Country Beta - which country's bond duration do I apply it to?

CFA Level III
#1

From 2013 CFAI Mock (PM Section) - Question #51

Seymour tells Bixby, “International interest rates are not perfectly correlated. We can see the impact of a change in U.S. interest rates on our model global bond portfolio. This portfolio contains U.S. and German bonds and is not currently hedged with regard to currency or interest rates. Our analysis shows that the country beta between the United States and Germany is 0.62. ” Model global bond portfolio data is provided in Exhibit 3. Exhibit 3 Global Bond Model Portfolio Duration Allocation (%) U.S. bond issuers 6.6 60 German bond issuers 3.9 40 My Question How do I know which country’s bond duration to apply the country beta to, per the question’s details in bold? In the answer explanation, they applied the country beta to the German component of duration, but how do you figure that out? The actual question below, for your own enjoyment: 51. Based on Seymour’s statement regarding international interest rates, as well as the data in Exhibit 3, the impact of a 100-basis-point decline in U.S. interest rates on the model portfolio’s value is closest to: A. 3.41%. B. 4.02%. C. 4.93%. Answer = C C is correct because the U.S component contributes 3.96 in duration to the portfolio (0.60 × 6.6 = 3.96); therefore, a 1.00 change will contribute +/–3.96% to the value of the portfolio. The German component has a contribution to duration of 1.56 (0.4 × 3.9 = 1.56) but moves only 0.62 times the movement in U.S. rates, thus contributing +/–0.97% to portfolio return (1.56 × 0.62 = 0.97). The total impact is +/–4.93% (3.96 + 0.97 = 4.93).

#2

the impact of a 100-basis-point decline in _ U.S. interest rates _ on the model portfolio’s value is closest to:

The question tells you what is going on. Technically there is a yield beta in the formula for the US, but it is 1.00 so you don’t see it. Basically, the yield beta they’ve derived is from a regression of US yield versus German Yields. You know that the regression of US Yields to US Yields will be equal to 1 so therefore your only other option is to apply it to the German position.

#3

Thanks, that makes sense! Think I’m getting tunnel vision after all these hours put in. This was kind of a “OH DUH” moment for me. hah

#4

^^^Yeah. It’s definitely the type of question that looks a little “too simple”.