### Tiburon Tenets (Part 2): Position Size is based on Probability Adjusted Risk/Reward

"As far as I know neither (Paul) Samuelson nor (Robert) Merton nor indeed Ophir has challenged the basic principle embedded in the geometric mean principle (Kelly Criterion) for long-run portfolio selection. If they or he wishes to adopt a significantly different policy and I follow the geometric policy, in the long-run I become almost certain to have more wealth than they. This hardly seems an erroneous or trivial proposition." – Henry Latane, professor, University of North Carolina at Chapel Hill

"When faced with a choice of wagers or investments, choose the one with the highest geometric mean of outcomes." – John Kelly, namesake of Kelly Criterion

It is impressive to see a firm like Tiburon speak so openly about their implementation of a portfolio management strategy that is profoundly differentiating. See the TabbFORUM article – you'll have to sign up for TabbFORUM if you are not already a member but it is free. I believe the answer lies in Peter Lupoff's, CEO of Tiburon Capital and formerly of Millennium and Third Avenue, quote, "it is my view that very few managers spend any time attempting to define the appropriate sizing of positions to mitigate downside and maximize returns." I have had conversations with over 100 portfolio managers and I can attest that even after proof of impact of position sizing and utilization of risk/reward in position sizing, dogma still causes most to fall back into their heuristic-based methods of portfolio management.

Tiburon's first step in the right direction is, in his words, "Getting a handle on "edge,", we create "base," "best," and "worst" case scenarios, probability weight them, of course." An overwhelming majority of firms do not explicitly define the economic outcome for the asset in their portfolio and even fewer express them in probabilistic terms. This is THE foundation for portfolio decision making. Without a probabilistic expression of risk/reward, the portfolio is left rudderless.

Once you have built a foundation on the rock of probability-based research, the natural evolution is to ask how should I size positions once I have all of this illuminating data? Tiburon builds the portfolio using Optimal F (see TabbFORUM article) and then makes proportional cuts to fit total exposure to a maximum of 100%. Additionally, they add two constraints; 1) maximum of 10% in one position and 2) minimum of 40% potential return. As I have highlighted before, the closed-form Kelly (Optimal F) was not built for portfolio management and has two flaws because it assumes you can invest your entire bankroll in a single bet; 1) it over bets very low expected returns with very little chance of loss and 2) it under bets some good risk-rewards because it doesn't want to inflict permanent damage, which a portfolio helps eliminate by defining a maximum position size (Alpha Theory Kelly blog). Alpha Theory and Tiburon are using the same logic but have mildly different functions for achieving the results. Alpha Theory uses a linear model to size positions based on a geometrically weighted probability-weighted return to adjust for the probability of extreme loss. This eliminates the two problems expressed previously for Optimal F and allows for Alpha Theory to add constraints like liquidity, return threshold, sector exposure, Beta, and portfolio gross / net exposure. Tiburon accomplishes much of the same by constructing the portfolio via "Fitted Optimal F" and searching for and hedging out exogenous risk.

That being said, the ideal way to construct a portfolio is to find the position weightings that maximize the portfolio's geometric expected return. This is not a closed-form solution like Optimal F and requires simulation. It would still be subjecting to the correlation effects that Lupoff mentioned in his article unless you could simulate position level outcomes that were interrelated with the other assets in your portfolio. Tiburon's and Alpha Theory's closed-form solutions are not perfect but they are lightyears ahead of the intuition-based position sizing that a majority of firms employ. I applaud Mr. Lupoff for speaking publicly about an issues that plagues the investment management industry and allows others to catch up with his competitive advantage. However, I bet he's performed the calculus to determine, much like I have, that people are very resistant to change, even when presented with a superior solution. Just ask Billy Beane how long it took professional baseball managers to catch up with his superior method for pricing players. As Buffett says, "Traditional Wisdom is long on Tradition and short on Wisdom."