Financial Mathematics Text

Wednesday, October 9, 2013

Junk Bonds: A Closer Look

So one of the questions I asked in Are Bond Yield Spreads Adequate? is whether or not junk bond spreads are adequate. I presented a simple model. The model predicted that returns on junk bonds would be about 2.27% in excess of treasuries. But the uncertainty in the model had a standard deviation of 2.36%. So if we were off by just 1 standard deviation, we would underperform treasuries.

But a model can't be better than the assumptions that one puts into it. I'd like to take a review of the assumptions I used in the model and change a few things. 

Essentially I used data from Moody's Corporate Default and Recovery Rates, 1920-2007. I noted this didn't include the recent period so I rounded up to take that into account. We'll take this into account more explicitly by looking at Moody's Corporate Default and Recovery Rates, 1920-2010.

But there's actually a greater concern here. Junk bonds are not the same now as they were in 1920. For much of our financial history, junk bonds were "fallen angels". These are bonds that were once held in high regard, earning investment grade ratings, but they "fell from grace" and now trade a substantial discount to par value.

But something different happened around the 1970s (and especially the 1980s). Low credit quality companies began issuing bonds. These bonds aren't necessarily the same as the fallen angels. So I believe I should not have looked at the data from the 1920s onward. So what does recent history look like as far as defaults?

Let's first look at the table from 1920-2007:

And now let's consider 1981-2010:

Average speculative grade defaults went from an average of 2.62% to an average of 4.58%. That's a huge difference!

For simplicity, I will assume annual default rate of $p=4.5\%$ with a spread of $s=4.5\%$ and a recovery rate of $r=30\%$

The predicted excess returns over treasuries is:
s(1-p)+p(r-1) &= 4.5\%(1-4.5\%)+4.5\%(30\%-1) \\
&= 1.15\%

Next, we'll factor in a margin of safety of one standard deviation of the model. Since standard deviation is still about $dp=3\%$, we'll just use that figure and we'll still use $dr=25\%$ as we did before. This gives us an uncertainty term of:
\sqrt{p^2dr^2+(r-s-1)^2dp^2} &= \sqrt{4.5\%^2\times 25\%^2 + (30\%-4.5\%-1)^2 \times 3\%^2} \\
So the uncertainty term is only slightly larger. But it does indicate that there isn't enough of a margin of safety that junk bonds will outperform treasuries.

And it may be possible for investment grade bonds to outperform speculative grade bonds as our model predicted about 1.32% premium over treasuries versus the 1.15% premium over treasuries we're predicting for junk.

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