Does Tail Hedging Help A Portfolio?

Tail hedging seems to be the talk of the investment world these days. Tail risk hedge fund managers are writing popular books. Others are becoming financial twitter rockstars. Are you behind the curve if you aren’t in on this game?

Well to answer this question we first have to understand what tail hedging is and what it’s supposed to do for your portfolio. Tail hedging is a wide field, so we’ll just tackle the most basic version. In doing so, you’re going to learn how tail hedging’s philosophical foundations originate from the geometric return.

What is a Tail Hedge?

Imagine a full distribution of returns. We will use a lognormal distribution for the example, even though actual returns are not lognormal.

See how a probability distribution has narrow sides that stick out far into either the left for losses or to the right for gains? Those narrow areas are called tails.

The goal of tail risk hedging is to cut off the left “tail” of this distribution so you don’t have to worry about large losses.

The simplest way to do this is to purchase a put option with a strike in the tail, which ensures that all losses beyond this point are offset by gains from the put option. The put option combined with the original distribution creates a portfolio distribution which doesn’t have a left tail.

And that’s the last time I’m going to reference options in this post.

I Don’t Speak Greek

The options world has its own lingo. Most of the terms and concepts are named after Greek letters, and listening to options experts often feels like listening to a foreign language.²

I don’t speak Greek. I can mostly understand it, but I don’t speak it, and I certainly don’t think in Greek. So if you don’t speak Greek either, don’t worry, this will all be in English–and coin flips.

Coin Flips

I find continuous distributions confusing to think about. I find it much easier to think of discrete outcomes, and I suspect many others do as well. So I’m going to build a pseudo lognormal distribution with 12 coinflips of:

Heads, up 7%
Tails, down 5%

The chart to the right shows the possible outcomes after twelve flips.

The geometric return of this entire distribution is just the geometric return of our base coin flip raised to the twelfth.

{sqrt(1.07 X .95)}^12 -1 = 10.3%

This game has respectable return properties, fairly similar to the stock market itself from an annual basis. Most of the time you’re going to be happy playing this game.

But Look at That Left Tail!

Look at the returns if you get unlucky and hit tails 12 times in a row. -46% down is bad. Even 11 tails, -39%, is going to sting. Ten tails -31% down is pretty painful too. And 9 tails down -23% is not great either. Now each of these events is rare, but play this game of 12 flips 50 times (50 years), and you are very likely to run into bad luck. You’re going to experience these outcomes. So we can’t just ignore them.

But if you could just ignore these outcomes? What if you could just pretend that all 9, 10, 11, and 12 tails flips are actual 8 tails flips. They would still be losses, just smaller. What’s the geometric return then?

I’ll spare you the math, but now the geometric return of this distribution is 11.6%.

Thats a lot higher!

1.3% more return with no left tail to worry about is a huge benefit. Now we did this shift imaginarily and for free, but what if there was a product that could do this for you? Any product that could provide this return improvement clearly has value. So up to a certain price, you would be happy to pay someone to provide this insurance. Let’s see how this would work.

Geometric Benefits of Tail Hedging

Say you find an insurance salesperson who will cover your losses beyond 8 tails for a price of 1% of the portfolio. The main game still exists, but as an offshoot of the main set of coin flips, the insurance salesperson will pay you for any loss you have beyond 13% (more than 8 tails). To receive this benefit, you would pay them 1% no matter what happened.

Our payout from this insurance contract looks like this:

And when you combine this insurance with the original set of outcomes of the coin flips, the combined outcome of our coinflips and tail hedge looks like this:

This distribution is the same as the hedged distribution above, it’s just been shifted down 1%. Now each good outcome provides a little less return because we have to pay the insurance salesman. But we get a clear benefit from this shift.

From the investor’s perspective, the tail hedge has increased our compound growth rate, decreased our volatility, decreased or largest potential loss, and increased our Sharpe Ratio. We get to sleep a little better at night and we get a little bit higher long term compound growth rate.

This is clearly a great deal for us. Repeat this gamble by rebalancing (repurchasing) the tail hedge after each set of 12 flips and your returns should trend toward the improved geometric return.

If you are going to remember anything from this post, remember this:

Paying for the tail hedge at a good price is valuable to the investor because it increases compound returns, while also reducing the amount you can lose over that timeframe.

That’s why you tail hedge, and at the right price it should help your portfolio after enough repetitions.

But you may be thinking, if this is a good deal for us, is it a good deal for the insurance salesperson?

Insurance Salesperson Perspective

The salesperson’s return table looks like this:

There a few very interesting points here.

1. The arithmetic return is positive. This means they should make a profit selling us this insurance. At this price, there is something in it for them.
2. The geometric return is also positive if you size it properly.³ So the insurance sellers could make money over time as well.
3. If the return is positive for the salesperson, then that means it’s negative for us. If you compare the original arithmetic return (12.7%) to the hedged portfolio (12.6%) you see it’s gone down. The insurance is going to cost us money.

But as we saw above, the insurance helps our portfolio. It provides us with a higher compound growth rate, lower volatility and smaller potential losses.

So the tail hedge helps both the buyer and the seller. It’s a win-win situation.

Hmmm, where have we seen this set-up before?

Proper Options Prices Create a Form of Cooperation

Both sides are getting a benefit from the tail hedge. The insurance salesman has small edge of 0.1%, and the investor has improved their compound growth rate by 0.3%. The trade benefits both parties.

This tail hedge is a version of cooperation. It’s another example of the Farmers Fable in real life, which shows that two parties working together can increase their individual compound growth rate to a level higher than either one can achieve by themselves.⁴

Tail hedging fits right in with the key themes of this blog, namely rebalancing and focusing on the geometric return.

Why Doesn’t Geometric Balancing Use Tail Hedges?

If tail hedging is so great, why don’t I use them?

Tyranny of Choice.

Well first, this example is simplified. Real life options have an enormous number of variables.

How far into the tail do you want to purchase the insurance? We did 9 tails and beyond in this example, but why not 10? Why not 7?

How long a period should you purchase the insurance for? We decided to buy insurance after 12 flips? Why not 6 flips? Why not 20 flips?

Should you wait until the end to settle up like we did? What if you could sell someone else your insurance contract if the first 4 flips are tails (indicating the chance of it paying out has increased).

Why buy enough insurance to cover the exact loss beyond 8 tails? Why not buy enough to cover twice the loss beyond 8 tails. Why not buy enough to cover half the loss?

Oh, and markets aren’t discrete distributions, so the math is more complicated than a set of coinflips. And returns aren’t lognormal either. Nobody really knows what the distribution will be in the future. Everyone is guessing. So how do you properly value the insurance in a world where you don’t even know the likelihood of each outcome?

Tail hedging in real life is really complicated.⁵

Price Still Matters

More importantly though, tail hedges have to be priced right. Too expensive and you aren’t helping your compound growth, you are just padding your insurance salesman’s pockets. The hedges wont work if they are too expensive.

The market is no fool, and plenty of other people have realized the great benefit of removing the left tail. So the prices of this insurance are often bid way up (we’ll explore this further in a future post).

If the market was a series of coinflip games I could figure out when this insurance is too expensive. But because real life tail hedges are much more complicated, I haven’t figured out how to properly value a tail hedge.⁶ So I’m still just studying tail hedging for now.⁷ Therefore please don’t take this post as a recommendation to go out and start purchasing tail hedges yourself if you don’t know what you’re doing.

But hopefully you now know why tail hedging priced properly and sized properly can improve your portfolio. Tail hedges perfectly fit into the ideas this blog promotes. They attempt to improve the compound growth rate through a reduction in portfolio volatility. In many ways they are the ultimate expression of the power of the geometric return.

But only at the right price.

Footnotes:

1-Although I don’t think many people truly have figured this out.

2-I really dislike how options and all things options, and all things related to “tail hedges” are always discussed in Greek. In my opinion this lingo prevents many others from grasping the concepts, which in theory aren’t really that complicated.

The best Rosetta stone for translating between options lingo and English is Kris Abdelmessih and his blog moontowermeta.

3-I assumed here for the geometric calculation that total investable amount was the same for the insurance salesperson as it was for the investor. So 1% to the investor means 1% for the salesperson means the same thing in terms of the geometric return. Clearly the insurance salesperson has to have cash on the side to cover the payouts if they hit.

The more and more I’ve looked into it though, I think it might be easier to be the insurance salesman than the one buying the insurance contracts. But right now, I don’t plan on getting into either world.

4-Tying back to Ergodicity Economics, this is the same effect found by Ole Peters when he looked at traditional insurance.

5-Honestly, I’m shocked at the number of amateurs on twitter who seem to get into options and think they are going to make respectable returns.

6-I’m not sure many professionals have either, but that’s another topic.

7-Tail hedges are also very unforgiving in terms of portfolio construction. I’ll explain what I mean by this in a later post, but if you want the story now, go to minute 55:40 of this interview with Jeff Malec of RCM Alternatives.

Also for some of my deeper views on tail hedging see this twitter thread.