Why S&P downgraded

I don’t think many serious investors care that S&P downgraded US debt. Bond yields are down (more on this in my next post), which means prices are up. US stocks are down, but that’s more about concerns about US and global economic prospects than the credit of the US government.

Nevertheless, S&P did downgrade. Why? I don’t think it is primarily to do with a materially increased estimated probability of default. It has more to do with a change in the payoffs in a ‘game’ (as in game theory) S&P is playíng.

Consider the quadrant of options. S&P downgrades or doesn’t and the US defaults or doesn’t. I’ve constructed totally hypothetically, but perhaps plausible scenarios below, for the S&P’s potential assessment of losses under each possibility given their views and external perceptions of them before and after 2008.

Before 2008, the fallout that would come from downgrading the US and the US not defaulting would be significant and cries of “un-American” might be heard again. Even if the US were downgraded, default would still be a blow for S&P since anything above a BBB rating really shouldn’t ever default if there models are “correct”. I’ve thrown in another hypothetical, a 0.01% probability of default – in other words very low, and as you’ll see in the next scenario, not necessarily higher now for S&P to change their view.

Now, either on a traditional minimax (minimizing the maximum cost) or an expected value basis, before 20008 S&P wouldn’t downgrade the US. This is an important calibration, since S&P didn’t downgrade the US.

After 2008, even if we leave the assessed probability of default unchanged, the world is different and therefore we have different costs.  If S&P doesn’t downgrade the US – even if the US doesn’t default, there will be a cost to S&P since might share the view that the US could default now. The dent in credibility since 2008 means that S&P has to try harder to convince the skeptics that they don’t rate risky instruments as AAA. Along with this goes a massive hit if the US does default and S&P hasn’t downgraded the US. The good news is that at least now a downgrade is viewed more with more understanding even if the US doesn’t default (although be sure Obama’s White House is not happy at the moment).

After 2008, even if the assessed probability of default is unchanged, the minimax and expected value rules both suggested a downgrade is the better option for S&P.

Before 2008

 Don’t downgrade

 Downgrade

 PD

0.0001

Default

-500.0

-50.0

No Default

0.0

-1,000.0

Expected

-0.1

-999.9

After 2008

 Don’t downgrade

 Downgrade

 PD

0.0001

Default

-10,000.0

-50.0

No Default

-10.0

-10.0

Expected

-11.0

-10.0

Now the example is contrived – I chose a set of parameters that demonstrates the point I’m trying to make. This isn’t a problem since I’m not saying this is what happened. I‘m saying it is plausible that S&P made a perfectly rationale (for them) decision to downgrade even if they didn’t think the US was more likely to default now than before.

In truth, the US might be more likely to default now than before, although the change is probability not sufficient on its own to merit a downgrade at this point. Especially since S&P have their maths wrong.