Asset Allocation / Currency Management

CFA Level III Portfolio Management
#1

Hi!

There’s an example in the curriculum in Reading 18 Currency Management. The topic is Hedging Multiple foreign currencies . Topic 6.4.1.

It talks about a fund manager (Mai Nguyen) who is based in US and has invested in Treasury Bills in Australia and New Zealand. (Equally weighted)

Foreign currency asset return for Australian T bills is 4% and for New Zealand is 6% . For its risk free, asset risk is zero. Currency risk SD(Fx) for Australia is 8% and New Zealand is 10%.

now could someone please explain how expected risk of domestic currency return is calculated ?

Here , the calculation given is :

expected risk = 1.04*8% = 8.3% which I’m not able to understand.

Thankyou.

#2

PLEASE READ THE TEXT INSIDE THE BLUE BOX JUST BEFORE.

Nguyen now turns her attention to calculating the portfolio’s investment risk [σ(RDC)]. To calculate the expected risk for the domestic-currency return, the currency risk RFX needs to be multiplied by the known return on the treasury bills. The reason is because RDC =(1+RFC)(1+RFX)−1 Although RFX is a random variable—it is not known in advance—the RFC term is in fact known in advance because the asset return is risk-free. Because of this Nguyen can make use of the statistical rules that, first, σ(kX) = kσ(X), where X is a random variable and k is a constant; and second, that the correlation between a random variable and a constant is zero. These results greatly simplify the calculations because, in this case, she does not need to consider the correlation

between exchange rate movements and foreign-currency asset returns. Instead, Nguyen needs to calculate the risk only on the currency side. Applying these statistical rules leads to the following results: A The expected risk (i.e., standard deviation) of the domestic-currency return for the Australian asset is equal to (1.04) × 8% = 8.3%.

#3

Hi. I still didn’t understand the statistical result σ(kX) = kσ(X), where X is a random variable and k is a constant; Also, what would K be in this case. And why do we need to multiply the FX standard deviation with asset return to arrive at risk ?

Thank you very much

#4

A great magician once said in 2015…

"Normally, to determine the standard deviation of returns in the domestic currency, you would have to analyze:

σrDC = σ[(1 + rFC)(1 + rFX)]

= σ[1 + rFC + rFX + (rFC)(rFX)]

This would require knowing the standard deviation of rFC and rFX, as well as the correlation of rFC with rFX. And it’s messy.

Here, however, rFC is the risk-free rate: it’s a constant, so its standard deviation is zero. This makes 1 + rFC a constant. One of the properties of standard deviation is that when k is a constant, σ(kX) = kσ(X). Another is that when c is a constant, σ(c + X) = σ(X). Putting all of this together:

σrDC = σ[(1 + rFC)(1 + rFX)]

= (1 + rFC)σ(1 + rFX)

= (1 + rFC)σ(rFX)

That’s the formula that they used: the standard deviation of returns in domestic currency is (1 + rFC) times the standard deviation of the currency exchange rate."

Now you are probably thinking… holy cow wtf is this. They talked about this in the beginning of the chapter.

But the great Magician also had a great example as well.

“You started with a portfolio containing a bond worth, say, GBP1,000. A year later you have a portfolio worth GBP1,030: a GBP1,000 bond and GBP30 in cash. The exchange rate volatility applies to the entire GBP1,030, so the domestic currency return volatility is larger at the end of the year than it was at the beginning of the year, by exactly 3%.”

Hope this helps. The power of Google is truly amazing.

2 Likes
#5

Thank you so very much for this explanation :slight_smile:

thanks a lot .

#6

thanks too! I did not find it via google by the way…BUT FOUND THIS SOLUTION ! :slightly_smiling_face:

#7

This explanation is still valid today :slight_smile: