Yes, You Should Gamble (Sometimes)

A few years ago, I transferred-in an account for a client. As I looked through the positions to prepare recommendations about which positions to sell and which to keep, I noticed a handful of penny stocks. Actually, to call them penny stocks would be an exaggeration. They were each worth fractions of a penny and, of course, only traded over-the-counter.

I assumed that these were positions-gone-bad—stocks that had fallen far from grace, trophies to amateur overconfidence. I called my client to discuss removing them.

“…Oh, and one more thing. I’ll send you a form to remove these stocks from your account since they don’t trade and aren’t worth anything.”

“What?! No, don’t do that!” was his urgent reply. “Those are my lottery tickets! I put about a hundred bucks into each of them and I want to see if they pay off!”

I chuckled. “Alright, no problem, we’ll leave them, but I’m not going to follow them, okay? Just let me know if you change your mind.”

I didn’t know it then, but I gave him terrible advice that day. In fact, I should have been the one to tell him to put some money in those micro-penny stocks.

* * *

Before you excommunicate me as a heathen, at least hear me out. Let’s take a step back and remember where the advice “never gamble” comes from.

A standard utility function taught in the CFA Program curriculum (sometimes called quadratic utility) determines an investor's happiness from her portfolio's expected return, minus the variance (volatility) of those returns, times her risk aversion parameter. The more averse to risk, the more unhappy she is with variance (volatility).

In this model, all else equal, higher volatility is always bad. In this model we would never expect an investor to choose a high volatility, low-return portfolio (i.e., a gambling portfolio) when low-volatility, high-return portfolios are on offer. We have this expectation because this model assumes that the thing our investor wants to avoid is volatility.

By contrast, goals-based theories of choice take a different approach. Rather than define risk as volatility, goals-based utility defines risk as “not having the money you need when you need it,” to quote my friend Martin Tarlie. Risk, in goals-based investing, is not volatility, but the probability that you fail to achieve your goal. 

Running with this more intuitive definition yields some surprising results because it changes the math of the portfolio choice problem. We move from an equation in which return and volatility are the only two variables, to a probability equation of which return and volatility are inputs, but not the only inputs.

All the variables which define our goal (minimum wealth level, time horizon, current wealth, etc), are also inputs in the probability equation. Lastly, when we remove the inexplicable academic assumption that investors can borrow and sell short without limit, then we find that the efficient frontier has an endpoint, the last efficient portfolio.

Here’s the catch: sometimes, investors have return requirements that are greater than what the last efficient portfolio can offer. When that happens, her probability of achievement is maximized by increasing variance rather than decreasing it, even if returns are lower.

And so we enter the world of rational gambles.

Rational gambles are those portfolios to the right of and below the last efficient portfolio, but for which the probability of achievement continues to rise. Irrational gambles are those for which the probability of achievement begins to fall. The plot below illustrates the point.

It has taken me some time to come to terms with this, professionally. Indeed I first wrote about this unavoidable point in these very pages, but I skirted the details for fear of the implications. It is those details which are the subject of my latest paper, soon to be published in the Journal of Investing,[1]. The paper takes a deep dive into when and how gambling is rational (the plot above is pulled from that paper).

What I find—and this part is a small surprise—is that gambles can be rational or irrational, depending on the circumstances. More surprising: whether a gamble is rational or irrational is not determined by the characteristics of the gamble itself, but rather by the goals of the individual considering it.

In other words, what may be a rational gamble for you may be an irrational gamble for me. More confounding yet: what may be a rational gamble for one of your goals may not be rational for a different goal.

Goals-based investing is wildly – and frustratingly – individual.

I find this surprising because we have been taught by orthodox economics to evaluate investment opportunities in a vacuum. If Apple is a good stock, for example, then it is a good stock for anyone (with sufficient risk tolerance). If Bitcoin is an irrational investment, then it is an irrational investment for everyone.

However, goals-based investing teaches us that investments are just tools to get a job done. We must have a thorough understanding of our tools, of course, but in the end, the job we’ve been asked to do is what dictates which tool we reach for. In that way, orthodox economics is wrong: investments must always be evaluated in the context of an investor’s goals.

Any practicing financial advisor has direct experience with investor willingness to trade away return to increase volatility. How often do clients buy penny-stocks as lottery tickets (as mine did!) while fussing at us because their retirement account is down 8%? What financial advisors may be surprised to hear is that this is a perfectly rational thing to do. When risk is defined as the probability of failure, there are times when increasing volatility is rational, and times when losses can be excessive.

So what does this mean to professional financial advisors and money managers? Should we recommend a client jet to Vegas and put half her retirement account on Red? Of course not (well, probably not). Yet, we cannot avoid the conclusion from the math: high volatility, low return “investments” can have a place in goals-based portfolios.

Perhaps, at a minimum, we should curb our first-judgement of high-volatility trades favored by some retail traders. A good next step may be to open due diligence on some “gamble-like” portfolios, with a full understanding of when and for whom they would be appropriate. I admit this is difficult for me, having been raised in the orthodox “gambling is stupid” mindset. Yet, it is what the math says to do.

What the math also makes clear, however, is that gambles are not all about volatility; expected return matters, too. Every goals-based portfolio will have its own rational tradeoff between return and volatility—a marginal rate of substitution. While we should sometimes gamble, we should gamble carefully and calculatingly, never wildly.

* * *

Fast forward about four years. I am headed to a lunch and this client calls me. He asks if I have seen one of those penny stocks he refused to get rid of that morning. It got caught up in the SPAC craze and went to $1.80, he tells me. He has over 400,000 shares. In his Roth IRA. Meaning he just made over $700,000 from a $100 “investment,” and it is completely tax-free. If I hadn’t seen it myself I would have dismissed the story as another unlikely water-cooler story. Or maybe one of those one in a million gambles that just happen to pay off.

What I know now is that my client was right. Gambling is, sometimes, perfectly rational. 

References
[1] Parker, F.J. (forthcoming) “Yes, you should gamble (sometimes).” Journal of Investing