Drawdowns Done Two Ways

Est. Reading Time: 10-12 Minutes

“They shouldn't even call it insurance. They just should call it ''in case sh*t.''

l give a company some money in case sh*t happens. Now, if sh*t don't happen, shouldn't l get my money back?”

- Chris Rock, 99’

Our typical opinion of insurance is influenced primarily by those forms being required of us by law such as driving a car OR when our downside loss is so great its utility is not questioned such as life insurance.

Although somewhat skewed by the requirement by law or your lender, the approximate percentage of Americans with various forms of insurance are as follows:

Health – 91.4% Life – 54.0% Home – 85.0% Car – 87.0%

If we held the costs of these coverages static but removed the legal requirement to carry it the percent of participation probably wouldn’t drop too much in aggregate. There would be some reduction, but the bulk would likely come from the uninsured drivers category.

The point is this, when it comes to risks affecting life, limb and our general comfort we seem to inherently understand the value of insurance. We may not like it, but we realize that the loss associated with a potential health, house or vehicle mishap can easily be greater than our earning potential to dig our way out of it.  

However, things seem to get reversed when we make investment decisions.

While there are many sentiment indicators and surveys on what participants in the market are thinking, perhaps the quickest way to gauge the opinion of the need for investment insurance is in the amount of margin debt investors are willing to take on.

Margin can be thought of as the anti-insurance. Rather than minimize our loses it exacerbates it. It should follow that the more margin debt you are willing to shoulder the less afraid of drawdowns you must be.

Looking at the red columns in the chart, which turn negative the more margin debt investors hold, it would seem that investors have not felt the need for too much insurance for some time now….Stocks only go up after all.

I can’t argue with the sentiment. Of the various forms of non-specialized insurance, they are all expensive.

Let’s take a look at buying puts (the right to sell a share back at a predetermined price regardless of how low it goes) and shorting credit risk (benefiting if fixed income goes bearish). Both of these are somewhat simple and binary forms of pure downside protection in the public markets.

For those who love white papers, The Best of Strategies for the Worst of Times: Can Portfolios be Crisis Proofed? is a great examination of a few popular methods of hedging downside risk (i.e. investing insurance).

For those who don’t need a sleeping aid, the highlights as it pertains to Put Contracts and Shorting Credit Risk are as follows:

• Puts are 100% effective in protecting against downside risk during drawdowns

• Average annualized returns were a disappointing (7.4%) despite an average gain of 42.4% during drawdown periods

• Shorting Credit Risk is also 100% effective during drawdowns

• While better than buying puts, shorting credit risk still returned a lackluster annualized return of (3.6%) across all time frames

The overall negative yield of buying puts and shorting credit shows that over the long run it is a losing strategy, and it is no secret that the people selling puts are the ones making all the money.

In fact, since 1996 you’d have to find puts priced at roughly one-third their historic averages before it reached a breakeven payoff expectation over longer time horizons. So, it’s no wonder insurance in the investment world is bemoaned and used sparingly.

But perhaps the investing world, and possibly you, are thinking about insurance and risk all wrong.

To explain we will need a refresher on mathematics.

Geometric Average, the Ugly Cousin of the Arithmetic Average

In a popularity contest of use, the arithmetic average typically gets all the praise. It is a bit tidier for how our brains view the world. It is what we are referring to when we use the term average as a standalone.

When I want to know the average run time for all six movies playing at the theatre tonight, I’d add up the run times of each movie and divide by six. Simple and easy to understand.

For more complex or growing systems whose changes influence the next data point (i.e. what if the addition of a seventh movie to the roster was influenced by the characteristics of the first six?) the arithmetic average comes up short. It is a singular frame of time or a static data set.

For that scenario we need to introduce the logarithmic function, which you can thank the Babylonians for discovering.

The logarithmic function allows for the mapping between multiplication and addition. If you add (subtract) the log of two numbers, you will get the log of their product (their ratio); divide the log of a number by n and you get the log of the nth root of that number.

The mechanics don’t really matter, what’s important is knowing that it gives us a way to represent an expected value or average of all potential outcomes of a system through a simplified equation. That is, outcomes that depend on the previous outcome(s).

Enter the Geometric Average. It is a clean way of leveraging the logarithmic function.

Stated as an equation: ( Outcome1 x Outcome2 x Outcome3 ) ^1/3

Unlike the Arithmetic Average, where we added everything and divide by the number of occurrences, to get the geometric average we must multiply and then scale the product back down to a uniform size.

In the case of a portfolio over time, one in which we can reinvest the proceeds, the geometric average is simply the equivalent of all potential ending values expected outcome.

This is the lens through which insurance should be viewed.

An Explanation via Two Merchants

Borrowing from Mark Spitznagel’s book Safe Haven, we’ll use an example of two young merchants entering the business of high seas trade.

We’ll call them Arithmetic Adam and Geometric Greg.

Each are starting with initial capital of $3,000 and will incur costs of goods sold (including shipping costs) of $8,000, which will be borrowed using the goods being shipped as the collateral.

For each shipment completed, they can expect to receive $2,000 of profit, or revenues of $10,000. This comes out to a gross profit of 18% (($3,000 + $10,000) / ($3,000 + $8,000)).

But, no business is without risk, and let’s assume their only risk here is the ship sinking, which occurs 1 out of every 20 trips for a probability for total loss of 5%. This is apparently a treacherous route.

As they are in the same business, they are both quoted a shipping insurance policy of 8% the value of cargo, or $800 ($10,000 x 0.08).

Adam, understanding how to calculate the value of a single wager, astutely takes the probability of loss (5%) and correctly calculates the loss expectation as (0.05 x $10,000) = $500. In Adam’s eyes this is a bad bet since he will be paying $300 more than his expected loss, and he passes on giving the insurance agent any of his hard-earned money. Adam is no sucker after all.

However Greg, aspiring to be in business for a very long time, calculates the risk of loss as the geometric mean of expected returns.

Greg understands that the arithmetic losses are an illusion, existing only in a singular instance that does not have to contend with time. While adding a zero to the average of returns does not pull it down all that much, in the course of business it would be devastating to incur a total loss.

Greg gladly pays for the insurance each and every time a ship goes out.

The flip side of that 18% return above, is a loss of 73% if the ship were to sink without the backstop of insurance. ($3,000/$11,000 = 0.27). Here our merchant is back down to his original capital balance, so he is down, but not out. But not being out of the game is not much solace when considering what it takes to get back to even.

To come back from a loss of 73% a gain of 270% would have to be achieved. This is true regardless of when this loss occurs in a compounding growth system.

So with the potential gain, insurance cost, and potential loss laid out, each scenario expressed as a geometric average would look like this:

Uninsured:

 [ (1.18)^95 x (0.27)^5 ] ^(1/100) = 1.098 or 9.8%

This is the gain of 18% on ninety five trips, compounded along with the loss of 73% on five. While the typical trip will net 18%, the effect of a large loss, even a few times, pulls Adam’s compound rate to almost half the per trip profit.

Insured:

($12,200 / $11,000) = 1.11 or 11.0%

With no risk of total loss, Greg’s return is simply the expect per trip profit minus his insurance expense.

Adam can expect to grow his wealth at the rate of 9.8% per shipment without insurance (i.e. lots of risk) while Greg will grow his wealth at a rate of 11.0% with no risk.

A look at the two graphs visually shows the effect of these two approaches. Not only is Greg compounding more effectively, but should Adam incur a loss (shown here occurring on shipment number 10), it is impossible for him to catch up to Greg unless he can materially increase the per trip profits from that point forward.

You might say a solution here would be for Adam to never increase the size of the shipment as shipments are completed. So long as you can get beyond a few shipments without loss this would indeed allow for a buffer to absorb the drawdowns and the arithmetic average might hold truer to that situation.

But, if Adam followed that strategy, he would not only be growing at increasingly lower rate (relative to his growing capital base) but in the real world he would likely get pushed out of the market by Greg’s now sizable shipping conglomerate.

While these numbers are a simplified representation of a mathematical principle, the idea to take away is that your insurance policy may not be as expensive as you think. This does not have to manifest itself within your portfolio as complicated beta neutral strategies or opening a futures account, simply not taking on investments with more downside than upside is a form of insurance.

To round off, take a look at a graphical representation of the effect of missing the ten best days in the market.

This is often touted as the clear cut evidence of why you should never sell. However, invert that and look at the even greater effect of avoiding the ten worst days in the market. While predicting any of those twenty days is impossible, it would seem some thought to avoiding a bit of downside may pay more dividends then trying to grab all of the upside.