Variance and Investing

One of the best things to come from my career as a professional gambler is a deep unconscious understanding of risk, odds, EV, and variance. The downside to this is that I see people make fundamental errors all the time, especially in investing, and it really bothers me. Usually I notice these errors not because I know whether they should invest in a particular thing or not, but instead because I see that they are investing for the wrong reasons. Most of these errors stem from a fundamental misunderstanding of the relationship between EV and variance.

Investing and gambling are the exact same thing. The difference between casinos and the stock market is that in the long run the casinos will win by a little bit and in the stock market you will win by a little bit. For my examples I will use betting, because it’s a little bit clearer, but the principles and effects are the same in investing.

Imagine that I offer you a bet. The bet is that we flip a coin, and no matter whether it’s heads or tails, we exchange no money. Not much of a bet, really. The EV of this situation is exactly zero, because even if we do this “bet” a million times, you will neither gain nor lose money. The variance is also zero, because your tally of how much you’re up or down will also never change.

Now Imagine that I offer you more normal bet, where we flip a coin and if it’s heads I give you a dollar and if it’s tails you give me a dollar. The EV of this bet is also zero, because in the long run we can expect you to have the same amount of money as when you started. It is higher variance, though, because at any given point of time you may be up or down by some amount.

If we up the ante and make it $100 per flip, the EV is still zero, but the variance is now VERY high.

Imagine that no one really understands EV or variance, but that all of them are choosing one of these bets to do every day. Someone doing the bet where nothing changes won’t think of himself as a winner or loser. Someone who happens to be up in the second one, due to variance, might believe that he’s a good gambler. Someone who happens to be down in that same bet might feel like he’s unlucky. Someone who happens to be up in the last example may feel like he’s a great gambler.

A good investor is looking for EV at the lowest variance cost. EV, or expected value, is just the amount they can expect to gain by investing. It makes sense that we would want to maximize that. It also makes sense that we would typically want to minimize variance. It’s hard to make future plans if we have no idea how much money we’ll have in the future. Lower variance makes that band of possibility narrower.

The reason people choose broad index funds or a balanced portfolio is for this very reason. It is the proven way to capture the most EV at the lowest “cost” of variance.

There are also people who choose individual stocks. They believe that they are capturing EV, but they are not. They are capturing variance.

Imagine that there are two people. One thinks that Gamestop is absurdly priced and decides to short it. The other decides that it’s going to go higher and buys it. The first thing that neither is considering is that the price is what it is for a reason, and that reason is that the price encompasses the average of all predictable possibilities.

If Gamestop goes up, the person who bought it will think that they are a good investor. They have beaten the market, which is considered to be impossible! However, what is more likely, that they knew something the entirety of the market did not know, or that they happened to be lucky and be on the positive side of variance? Well, considering that 50% of all people will be up… it’s almost certainly variance.

Variance is such a likely reason for success in stock trading, that it must be assumed to be the reason unless you know exactly what your edge was.

The first guy to realize that Gamestop was subject to a short squeeze had a legitimate edge. The early people to read his theories before wall street caught on may also have had a legitimate edge. By the time hedge funds were talking about Gamestop, all further wins and losses were due to variance.

There’s on additional layer to think about, though. Not every dollar is equally valuable in terms of utility. If you give five dollars to someone who is starving and standing next to a McDonalds, he can derive a lot of practical utility out of that five dollar bill. If you give five dollars to Jeff Bezos, it has utility approaching zero.

In your own life, this is also true. Imagine that you were on the verge of bankruptcy because of a $10,000 debt that had to be paid, and you only had $500. If you bet it all on one number in roulette, which is a strictly negative-EV move, it may actually have a positive EV for you. If you lose it doesn’t matter because you were going bankrupt anyway, and if you get lucky and happen to win, you don’t have to declare bankruptcy.

If you need a life saving medical treatment and only have half the money necessary… maybe you’d bet it all on one coin toss because you’d go from a 0% chance of living to a 50% chance.

If you’re working a job with no sign of being able to retire, you might want to take on more variance just to give yourself some chance to retire early, at the cost of having a slightly lower quality of life if you lose.

Any investment other than a risk-free investment or very safe index-fund based portfolio will be higher variance. In order to accept that higher variance you must either have a defensible explanation for why it is higher EV, or you must have a reason why variance will help you. If you don’t, stick to safe investments.


Photo is a Maui sunset.

No tea time this week, sorry!






4 responses to “Variance and Investing”

  1. Dan Avatar

    Interesting post.

    What is your favorite stats book?

  2. Reader Avatar

    > If you give five dollars to someone who is starving and standing next to a McDonalds, he can derive a lot of practical utility out of that five dollar bill. If you give five dollars to Jeff Bezos, it has utility approaching zero.

    > In your own life, this is also true.

    I’d argue these are different, and the first claim is wrong. It seems intuitive and many economists claim that $5 don’t mean as much to a billionaire as to a poor man, but the Austrian school of economics argues this is a nonsensical claim.

    You can claim that you prefer $5 to a hamburger, but it doesn’t make sense to say you like $5 more than I like $5. Does it make sense to say you like your grandmother more than I like my grandmother? It’s not wrong, it’s just nonsensical. You cannot compare interpersonal preferences.

    You can compare intra-personal preferences – maybe you like your grandmother more than $5.

    1. Tynan Avatar

      I think it’s pretty uncontroversial to say that the marginal value of money decreases as you get more.

      1. Reader Avatar

        Sure, but that doesn’t translate to other people who have more. That’s what I mean by inter vs intra personal comparison of preferences.

        Do I like the color blue more than you like Chipotle? What does that even mean?

Leave a Reply

Your email address will not be published. Required fields are marked *