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2 posts from April 2010

April 23, 2010

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."

April 20, 2010

Tiburon Tenets (Part 1): Capitalizing on the Random Walk

When asked how he had become so rich?  He replied, "I sold too early." – JP Morgan, famous financier

In an article by Peter Lupoff, CEO of Tiburon Capital and formerly of Millennium and Third Avenue, he discusses how Tiburon actively trades around core positions as a way to increase returns and decrease risk (TabbFORUM article) – you'll have to sign up for TabbFORUM if you are not already a member but it is free. These are concepts that we have articulated through our explanations of "Capitalizing on the Random Walk" and the "Good Stock Paradox" (minute 5:30 of webinar link). The point being that if you have a sense of intrinsic value and the stock trades around that value, then the market is providing dislocations in value that should be traded upon. For instance, Microsoft's stock has ranged between $17 and $31 over the past 52 weeks. That would suggest that the company has created or destroyed over $100 billion dollars of value which seems a bit excessive to me. I'm guessing that within that period there were deviations from intrinsic value that would suggest a core position should be trimmed or added to.

In a more illustrative example, let's assume we have a $30 stock which currently represents 3% of our portfolio and we currently calculate a 30% probability-weighted return. Now let's move forward to a point where the stock has gained 10% and trades at $33. Assuming we do not sell any shares as the stock accretes, we now have a 3.3% position in a stock with less potential upside and more potential downside. Increasing our exposure to assets with lower probability-weighted return sounds like flawed portfolio management to me. Let's extrapolate the example and assume two funds. Both own 3% of the same $30 stock. The first fund owns the same number of shares as the stock goes from $30 to $33 to $27 then back to $30 for a total gain of $0. The second fund cuts the position in half as the stock rises to $33 and then adds back to the position as the stock falls to $27 and then trims again when stock rises back to $30. The second fund would hold the same 3% position at the beginning and the end of the move as the previous firm that made $0, but would have generated 50 basis points of portfolio alpha net of $0.03 commission.

Buy and Hold is a flawed strategy in a market where the probability-weighted return of portfolio assets are constantly changing. If, at the end of the day, you are trying to construct a portfolio where the best probability-weighted return are your largest positions and the worst are culled out of the portfolio then you must have an active trading mentality. If the market were more efficient and less volatile, then you could buy and hold, but thank goodness for thoughtful investors, it is not.