Law of Large Numbers In Deep Value Investing
The law of large numbers is a concept borrowed from the field of statistics and probability. The idea is that within a large sample size, a statistical mean can be deducted from a population of events. What is that population? In statistics, the population is the number of events of interest to an experiment. For investors like me, events of interest to me include my portfolio of deep value stocks and how much I can reasonably earn on a net net and/or deep value portfolio re-balanced annually and eventually figure out what are the expected returns observable from such a portfolio.
However, to attain a statistically significant mean from a population, you would need a large number of events in order to draw statistically significant conclusions. And that is where the law of large numbers come into play. As a statistician, you would want the sample size to be as large as possible. Think about 10 coin tosses. One may get a skewed result of 20% heads and 80% tails. But in a sample size of say 1000000 coin tosses, a mean of 50% heads and 50% tails would be the likely result.
And as investors, that is what we are trying to do. We want a achieve a certain “mean” in our results and that is likely to come from a large sample size. Hence, we use the law of large numbers to do that. We want as many events of interest as possible. As investors in deep value stocks, we want a large number of stocks, which is akin to saying that we want the law of large numbers to work for us.
One of the reasons why we would like to use the law of large numbers is because we know that over any given amount of time, some of our stock picks will go wrong. But we don’t want to be affected by it too badly. We expect that and hence, diversification solves that problem.
I have spoken about this as a phenomenon called gambler’s ruin. Basically, you want to outlive bad luck and live again to fight another day. That is what this is about.
So with regards to net current asset value investing, we have a situation where if you can assess a stock with certain criteria, (do check out my checklist for selecting net current asset value stocks), especially for amateurs in investing, take care that you do not suffer from the unfortunate situation of gambler’s ruin. So gambler’s ruin can occur when you bet too much on a few and if bad luck hits you, you lose your entire portfolio.
Expected Returns Goes Beyond Simple Probability
So what you want to do is to actually get as many trials/investment attempts as possible. And each of these attempts should have a positive expected return so that one can actually earn money. Statistically, if an investment has a negative expected return, it is improbable to earn money. Just go to a casino and spend a day gambling and you understand what I mean. In all likelihood, one would have lost money because the edge is with the casino and not the gambler. In other words, the casino’s rules are designed to give the casino a positive expected return. Just to give you an idea, we look towards the game of roulette. There is a 1 in 38 chance of winning.There is however a 37 out of 38 chance of losing. For every dollar bet on a roulette wheel the maximum payoff is $35 and the maximum loss is $1. Decent risk-reward ratio one might say but when you consider the probability attached to the payoffs, you get what you see below.
Expected Return Of A Roulette bet:
(1/38)(35) + (37/38)(-1) = -0.526
The expected return of a roulette is negative. It is nearly impossible for a gambler to win on a roulette in a great number of trials. So an investor or a gambler needs to consider payoffs as well as probability in investing and gambling in order to earn a return on investment.
Let us bring that concept back to net current asset value investing. The stocks that we purchase are trading at prices below the liquidation value, and if you can find those that will not just survive but also recover in terms of earnings, dividends and a return to positive cash flows, you encounter a scenario with a high payoff. And also, as you get better at picking net net stocks, you may increase the probability of these stocks getting a positive return. When you maximize expected return on each individual stock, your entire portfolio is affected – positively. That is because expectation is additive in statistics.
Expected Return Of A Portfolio
E(X1 + X2+ ….Xn) = E(X1) + E(X2) + ….E(Xn)
So the idea is to make a series of bets that have a net positive expectation. As number of trials increases, the law of large numbers converge the ratio of success to failure towards the expected result. The expected result is a positive return on investment.
Ben Graham & The Margin Of Safety
If you look at what Ben Graham practiced with his net current asset value portfolio, you will find that he believed in diversifying and that is basically the law of large numbers at work. And also, he insisted on a margin of safety. Without that margin of safety, there is no way to get a positive expected return on a net net portfolio. And the other thing is that if you know how to select the right stocks, you can get a hugely positive expected return in each stock that you select and that will affect the outcome of your investing results. Hence, a margin of safety is necessary. If you want to know more about how the margin of safety ties in with positive expectations, please look at another article which I wrote here.
So the numbers make sense statistically. These are the concepts that we can borrow from statistics. But, in net current asset value investing, there is a psychological element to it as well that can make or break an investor. I know this because I have lived through this and still continue to do so. Imagine a company losing money and most times, you really have no idea as to when it will continue making money and become profitable. In such an instance, I can tell you that most investors will be in avoidance mode. Investors typically want to see high earnings growth, positive earnings and good financial results from companies. There is nothing wrong in that. But poor investing results go hand in hand with a competitively bidded up stock prices. And most times, investors overpay for such stocks which is really a situation without a margin of safety and without positive expected returns.
That is also the reason why I have written in my books and in many of the articles on this site here that one really has to conquer to psychological urges within ourselves in order to do well in investing. This is not to be taken lightly if you want to be a good investor, producing market beating performances. There is not much more I can say for this little article on statistics. But I am sure you can see how it is all interconnected. The margin of safety is connected to expected returns and the law of large numbers is connected to overcoming the overconfidence bias and producing an overall gain in ones portfolio.
Thank you for reading. As always, may you be blessed with prosperity, health and happiness!
These books which I have written are case study driven and discuss strategies, mindsets and situational approaches to employing the net current asset value strategy.
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