In Jeremy Grantham’s 2017 third quarter letter, he posed a question: What should you do if you are tasked with managing Stalin’s pension portfolio? The specific scenario he painted was that Stalin has ordered you to achieve inflation plus 4.5% on his pension assets over the next decade. If you succeed, you get a nice dacha on the Black Sea and a pension of your own. If you fail, you get shot. It is an entertaining problem set-up, and for the more quantitative among us, leads to a refreshingly simple utility function – maximize the probability of meeting or beating the target return. But if Stalin actually had any intention of living off of his pension, it is a lousy ultimatum to give his chief investment officer (CIO). It completely ignores the impact of magnitudes, and magnitudes matter. Barely missing the goal and achieving 4.4% above inflation is importantly different than returning 15% below inflation, and for Stalin, they are the same – failure. But Stalin may be on to something… just not quite the way he originally intended.

It is hard to imagine why any individual or institution should want an overall portfolio managed in as high-risk a fashion as Stalin’s pension implies, but it might make sense to hire a number of managers who do act that way. While I admit that I haven’t come across any managers who actually think about things quite the way Jeremy does in posing the Stalin problem, there is a class of managers who manage their portfolios as if they were solving that problem. They are the concentrated, high tracking error, “high conviction” managers that have gained a significant following, particularly in the endowment and foundation universe. So should you hire that type of manager? It depends. Hiring such managers only makes sense if you think you are good at identifying talented active managers, of course. But just as important and somewhat less intuitively, it also requires that you are significantly better than the average CIO at avoiding the performance chasing that traditionally accompanies the firing and hiring of managers. If (and only if ) you can meet those two requirements, a portfolio built from a number of Stalinesque pieces will give you higher returns without much downside in the form of greater volatility or tracking error. If you can’t meet both requirements, such aggressive managers are more likely to hurt you than help. In GMO’s asset allocation group, we historically haven’t run “Stalin-style” portfolios, but for clients who believe they meet the requirements to handle them well, we would be happy to discuss whether we could put together a portfolio that would make sense for them.

What does Stalin make you do?
I’m going to change Jeremy’s framing of the Stalin problem slightly to make the analysis a little simpler. Rather than frame it as a total return, I’m going to look at it in relative return terms versus an ownable benchmark.1 Let’s frame the Stalin problem as maximizing the likelihood of outperforming a benchmark by at least 3%. While 3% alpha doesn’t seem like an exceedingly high target level for a “Stalinesque” portfolio, the reality is that under almost all circumstances, the portfolio that maximizes that probability will have an expected alpha significantly higher than 3%. This may sound a little weird, but it becomes clearer when you think about it. If you run a portfolio targeting an expected alpha of 3%, you should have a roughly 50% chance of achieving 3% or higher alpha. If you run a portfolio targeting an expected alpha of 7%, your chance of achieving or exceeding 3% alpha is almost certainly higher than 50% – you could underperform your alpha target by up to 4% and still achieve 3% alpha. The probability of achieving at least a target return is a function of both your expected alpha and your volatility, where higher alpha is good and higher volatility is bad. Exhibit 1 shows an efficient frontier with a “normal” and Stalin version of achieving 3% alpha.2

The portfolio to the lower left is the “normal” way of thinking about achieving 3% alpha. It is the lowest tracking error portfolio that has an expected alpha of 3%. It has a tracking error of 4.4% and an information ratio (IR) of 0.68. The portfolio to the upper right is the Stalin version – the portfolio that maximizes the probability of achieving at least 3% alpha. It has an expected alpha of 6.9%, and a tracking error of 13% for an IR of 0.53.