In Defense of Trills (and Bob Shiller)

So trill.

I love reading Felix Salmon’s blog, but today he goes off the rails a bit when discussing the prospect of GDP-linked bonds, as recently proposed by Bob Shiller.  The basic idea is that countries would issue a security where the coupon is linked to that country’s GDP.  GDP-bond supporters say that the bonds would help government issuers because they’d be counter-cyclical, helping countries in times of distress and lessening the probability of a default or a crisis.  Furthermore, the bonds would give investors the ability to gain diversified exposure to a country’s future prospects.  For a more in-depth look at GDP-bonds, I highly recommend checking out this 2006 paper by Stephany Griffith-Jones and Krishnan Sharma, which explains the benefits and challenges of GDP-linked bonds really well.  (I’d also recommend the commenters on Salmon’s post today, who make a lot of strong points.)

Salmon’s not a fan though, but after reading Salmon’s post today on GDP-linked bonds and his previous posts on the topic, I’m pretty confused about why.  In this post, for instance, it seems like he’s saying they’re a bad idea because they’ll be too expensive to issue:

Bond investors in general, and government bond investors in particular, are highly loss-averse — they’ll require much higher yields if there’s a real risk that they won’t be repaid their principal in full.

What’s more, bond investors valued those Argentine GDP warrants at zero when they were issued. If a detachable option with upside but no downside is valued at zero, then a built-in option with symmetrical upside and downside will clearly be valued at less than zero: the government is going to have to pay a big premium to complicate matters in this manner.

Yet yesterday he wrote that their value could be infinite:

If the coupons are steadily increasing, however, the math becomes very dangerous. The coupons will rise at the rate of nominal GDP growth, which in the US will probably be somewhere in the 4% to 5% range over the long term. As a result, if you’re a risk-averse person who wants a perpetual US government security and your discount rate is say 3%, then the expected value of a singe Trill is actually infinite. Of course, no security trades at a price of infinity. But the fact that valuations can get so high in a low-interest-rate environment is all you need to know about just how volatile Trill prices could get.

Well, yes, if you’re discounting future cash flows at a lower rate than their expected growth rate, then the security would have an infinite value.  That doesn’t mean their value is infinite–it just means your discount rate is wrong.  In this case, you shouldn’t use the risk-free rate to value the security just because it’s issued by the government.  You use the risk-free rate for a Treasury bond because the coupons are fixed and there’s (theoretically) no danger of the U.S. government defaulting.  For a trill, though, while there still might be no U.S.-default risk, your cash flows depend on GDP, which creates risk that needs to be incorporated into your discount rate.  An equity-like instrument like trills with exposure to the whole market should be discounted at something between the risk-free rate and the cost of equity.

Salmon tries to make the case that trills would be more volatile than the S&P 500, but I don’t think that can be true, simply because the S&P is a subcomponent of GDP, so exposure through trills is going to be more diversified than exposure through the S&P.  Salmon writes about the value of trills, “What really makes a big difference is the interest rate you use to calculate net present value. In other words, while Trills are designed to respond to news about the economy, in fact they would be an incredibly noisy and volatile instrument reacting mainly to changes in long-term interest rates.”  But the value of the S&P is theoretically calculated in precisely the same way–by discounting the value of future cash flows (dividends) that you get by owning the stock.  If the discount rate that you use to value trills is volatile, then the rate you use to value the S&P portfolio will be as well.  The only difference is that with trills, you’ll have more (or at least as) stable cash flows, so they should be less, not more, volatile.

The bottom line is that trills would cost more for countries to issue but would carry substantial benefits, which makes sense.  Equity costs more for companies to issue than debt because it’s riskier.  Trills would cost more than bonds for countries to issue, so countries should issue trills until the costs outweigh the benefits.

Lastly, I think Salmon takes a bit of a cheap (and unsubstantiated) shot at Shiller when he says that Shiller’s pushing trills because he’ll benefit financially through his firm, MacroMarkets.  It’s a bit absurd to suggest that Shiller feels the need to create business for his firm by convincing governments to issue trills.  Even if it were the case that it would be a boon for their business–which I don’t think would be true–there’s no basis for suggesting that Shiller is subverting his scholarly reputation and recommending a flawed idea just to make a few bucks.

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