Financial Mathematics Text

Wednesday, September 11, 2013

Bond Returns Given a Change in Interest Rates

This post was inspired by a tweet by John Hussman:

The other important observation Hussman made was the fact that as the bond approaches maturity, it moves along the yield curve to maturities with lower rates. So the upside is enhanced by that as well.

The idea is pretty simple. So I decided to see what this would look like for my favorite bond funds: Vanguard Corporate Bond funds (VCSH, VCIT, VCLT).

I like these funds because of the low expense ratio. I also prefer investment grade corporate bonds to treasuries as I think the spread is generally more than adequate to compensate for the low risk of default.

Instead of just looking at a 50 bp (0.5%) change in interest rates, I considered three scenarios: 0.5%, 1.0% and 1.5% (well, 6 scenarios, since we're looking at both upward and downward changes).

A 1.5% change in interest rates is not unfathomable. In fact, according to figures from Yahoo Finance, within the last year 10 Year Treasury Bonds have been anywhere from 1.56% to 2.98%, a difference of almost 1.5%.

So here's the chart:

Vanguard Corporate Bond Returns Given Change in Interest Rates

Now, I don't have detailed information on Vanguard's portfolio so I made some simplifying assumptions. I assumed that the portfolio consisted of one bond that had the average characteristics that Vanguard provided for the fund. While not perfect, it's probably pretty close. For example, my calculation of the duration of the securities ended up being 2.9, 6.4 and 13.3 years which is pretty close to their average figures.

I also ignored defaults which is obviously not true but may be an OK approximation given the low default rate of investment grade bonds. So actual returns may not be exactly those figures but I think they're decent estimates.

About as you'd expect, the higher duration funds are more sensitive to changes in interest rates. But the overall tradeoffs don't seem too bad.

If you're interested in the actual calculations, I'm currently working on a quasi-textbook for Financial Mathematics. While the section on bonds has not been added as of yet, if you check in every now and then, it will eventually appear. Working through some of the other sections are prerequisites to understanding bond valuation so it won't hurt to start taking a look.

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