Mental Capital – Pulling the reins on your brain

Funds have limited financial capital that they can deploy based on their asset under management. Portfolio managers work within those constraints to maximize return. Just like financial capital, the human brain has limited capital that can be allocated, but many portfolio managers don't approach the Mental Capital constraints with the same rigor they employ to financial capital restrictions. This causes funds to expect too much from analysts with a resultant degradation in research quality.

We can approach Mental Capital from the bottom-up. Let's say a firm has a portfolio manager and four analysts. All five of these investment professionals (IP) have limitations on the amount of time they can dedicate to research, their Mental Capital. If we assume that each IP can perform research for 40 hours a week (excludes non-productive time like staring at the P&L) and they work 50 weeks a year for a total of 2,000 hours per IP per year that results in 10,000 hours for a five IP fund. Now let's assume that each analyst needs to perform 100 hours per year of research per name (about 8 hours per month per stock). That means a total of 100 stocks can be effectively covered or 20 stocks per IP.

20 stocks per IP or 100 positions for the fund seems like a reasonable figure, but remember this includes ideas, as well as active names in the portfolio. If we assume that half of analysts' time is spent working on new ideas that would cut the number of active names per analyst in half to 10. This means a fund with a team of five can reasonably cover 50 active positions. But a majority of funds end up with 100+ positions meaning that something is being sacrificed for the sake of diversification. More than likely, the portfolio ends up with a mix of insignificant positions that take just as much time as the "core" positions, but have very little impact on the portfolio's returns. Very rarely will the 50bps position have a large impact on portfolio returns but it can be a big expense of precious Mental Capital.

To cut down on pointless wastes of Mental Capital, it is important to have a checklist of requirements before spending time on research. Does this stock meet our liquidity requirements? Is this stock is in a sector we know, or will we have to spend time on exhaustive background work? Do we have an edge? Perform a quick valuation analysis and if it doesn't look sufficiently cheap (or sufficiently expensive) then move on. Purge names from the existing portfolio that also are no longer sufficiently cheap or expensive. Mental Capital is a finite resource that is to be spent with caution. Treat it with the same care as financial capital and you'll end up with a better portfolio.

Debating Dividends – Fox Business News

I recently appeared on Fox Business News with Cheryl Casone discussing Apple's recent dividend. As I've stated in numerous posts and articles, I believe dividends are a tax-inefficient way of returning capital to shareholders. Corporate boards should encourage management teams to buy back shares instead of issuing dividends. You can check out the discussion through the Fox Business Interview here.

March Madness Math

AUTHOR’S NOTE: My second child was born less than 24 hours ago but I felt like I had to get this out by tip-off. Please excuse any errors.

 

I love college basketball. I’m a graduate of UNC-Chapel Hill (home of Michael Jordan) and grew up a fan living thirty minutes away. Needless to say, I spend a little too much time filling out brackets and watching hoops during business hours this time of year. And in the spirit of all things Alpha Theory, I have a systematic approach to filling out my NCAA brackets. But my system needs a little fine tuning. I’ll give a little background to set up the problem and hopefully someone will have an answer.

GENERATION ONE. Creating a systematic approach to fill out the brackets requires good input. From 2008-2011, I took Vegas odds for each team to win the national championship to serve as a proxy for team quality and strength of the path they’ll have to travel. For an example of the calculation, see the chart below. Kentucky is the favorite at 8/5 odds. If I bet $5 on Kentucky and they win, I receive $8. That assumes that 8 times out of 13 (8+5) Kentucky will win or 61.5%¹ (8/13). The next step was to calculate the percentage for every team in the tourney, sum up all the percentages, and divide the individual teams win percentage by the sum of all the percentages to get a true probability of winning the tourney². The next step was to use those probabilities to create a forecasted probability of winning for one team versus another. For example, if Kentucky (29% chance of winning it all) plays Missouri (4.6% chance) then the adjusted probability of Kentucky winning is 86% (29% / (29% + 4.6%)). At this point I could have filled out my brackets using a random generation (i.e. use a random number generator to pick a random number between 0 and 100 and if it falls above 86 then Kentucky loses, and if it falls below, they win. Or I could have just used Vegas probabilities to pick the winner which pretty much means picking the Vegas favorite in each round. But here is the problem, Vegas odds don’t give the granularity necessary to pick the early round games because they make very little differentiation between teams (see the clusters of odds below).


 

GENERATION TWO. While looking for a solution, I came across KenPom.com. This is a sophisticated site steeped in the teachings of Bill James, the pioneer that created the statistics that led to the Moneyball movement. KenPom creates an adjusted winning percentage that controls for a multitude of factors. This winning percentage allows for comparison of teams across the spectrum. Additionally, in the KenPom blog there is reference to the Log 5 method which takes two teams’ winning percentages to determine the probability of one team beating the other. This is the breakthrough I was looking for.

This allowed my NCAA bracket generator to have much more precise winning probabilities and thus a much more accurate forecasting engine. Here are the brackets based off KenPom adjusted winning percentages and Log 5-based probability of head-to-head success:

THE PROBLEM. Now here is the rub. Let’s say that I’m playing in an NCAA pool that has Cinderella points (1 point added for each point of difference in the seed). I can calculate an expected return using the probability of winning (i.e. Wichita St. (#5 seed) versus VCU (#12 seed) – KenPom is 93.5% and 80.4% respectively). Using Log 5 we calculate a 77.1% chance that Wichita St. wins the game. The expected return for Wichita St. is 77.1% * 1 pt = .8pts and the ER for VCU is 22.9% * (1pt for win + 7pts for seed) = 1.8pts. In this case you would pick VCU because they give you an expected value of 1.8 versus .8 for VCU. If the tournament were one round, this method would maximize expected return. But if I pick VCU to beat Wichita St. in the first round, then I can’t use Wichita St. in future rounds. If I wouldn’t have chosen Wichita St. or VCU to move beyond the second round, then I should definitely pick VCU in the first round because there is nothing lost for not having the right team lose in the second round. But if I would have had Wichita St. win a future round, which I would have in this case, then I’ve done myself a disservice by eliminating them in the first round to maximize first round expected return.

I’m looking for a good way to account for this dynamic. I’m assuming someone with a good grasp of Bayesian/Stochastic tools may have a solution. Anyone have a suggestion? I would be glad to send my sheet along to anyone that would like to try and take a stab at solving the problem or would just like to use the sheet. Please help me solve this March Madness Math.

¹ Clearly 61.5% is too high a chance of Kentucky winning the tournament. But if Vegas used realistic probabilities, then they wouldn’t make money from the spread. But how unrealistic are the probabilities that they use? Let’s assume that Kentucky is the best team in the country by a wide margin and figure out the odds of winning the six games necessary to win the national championship:

First game – 100%, no chance they lose. If they play 100 times, they don’t lose once.

Second game – 95%, they’ll be playing an 8/9 seed, play 100 times, they lose 5.

Third game – 80%, playing a 4/5 seed

Fourth game – 70%, playing a 2/3 seed

Fifth game – 65%, playing a 1/2 seed

Sixth game – 60%, playing a 1/2 seed

 

Multiply them all together and the probability of winning is 21% for the best team in the country. Even if I raise the winning percentage to 80% for all the rounds from the third round on, it is still only 39%. So 62% odds are off the chart and tell you how expensive it is to do prop bets in Vegas. What this also tells us is that fans really shouldn’t be upset when their team doesn’t win the national championship. The odds of the best team in the country are only slightly better than rolling a die and landing on 1. Take solace in the fact that single elimination tournaments are subject to all kinds of luck and be happy that your team is dancing.

 

² Sum is greater than 100% because Sportsbooks make their money from the spread. If the odds were reflective of the real probability, then Vegas would just breakeven…and we can’t have that can we? For example, Kentucky is forecasted by Vegas to have a 62% chance of winning it all, but adjusting by the sum total of all teams’ odds of winning, which is 215%, the true Vegas probability of Kentucky winning it all is 29% (61.5%/215%). So instead of paying $1.60 (8/5) for each dollar bet, Vegas should actually be paying $3.50 for each dollar bet. Needless to say, the futures bet on NCAA champs is a real suckers bet.

 

 

I Fell In a 10 Foot Hole…How Far Do I Have To Climb to Get Out?

If you fall into a 10 foot hole, you have to climb 10 feet to get out. That simple physical rule doesn't work for portfolios. I have written a few times about the asymmetry of loss and gain in portfolios (Asymmetry, Which Way is Up). The basic concept is that risk is not equal to a commensurate amount of reward. For example, if I lose 25% of my $100 million fund, then I will have to be up by 33% the following year to be back to break even. Because of this asymmetry, it is critical to calculate risk for every investment and avoid potential loss that does not give a more than adequate level of reward.

Because I spend so much time talking about this concept (and I'm not good with math in my head), I was looking for a quick way to calculate the reward I need to break even after a loss. After writing out the formula and then refining it, I came up with a simple formula:

 

For example:

As you can see, the sum of each fraction is 100%, so it is very easy to compose the formula. The only problem is I still have to do math in my head. So I then tried to create a ratio, but I realized after plotting it out, that it is logarithmic (see chart below) and above my pay grade.

Although the BreakEvenReturn formula definitely makes the math easier, does anyone know a simple way to perform the calculation? Or at least point me to a quick way to turn fractions into percentages in my head.

To Buy or To Sell, That is the Question

I was reading a recent article by Bloomberg news about Todd Combs, Warren Buffett’s new right-hand man on stock picking. The article illustrates how Combs consistently buys when prices fall. This buy-low/sell-high strategy is the counter-strategy of riding winners/paring losers which I’ve seen recommended by many traders, behavioral economists, technicians, and statisticians. So where is the truth? Like most disputed questions, the answer lies somewhere in between. Technicians, traders, and statisticians cite the fact that stocks that are down have a better than average chance of going down more and that the market probably knows something that you do not. Behavioral economists cite our tendency for loss aversion which causes humans to hold onto losers too long because of the aversion to realizing those losses and our tendency to sell winners too early because of a desire to “lock-in” profit. The problem with these arguments is that they ignore the crux of any rational investment decision.  Specifically, they should simply ask, “What is the value of the company? “

As can be seen in Todd Combs’ strategy (which just so happens to be the philosophy of Buffett as well), a true sense of business value is the driver of buy and sell decisions. When a stock price falls, all else being equal, the risk-reward has become more favorable. When the stock rises, the risk-reward becomes less favorable. This reason alone should be the driving force behind buy and sell decisions for those who actually fundamentally research companies and stocks. Clearly, if the stock is down, the market could be signaling something that the analyst has missed. It serves as a notice to question one’s research, to find the devil’s advocate. But after doing so, if the analyst finds that the facts have not changed, then the improved risk-reward created by a lower price gives the value investor an opportunity that other investors are willing to let slip by.

So what makes the value investor so special? Due diligence. Investors that lack the in-depth research required to understand the company, its financials, and its valuation are subject to the pressures of the market because they do not have the anchor of their conviction. Investors that do not have a calculated potential downside risk and a calculated potential reward, do not have the triggers that allow them to buy and sell with confidence. While clearly, these price objectives are only subjective estimates, they are rooted in concrete research and serve as the critical focal point in any conversation about buying and selling. So, if we want to answer the “To Buy or To Sell” question, the first question an investor must ask is “what is this thing I’m buying or selling worth?”  Even though most investors do ask this question, very few actually answer it with a number.  Doesn’t that seem odd?

The Role of Diversity in a Better Future

The future is like a complex algorithm with virtually infinite variables. Mankind does not know the optimal inputs for the variables. Nature controls a large number of the most powerful variables, but mankind can shape many others. One way to think of the future is that mankind is in a constant search for the optimal set of inputs to determine the future. This is not a conscious goal, but if you think about it, each individual, in their own tiny part of the world, is influencing the future by making decisions every day. Each decision affects a variable in the algorithm that results in our future. To determine the optimal set of variables, mankind uses a crude genetic algorithm (of course without knowing it) to search for the optimal set of inputs.

From Wikipedia: “A genetic algorithm (GA) is a search heuristic that mimics the process of natural evolution. This heuristic is routinely used to generate useful solutions to optimization and search problems. Genetic algorithms belong to the larger class of evolutionary algorithms (EA), which generate solutions to optimization problems using techniques inspired by natural evolution, such as inheritance, mutation, selection and crossover." 

A genetic algorithm (GA) is pretty much a fine-tuned method of making educated guesses, analyzing the results, and then using that information to make more guesses until a final set of “optimal” results is found. Each variable has a range of possible inputs. The GA will randomly mutate variables to make sure it isn’t going down a sub-optimal path. Mankind is similar in that its seemingly chaotic nature allows for a wide range of inputs. This wide range (diversity) and chaos (mutations) allows for more optimal results without getting stuck in rut (local minima). With diversity and chaos, the world is able to keep variables from falling into ruts and settling on sub-optimal solutions. This is why it is important to have Type As and Type Bs, OCDs and slobs, democrats and republicans. Each play their part in making the range of inputs as wide as possible.

Without differing opinions, the algorithm has no method to optimize the final results. It takes extreme inputs with sometimes horrific results for the system to purge sub-optimal paths (slavery, eugenics). Just like it also requires extreme inputs to find sea-change pulls towards optimality (democracy, language). So next time you get frustrated by an extremist pundit you don’t agree with, realize that they serve an important purpose in society. Without them and everyone else, the future would be sub-optimal. And if you still want to call them a name, call them what they probably are, a mutation.