Brad DeLong bended Eric Zitzewitz’s ear, and now our Dartmouth padawan wants a bet:
Brad,
The post you refer to is a follow up post to a post in March that does a similar analysis about the S&P 500.
http://freakonomics.blogs.nytimes.com/2009/03/02/quantifying-the-nightmare-scenarios/
In that post (linked to in the post about Treasuries) I make the point about the marginal utility of wealth. The marginal utility of wealth is clearly likely to be different at different levels of the S&P 500, so that is very important to keep in mind when interpreting that analysis.
It is less obvious how aggregate wealth will covary with Treasury yields. Perhaps you are right that the “>10% yield” scenario is a higher marginal utility of wealth scenario. High inflation and yields can be consistent with growth too though, so I do not think the sign of the difference is obvious.
And I do think you are overstating when you suggest that the marginal utility of wealth is 3.5-7 times higher in that scenario. But it is difficult to know what adjustment to make without knowing how investors expect bonds to covary with other assets (history is arguably not that helpful here) and without knowing what level of risk aversion is reflected in these prices.
It’s a blog post, not a paper, so I left this level of detail out. The issue though is incorporated by reference to the earlier post — I am not ignorant of it, as you seem to imply.
Eric Zitzewitz
Posted by: Eric Zitzewitz | June 16, 2009 at 04:30 AM
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Brad,
One further thought. Perhaps we can follow the advice at the end of my post and settle this dispute civilly “like gentlemen” (as opposed to talking about who wrapped what around what tree).
Apart from perhaps differences about the optimal level of technical detail in a blog post and the exact definition of “option implied”, our main difference seems to be over E(u’(w)|yield>10%)/E(u’(w)). You think this ratio is 3.5-7, I think it is likely much closer to one than that.
Let me propose the following. Let’s use the level of the S&P 500 as a proxy for u’(w). You sell me a conditional forward contract. Specifically, you sell me forward a single share of the S&P 500 fund SPY, with settlement at the close on witching day in January 2011 if and only if the 30-year Treasury yield is above 10%. If the Treasury yield is below 10%, the trade is off. This is essentially a bet on E(S&P500|yield>10%).
There’s just the matter of the appropriate conditional forward price. You have strong views about this relationship and I don’t want to get in the way of your expressing them (credibly). So perhaps a forward price of 50 (corresponding to an S&P level of roughly 500) would be acceptable.
Let me know.
Eric
[The price of 50 is roughly what would be implied by your lower bound of 3.5, a representative investor with a CRRA of 4, and aggregate wealth comoving with Treasuries about half as much in percentage terms as the S&P).]
Posted by: Eric Zitzewitz | June 16, 2009 at 06:09 AM
It seemed like Delong interpreted the mere suggestion of 10% interest rates as a veiled attack on the Obama administration. That would explain the unfairly harsh and pedantic manner of his post.
I think that Delong is right to be sensitive on this subject. Trading in Treasuries has recently seemed a bit aggressive and not altogether related to inflation expectations, at least not in an innocent, passive sense.
Anyway, the apparent probabilities could also be explained by the same structural forces that sometimes cause the longshot bias. (not formal risk aversion)