Modeling The Dangers Of Averaging Down

by: Zhiyuan Sun
Summary

Averaging down into a losing trade to lower cost basis is a popular yet potentially disastrous strategy.

It is much easier to "buy more and hope it'll come back" rather than to accept one is wrong and get out.

Most often that not, the strategy appears to work due to the clusters of other speculators "buying the dip" as well.

Yet, in a small number of occurrences, one is really averaging down into a black hole rather than early retirement.

Introduction

Have you ever come upon a stock which seemed like a grand slam home run; did all the required due diligence; did background checks on management; opened a position; immediately have the trade go against you; bought more to average down; only to have the stock dip, and dip, and dip.... for a never ending stream of selloff? Of course, the most prudent action to take in this instance is to simply, take the loss and move on. We make mistakes, and after all, no matter how good our skills are or how well of an education background, the market just doesn't agree with you.

Yet, humans are not psychologically wired to accept our mistakes. The most tempting action to take when our ideas go the wrong way, is to double down. This is more or so evident amongst retail investors, where the most common quotes I've come across are:

"If a stock is a good buy at $40, it is an even better buy if it went down to $8!"

"Shorts are just taking down the stock to buy it at a better price!"

"The more it goes down, the more I buy"

Somehow, doubling down on a losing trade has become a staple of investing due to its tendency to generate a large number of small winners, which in turn creates positive feedback the idea is "working" and the more the profit, the more the investor believes he is right. This article, however, will demonstrate how disastrous this can be, as all that matters and the details. And in terms of the averaging into losers trade, the 5% or less of cases where doubling down goes haywire will have devastating effects on one's investment portfolio.

Methodology

Curated by Author

The author will create the cumulative P&L of averaging down into a losing trade using empirical data on stock indices (namely, the SP500). Assuming the trader will 1) doubles their stake whenever a -10% is drawdown is triggered in any given month and 2) Deleverage and reduce his stake to the original size of x1 whenever the next trade is a winning one.

For this index, the security has 51% chance of going up 1.5% on any trading day and 49% chance of going down 1.5%. The expected outcome of this security is positive, that is, if held for a long time, the investor is guaranteed to make money albeit with significant drawdowns. However, for our strategy, we will assume the investor doubles down every time the index goes down. Below is the result of this empirical simulation over a 2 year period:

Results

Figure 1. Source: Author's Curation

As we can see, the investor was able to develop a whopping +67% gain before a total loss of account equity! To analyze the trade in more detail, here is a more detailed description of differences between the strategy whilst winning and the strategy while losing:

From the chart above, it is evident above averaging down can lead to severe distortions in the investor's analytical abilities, taken at face value. Over 95% of trades result in steady, small, and consistent winners with little or no volatility. These winning trades are so appealing to our thought of generating stable, consistent cash flows that they can easily cause anyone to think they have found the "holy grail" to investing. Yet, all it takes is one big loser, that is, averaging a few times on a losing streak, to completely wipeout one's account equity. For more clarity into this concept, let us look at the P&L histogram of this strategy on a one year period:

Figure 2. Source: Author's Curation

Just as explained above, the strategy creates a gigantic number of small, +1-3% winners and one or two devastating -50% to -100% losses. Adding a distribution curve yields the following:

Figure 3. Source: Author's Curation

This is what is known as a fat-tail distribution

Figure 4. Source: Author's Curation

Figure 5. Source: Author's Curation

Limitations

This model tests an average down strategy derived from martingale betting, a class of strategies popular in 18th century France where the speculator would double down one's bet with every loss taken on a fair coin toss. For my study, investors and traders are assumed to increase their position size by x2 after a -10% loss in any given month. The results of the study could change drastically should these initial variables change, say, increasing position size by x1.5 after a -20% loss in any given quarter, or where the investors stops doubling-down at some point in the process. More tests regarding initial conditions would be a great conversation starter for future articles.

Conclusion

What this chart tells us is, the large number of winning trades for averaging down does not even matter. So long as the investor follows a strategy which involves averaging down, refusing to take his loss (or go short), eventually, and it is only a matter of time, the investor WILL blow up his trading account and take down all of the profits he made with it. This feeling is inevitable, and as we all know, making a lot of money and then losing it all is not the same as not having any money in the first place. Prudent investors should simply accept their loss and move on after a losing trade. After the quantitative data present here, hopefully we can learn to accept failure while we can instead of letting our mistakes snowball into an avalanche.

Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.