%*10%=6.995%而不等于7呢？
另外,问题是问，foreign currency return 对整个portfolio的贡献。 为什么不能理解为[R(dc)-euro]+[R(dc)-japan]对于总体return的贡献呢？
