Here I continue my review of "The Investor's Manifesto" by Bernstein with my notes from Chapter 2. In Part 2 of my notes, we cover estimating returns on bonds.

One important note: In Part 1 of my Chapter 2 notes, we talked about how unwise it is to use historical returns to predict future returns. Yet when we calculate estimated return for stocks and bonds, we're basing those calculations on historical data. Don't let the precision of the mathematics make you forget that we're attempting to predict the future. These are estimates, and are very valuable to give you a range of possible returns -- but the actual returns could certainly be outside the range of your estimates.

### Estimating Bond Returns

We'll start with bond returns because they're simpler. Estimating bond returns is easy in theory, but I found it quite difficult in practice. The difficulty was in getting the necessary data to make the relatively simple calculations.

The estimated return of a US Treasury bond with a 2% return is 2%. This is because we are assuming the US Government will not default on its loans. (Let's ignore the possibility of US bond default while we focus on learning the math here.)

To get the estimated return of a corporate bond, we subtract the likelihood of default (the company failing to pay its debts) from the percentage yield to get the estimated rate of return. If the corporate bond pays 7%, and the historical default rate of bonds of the same rating is 2%, then the expected return of that bond is 5%. If the actual default rate grows to 5%, then investors would get the same return (and much less stress) with a 2% Treasury bond.

To make our estimates more accurate, we calculate the rate of return for a class of bonds rather than an individual bond. Thus, just as in our coin-tossing game, we increase the likelihood that our actual return will be close to our estimated return.

We know the interest rate of the bonds at the time we make the calculation, but we're going to estimate the default rate based on historical data. What period we use to select the data can make a big difference in our estimated return.

I found it quite difficult to find good data, and had to do quite a bit of digging. Here's the sources I've found with the years they cover:

- Standard and Poors: 1981 to 2011 [Link no longer works]
- Municipal Bond Fairness Act of 2008: 1970? to 2006 (date range not exactly clear)
- Moody's: 1920 to 2007

OK. Let's try and look at a particular asset class: 10-year investment-grade corporate bonds. Currently, AAA, AA, and A rated 10-year bonds appear to be giving 2.29%, 2.76% and 2.74% annual returns. Let's average that out to 2.60%.

Standard and Poors gives us investment-grade default rates ranging from 0.00% to 0.41% in 2008. The average over the 30-year period is 0.1063%.

Moody's gives us the range of 1920 to 2007, and gives us a mean of 0.068% on investment-grade bonds. (Moody's exhibit 25.)

The Municipal Bond Fairness Act quotes numbers from Moody's and Standard and Poors, and gives 2.09% as the Moody's default rate and 4.14% as the S&P default rate for investment-grade assets.

What. The. Heck?

First of all, my numbers don't match up. Why the wide spread on default rates from Moody's and S&P? Why the other disparities? Second, these returns look like crap. We've got a 2.5% return with a default rate (which we subtract from the return) of anywhere between 0.1% to 4%. At 4%, you're guaranteed to lose money on the deal. Even if we assume a zero default rate, inflation would have to be near zero to make these yields even remotely attractive, and inflation is unlikely to be that low in the future.

I see three possibilities:

- I'm doing this wrong -- my numbers are wrong, and any analysis past that is pointless.
- I'm doing this right, and other people are dumb -- anyone investing in bonds at these rates is guaranteed to lose money.
- I'm doing this right, and other people are smart -- they know something I don't know that makes investing in bonds a good deal. (If the future holds significant deflation, does that make these bonds a good bet? I think it's unlikely that all other asset classes are going to receive an even worse yield, making these numbers look good in comparison.)

I'm going to continue exploring this further, and trying to see whether or not my analysis holds water. I've obviously still got a lot to learn, and I'd love your help learning it! Got comments about my bond analysis? I'd love to hear them.