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October 21, 2005
Selling Tail Risk – An Example
Brad Setser and I once had a conversation regarding Andrew Lo’s paper that hedge funds basically sell investors liquidity preference (by purchasing less liquid securities) to make there excess returns. I, on the other hand, feel that the illiquidity of credit derivatives (while untested by crisis yet) is over estimated. My thought (and I make no claim to its uniqueness) is that hedge funds mainly sell tail risk in one sort or another to gain the excess returns.
An interesting example of this happened to us yesterday. There was an opportunity in the marketplace to make a guaranteed profit as long as the Fed did not hike by 75bps in the next two meetings (I will spare the details since they are convoluted and I have no ideas if it would be even legal nowadays) which would imply a 50bps hike in one of the next two meetings. If they did hike by 75bps in the next two meetings the losses were quite large. To give a sense of the magnitude, let’s say we would have made $80 vs. losing $1,110.
Since I assigned a true 0% probability of this event before looking at the numbers this trade looked great. After all if there really is a 0% chance of losing money, then however big the loss is has a $0 expected value. However once I had to commit money to this (one of the reasons markets can be better at predicting things, people have to put up or shut up) I thought, well maybe the probability isn’t zero, maybe its .1% or some non-zero value. While I cannot imagine what could make the Fed hike by 50, there still is time; maybe core comes in at 1% in October or something else extreme. The point is if the true probability is not zero, this suddenly becomes a different problem.
Now using the payoff’s I showed above the market is basically pricing in a 7% chance of a 50bps hike. Even if I do not think the probability of the Fed hiking by 50bps is zero, it is most certainly not 7%. Let’s say I think the probability is 1%, this trade would have a positive expected return on $68, it should be a no brainer right?
Here is where behavioral finance comes in; most people (myself included) are loss averse (editor’s note: I once had the pleasure of seeing Daniel Kahneman talk about this). The pain of the massive loss overweighs the pleasure of the small gain, even if the expected return is positive.
Where it gets interesting is that since loss aversion appears to be so prevalent in the investing world, these types of trades will often be present. To reverse perspectives, the person on the other side of this trade is overpaying for the insurance that they will avoid the low probability event of massive losses. If this is the case an investor without this loss aversion can make excess returns by selling overvalued tail risk On other words, even if hedge funds only sell tail risk (no matter how fancy they describe it) they still might be able to earn excess returns by, in essence, providing insurance. Providing insurance has a useful economic value if people are loss averse and thus, hedge funds should be rewarded for it.
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Comments
Obviously, the real question is what gives you any confidence that your "current" conviction that the FED will not go 75 bp's will not change between now and say December..
The bet that you think is so attractive is unfortunately a "commonplace" in the market...
More interesting bets are: the market is simultaneously pricing the probability of a 50 basis tightening in November and a pause..
Now those are two states of the world that one doesn't have to make subjective judgements about...
Niether will happen
or just one...
and one only has to wait two weeks to find out..
Selling OTM options always looks like insurance... suggest you re read Definnetti to get a better grasp on what probabilities and Dutch books really mean..
and stay away from Fed Funds options.. they may surprise you..
Posted by: sjonas at October 22, 2005 03:48 PM
Though the probability of gaining $80 is 99.9%, and that of losing $1,150 dollars is only 0.1%, as long as the probability of losing is non-zero, you are taking a chance on being annihilated unless you limit the size of your bet such that a loss won't wipe you out. If you limit the size of your bet such that your worst-case loss is, say, 50% of your capital, then your return on capital is going to be only about 4% above what you are getting on whatever investment you've parked it in for the duration.
And is there any adverse outcome whose probability is as low as 0.1% over any significant term? If the term is three months, then 0.1% is one occurrence in 3000 months. That's 250 years. Consider the events that we've seen since 1755. Surely quite a large number of them would be much less likely than the Fed doing 75 bp's. But they happened.
Posted by: jm at November 3, 2005 12:08 AM
