# Reading 44: Benchmark/Portfolio = weights: Effects

This may have been covered here, but my thread search yielded nothing. Reading 44 Currency/Market/ Allocation effect Here’s a question (and my answer) If the benchmark and the portfolio have the same weights (i.e. both split 50/50 between 2 countries), will the currency allocation and the market allocation automatically be zero? My answer: Market allocation MUST be zero, because it is calculated as SUM (Wj,p - Wj,b)(rj,b,f) I’m not sure about Currency Allocation The formula is SUM [(Wj,p)(rj,p,d - rj,p,f) - (Wj,b)(rj,b,d - rj,b,f)] I’m not sure about currency. At first, I would have guessed that the home/local return differentials would be equal . However, the examples indicate that they are not. According to examples, it looks as though there can still be a non-zero currency effect when the weights are equal The “Brand X” book says that there can still be a non-zero Market allocation effect, but that currency effect must be zero I’m confused about the currency effect, but absolutely mystified about the market effect. Is that an errata? Thoughts?

Let me make up some numbers, assume US-based investor invest in Franc Portfolio § Benchmaret (B) Pw=50% Bw=50% P (local return)=11% P (US return)=15% B (local return)=13% P (US return)=16% So, currency allocation effect is (0.5)(15-11)-(0.5)(16-15)=0.5% (non-zero) Helps??

So, even if Portfolio and benchmark has the same weight, currency allocation effect can be still non-zero. What is that “Brand X” book? whatever it says, it doesn’t sound right.

That’s what I thought. But if that is correct, then there is a definite error in the book I read (I’d post the question, but I can’t becuse of this stupid copyright law). Anyway, it is Schweser book 5, Page 78. Question 6.

Did you check the existing errata for “Brand X” book?

the example above is written poorly, but it’s still true that there can be a currency effect. Lets say that, as an extreme example, both the port and benchmark are 100% invested in Euros, and the investor is based in Dollars as local currency. Benchmark return is 0% in Euros, +10% in Dollars. Portfolio return was +100% in Euros, and +120% in Dollars. This would be the actual case, for example, if the portfolio’s value doubled on day one and did nothing else all year, and the index was perfectly flat all year (in Euro terms). The formula is SUM [(Wj,p)(rj,p,d - rj,p,f) - (Wj,b)(rj,b,d - rj,b,f)] so in this case: (100% * (120%-100%) - 100%*(10%-0%)), which simplifies to 20%-10% = 10%.

There is a currency even if benchmark and portfolio weights are identical because of the cross product of exchange rate and portfolio/benchmark return. Remember the currency effect for each market is: ws(1+rp+dp) - Ws(1+rI+dI) w = portfolio weight of the market W = benchmark weight of the market rp = portfolio return for the market dp = portfolio yield for the market rI = index return of the market dI = index yield for the the market If w=W, the currency contribution is non-zero because of the cross terms s(r+d) above. Am I correct - I am testing my memory here