International Fixed Income Topic IIIA: Stylized Facts and Their Implications

Outline Explaining the Term Structure The Effect of Currency Movements

I. Explaining Term Structure Movements What factors explain movements in the term structure across countries? Case study: –G7 countries (US,UK,JPN,CAN,GER,ITA,FR) – –Weekly movements in zeroes of 1yr-30yr maturities

Principal Components Analysis Find the principal component that explains most of the variation in term structure movements across the maturities. –How much does it explain? –Are there additional components –How correlated are these components across countries? –How much does the U.S. explain of movements in foreign term structures?

How Many Factors?

What Do These Factors Look Like?

Worldwide Principal Component Analysis (US,UK,JPN,GER)

% of Worldwide Movements in Term Structure Explained by Factors

Implications Continued... APPROXIMATION of CHANGE IN BOND’S VALUE: What’s the exposure of the foreign bond’s value to US rates? In other words, the % change in the foreign bond to a change in US rates is just the US bond change times the sensitivity of foreign rates to US rates.

Implications of Factor Analysis Most of the movements in the term structure, e.g., 90%, can be explained by one factor. –Caution: Ignoring short-term rates here and focusing on 1-30 yr zeroes. This factor looks like a parallel shift in rates. (The second less important factor looks like a steepening/flattening.)

Sensitivities of Foreign Factor to US Interest Rate Factor (i.e.,  )

Sensitivities of Foreign Factor to German Interest Rate Factor (i.e.,  )

Example Consider from earlier in class, the 1.5-year and 30-year zeroes with durations of 1.46 and 29.26, respectively. If these were the durations of the foreign bonds, and you had them in your portfolio, what does that say about their durations in your $ portfolio? (That is, your exposure to US rates, not currencies).

Durations of Foreign Bonds

II. Currency Movements Introduction about bond price variation Facts about currency and interest rate co- movements

Rates of Return on Zeroes Consider a T-period zero in a foreign government bond. What is it’s US $ rate of return? Taking logs of the above and rearranging gives us This is approximately equal to: [zero rate] - [dur x (  r)] - %  S(Fn/$)

Rates of Return: Summary The $ return on a foreign bond has three components: –It’s yield (e.g., coupon, or imputed yield) in the foreign currency. –It’s duration component in the foreign currency. –It’s exchange rate exposure. The first two components are always true, while the second is unique to international fixed income.

Rates of Return: Summary Continued... The risk associated with this return can be broken up into two pieces: –interest rate risk (i.e., duration and maybe convexity) as the first component (i.e., the coupon) is fixed. –exchange rate risk. Of course, if there is no exchange rate risk, we just get the usual result that the volatility of a bond is its duration times the volatility of rates.

Interest Rate & Currency Factoids Correlation between interest factor in foreign country and the F/$ exchange rate. Volatility of interest rate factor. Volatility of % change in exchange rate.

Correlation Between Foreign Interest Rate Factor and Exchange Rate Changes

Volatility of Interest Rate Factor Weekly in Basis Points

Volatility of % Change in Fn./$ Exchange Rates (Weekly % Terms)

Estimate of Volatility of US bond & $-adjusted Foreign Bonds

% of Volatility of $-adjusted Foreign Bond Due to Currency Risk