Lowered Expectations, part 3

Hey, I did not say which Wednesday… But I do want to finish this up before the Fed embarks on their new M.A.D. policy (Mutually Assured Devaluation).

Let me go back to my original example, supposing I give you a lottery ticket that says: “Nemo will flip a fair coin tomorrow. He will pay $1 to the holder of this ticket if and only if the coin comes up heads.”

I asked how much you could get selling that ticket today into a market of risk-averse people. (Recall that risk aversion, by definition, means a preference for certainty over uncertainty; or equivalently, a willingness to sacrifice expectation value for certainty.) Since the expected value of your ticket is 50 cents, I said that no risk-averse person would be willing to pay 50 cents or more for it.

But I was wrong. As it turns out, there is one person — just one person — who can offer you more than 50 cents for your lottery ticket and still be risk averse. Before reading on, can you figure out who?

Just as that lottery ticket represents an asset to you, it represents a liability to me. Put another way, you hold a ticket with an expected value of 50 cents, but I hold the corresponding “anti-ticket” with an expected value of -50 cents. If I should buy the ticket from you, that anti-ticket would be canceled and the liability extinguished. Just as your risk aversion will lead you to prefer a certain 50 cents to a possible $1, my risk aversion will lead me to prefer a certain 50 cent loss to a possible $1 loss. And so I can pay you more than 50 cents for the ticket and still be risk averse.

Put yet another way, your risk aversion makes you a natural seller of the ticket, while mine makes me a natural buyer. So how much can you sell it for? That depends on which of us is more risk averse, which of us is the better negotiator, etc… But it could wind up being less than, more than, or equal to 50 cents.

The moral is that risk and risk aversion are meaningless without reference to a portfolio. (Well, the other moral is that sometimes I fail even to get my toy examples right. You want fully-baked analysis instead of some guy thinking out loud, stick with Bond Girl.)

The toy example I should have used is fire insurance. When you own a house, you are exposed to the risk that it burns down. That is a pretty unlikely event, so the expected value of your loss is not very large… But as a risk-averse homeowner, you will be willing to pay somewhat more than that expected loss for an insurance policy, trading the uncertain (enormous) cost of losing your house for the certain (modest) cost of your insurance premium.

In other words, as a homeowner you are a natural buyer of fire insurance. Who are the natural sellers? Well, there aren’t any. Unlike a lottery ticket — for which there is always a corresponding liability somewhere — your house is your asset but nobody’s liability. There is no “anti-house” out there whose value is enormous only if your house burns down. (Good thing, too, I should think.) And that is why the risk premium for fire insurance is always positive.

Which brings me back to inflation swaps. The observation that the nominal fixed payments are actually variable in real terms (and vice-versa) is still valid. But that does not answer the question of whether the risk premium will be positive or negative. To know that, we need to ask whether inflation swaps are more like a bet on a coin toss, or are they more like fire insurance? Who are the natural buyers and sellers of inflation swaps?

Any holder of dollars is a natural buyer of insurance against the Fed “burning them down”. And a dollar, like a house, is an asset with no corresponding liability… Unless you count the Fed’s own balance sheet, which I don’t.

Any dollar creditor is also a natural buyer of an inflation swap, while the corresponding debtor is a natural seller.

My suspicion is that during normal times, the dollar creditors and debtors balance out and inflation swaps act more like insurance with a solidly positive risk premium. But when the expectations become extreme, the pool of natural buyers and sellers can change significantly. For example, as an ordinary working person, I am usually not too concerned about the rate of inflation, because even if the prices of goods and services rise, my salary will rise also. But if I start to worry about deflation or hyperinflation, the equation changes; my concern becomes losing my job entirely (making me a natural seller of inflation swaps) or seeing my salary fail to keep up (making me a natural buyer).

According to those Cleveland Fed papers, the inflation risk premium is generally +50 basis points. And you will find that if you compare their 10-year expected inflation estimate each month with the 10-year zero-coupon inflation swap, they do differ by roughly 50 bps. If expectations become more uncertain — e.g., because nobody knows what the heck the Fed is going to do — that risk premium could rise even if the numerical expected value remains the same. (This may be happening right now.) And if expectations turn negative again, all bets are off… Even a negative risk premium is quite possible, since a deflationary depression makes almost everybody into a natural seller of inflation.

If you just cannot get enough of this “inflation expectations” stuff, check out Using TIPS to gauge deflation expectations, a recent post from an Atlanta Fed economist where he describes how to estimate deflation probabilities from the difference between the yields of on-the-run and off-the-run TIPS. I admit I have not yet tried to follow the math, but if I do and it is interesting maybe I will make a follow-up post.

1 comment to Lowered Expectations, part 3

  • I feel like I have to say something about the guy in Tennessee not paying the $75 fire department fee in response to your fire insurance risk aversion comment… 😉

    “And if expectations turn negative again, all bets are off… Even a negative risk premium is quite possible, since a deflationary depression makes almost everybody into a natural seller of inflation.” Ah HAH! So I think we finally agree.

    good post.

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