Scaling Into Positions: The Anti-Martingale Strategy Applied to Value Investing

One of the consequences of using a volatility based position sizing strategy (we use the risk parity method) is that for highly volatile stocks, you may start out with a very small initial position. However, the level of undervaluation in the stock may call for a larger position to be eventually established.

This may lead you to wonder if the philosophy of value investing precludes us from using these portfolio optimization strategies.

Not at all. This indeed creates a conundrum, but it is easily fixed.

What is the Anti-Martingale Strategy?

Please note that these terms come from gambling and we are borrowing these concepts to use it in investing. Investing is similar to gambling but with the right strategy, the investor has an “edge”. Value investing is one of these strategies that creates an edge.

Before we go into this, let’s look at what is a Martingale strategy.

A martingale strategy calls for a gambler to double his bet after every losing move. If the results are random, it is possible that the gambler may endure a string of losses but as soon as a bet wins, he is made whole again.

Martingale strategy works but it requres the speculator to have unlimited amount of capital. There is no telling how long the string of losses can be before a win. I don’t have unlimited funds and most likely you don’t either.

Anti-Martingale strategy works differently.

Here, a speculator increases his bet when he is winning. The idea is to maximize gains when he has a “hot hand”. Conversely, on losing streaks, the gambler will halve his bet every time. This way, he will not be completely wiped out.

How do We Apply Anti-Martingale Strategy in Investing, Specifically Value Investing?

First of all, value investing is not gambling. However the theory is sound, and cross pollination of ideas makes the value investing practice stronger.

From earlier discussion about the risk-parity position sizing method, and specifically if you have read the ebook (greater detail), you will recall that the initial position in any stock depends on its volatility.

We start out by deciding that each position will expose the portfolio to a fixed amount of risk. For example, you may choose to expose 1% of the portfolio value to the risk in the stock you are buying.

(1% risk exposure is not the same as 1% allocation to the stock. The stock allocation will be higher, but the value at risk is only 1%. This is a critical concept to understand, without which any portfolio management strategy will not be complete. If you buy a stock and believe that the entire position is at risk, you are not managing your portfolio correctly).

Thereafter, the volatility of each stock tells us how much of the stock we should hold in the portfolio so the risk exposure is 1% or less (or whatever limit you decide). This way, we will own more of the less volatile stocks and less or the highly volatile stocks.

(Please note that as a value investor, risk is not the same as volatility. Here we are using the typical characterization of risk as volatility. The risk-parity method can be more appropriately termed as volatility normalization method)

The Process

Lets say when you buy a stock, you have 1R risk exposure. You bought N number of shares.

When the stock appreciates, you will move your trailing stop loss and limits with the stock. When your stop is at the price you purchased the stock at, your risk in the stock is now 0.

Any further appreciation, and you will be profitable.

At this point, you can increase your position size by another N number of shares. Now you will own 2N shares.

The first N shares is at 0 risk, the 2nd N shares will have the purchase price of Original purchase price + 1R, and will therefore have 1R risk.

Essentially, you just doubled your stake in the stock while keeping the risk exposure to the original level.

You can double your stake again when the stock price appreciates by another 1R. Now, you will have 4x the original investment, with the same 1R risk exposure.

You can potentially keep on increasing your stake this way (scaling in), as long as the stock price keeps appreciating. You will stop when the stock price goes beyond the intrinsic value of the stock (there is no reason to overpay).

Discussion

1. Astute readers would have realized by now that if the margin of safety is large, we can scale in bigger stake in the stock. At Value Stock Guide, we do not like to allocate more than 10% of the portfolio in any single stock (if it appreciates to higher levels, it is okay). Therefore we will stop scaling in at some point. This is important for us because we do not use margin.

If you use margin (I do not advise it), you can potentially keep on going even beyond a 10% stake. This is possible since your individual stock holdings will add up to more than 100% of the portfolio value.

2. Another thing that many investors might find strange: The strategy advocates buying more as the price rises. Don’t value investors buy more when the price falls? What is this nonsense :)?

I suggest you take a more holistic view of what value investing is. It calls for you to invest when the market price is below the intrinsic value. You will do so with this strategy and you will stop buying once the market value exceeds the intrinsic value. This is no different than entering a position with a small stake and then adding more over time. It is just a more structured process, and is designed to lose you least amount of money over time.

You are potentially giving up some profits in the beginning by not getting the best possible price for as large number of shares as you can. This loss is more than offset by the increased profits by 1) risk reduction through intelligent stops, and, 2) not having to sell the stock as soon as it hits your fair price (we will now let the stocks appreciate as far as they can and get stopped out for exit).

3. Please note that all our discussion of stops imply sufficient liquidity is available. If this is not the case, you should use Stop-Limit orders, or alternatively set mental stops and make manual orders.

Thoughts?