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« Alpha Theory 2018 Year in Review | Main

March 01, 2019

Your Position Size is Wrong: A Plea to Put Down the Mental Calculator


Hedge funds throw away half of their potential returns by not explicitly calculating probability-weighted return. After working for a fund and having numerous conversations with hedge and mutual fund managers over the past decade, it is obvious that an overwhelming majority of funds’ mistakes come from poor estimation of risk-reward. In fact, most funds have not explicitly defined an upside price target, downside risk target, and conviction level for each investment in their portfolio. This is because most fund managers trust that they can manage the portfolio in their head. They analyze and discuss the upside, downside, and conviction level for every investment, so they assume these factors’ influence is carefully measured into every decision. But I would posit that there is a distinct difference between factoring in upside, downside, and conviction level through mental calculation and measuring it with probability weighted return. Why would you trust your mental calculator for such an important decision? Could you imagine a bungee jumper that knows the height of a bridge, tension of the bungee cord, and weight of the jumper but just estimates the correct length of the bungee cord? Absolutely not. For every jump, a calculation is performed to make sure that easily avoidable risk is eliminated. Investors all too often skip the “bungee cord” calculation of probability weighted return and end up assuming undue risk.


Empirical research and common sense prove that probability-weighted return is the optimal method to measure an asset’s quality. But most firms do not use probability-weighted return because it questions the output of their mental calculators. Researchers in Behavioral Finance and Neuroeconomics have cautioned investors for over 30 years that their brain is poorly designed to make financial decisions. Armed with this knowledge, investors still do not adjust their process to eliminate known decision-making frailties. In most cases, these shortcomings can be eliminated by calculating a probability-weighted return for every investment.


A quick example from a meeting with a portfolio manager highlights the problem of not using probability-weighted return. I was working with a successful fund manager when I asked for the logic behind the largest position in his fund. He told me that it was a company that he knows well, and he is sure they are going to beat earnings. I asked for his upside target if they beat earnings and the probability of it occurring. His best estimates were a profit of 10% and a probability of 90%. I then asked him to explain what would happen if they did not beat earnings. He described a dire scenario where the stock would be down at least 20% because the Street was expecting a beat. I quickly took his estimates and calculated a probability-weighted return of 7%. This caused the manager to change his exposure to the relatively weak idea. He had all of the correct information in his head, but his mental calculator was being corrupted by his over-confidence in his thesis. If this happened with the largest position in the portfolio, you can guarantee that there are other inefficiently sized positions. 


It is all too common that funds perform the intense research to drive the ball 99 yards down the field but do not “punch it in” by explicitly defining upside profit, downside risk, and probability. Probability-weighted return takes into account the full breadth of your fundamental research and creates a discipline that treats each position like it is brand new every day and performance-draining oversight is eliminated. As you can see from the example, calculating probability-weighted return is easy and only requires that the firm explicitly define upside, downside, and probability and then compare the probability-weighted sum to the current price. 


Once you calculate a probability-weighted return for every investment in the portfolio, you will quickly point out position sizes that do not match your research. Probability-weighted return becomes the synthesis of your research, the common vernacular of investment discussions, and the anchor for decisions.  Your portfolio generates greater returns because you are continuously improving the portfolio to give more exposure to the firm’s best ideas while constantly pruning the weakest. Return is only half the equation. A portfolio constructed with probability weighted return has considerably less risk. Every decision is now made in the context of downside potential. If the downside risk increases, the probability-weighted return falls, which in turn lowers the position size.


The benefits of probability weighted return position sizing are profound and because the process is based on common-sense and sound math, it will become the de facto standard in the coming years. Some of the brightest fundamental managers in the world have been utilizing this discipline for years and your firm can capture the benefits of probability weighted return in as little as a few weeks. Make a commitment to put down the mental calculator and you are guaranteed to make better decisions.