March Madness 2013 - Your Mom Always Wins

I first posted the blog below in 2012. As I'm preparing my brackets for 2013, I was referencing this post as a reminder of how to operate the machine I built last year. First step, download data for 2013. I typed in KenPom.com to get Winning Percentage scores to drive my March Madness Machine. KENPOM.COM WAS DOWN!!! Apparently, I'm not the only one heading to the KenPom site to get my stat fix (apparently the NCAA site was down for a little while too). So, what do I do? Be patient and wait for the mad rush to subside? No, I do a Google search for KenPom to see if I can find a backdoor. No luck, but I do come across this article that may change everything: KenPom vs Your Mom. 

The article was written by Peter Tiernan who has been using stats to analyze March Madness for 22 years (this according to his bio) and is an expert that writes for CBS during the tourney. The point of the article was to compare the new BPI system to KenPom. No need to go into results here, but basically no real difference. The more interesting section of the article was the comparison of KenPom to Your Mom. "Your Mom" is basically, just picking the higher seed in every round.

"Okay. So I did one other analysis yesterday—and I think it’s more relevant than determining round-by-round prediction accuracy. This analysis compared the accuracy of KenPom to YourMom in filling out your entire bracket and living with the consequences of lost games in previous rounds. I was able to go back nine years for this analysis. What did I find? Using KenPom efficiency data would’ve predicted 376 of the 567 tourney games played between 2004 and 2012. That’s a 66.3 percent accuracy rate. And how would’ve YourMom done? Amazingly, two games better—for a 66.7 percent accuracy rate. That’s right. Picking by seeds and margin beats out using KenPom."

Your Mom wins!!! Actually, this isn't that surprising. I've filled out my bracket using KenPom and Vegas odds for many years and I always notice that I'm pretty much picking the higher seed. Very rarely (and I'm not counting 9 vs. 8) does the underdog have a higher KenPom Winning Percentage, so I pretty much end up filling out my bracket picking the higher seed. I knew I ended up picking more favored seeds than the average bracketeer but now I have some emperical evidence to support my choice. 

Here's the rub, most NCAA pools only pay 3 places. Over the long-run, I will almost certainly be better than average, but randomness places in the the top 3 spots more often than not. For example, imagine I'm competing in a pool with 99 others. Assume all 99 are randomly generated and assuming my method is the superior statistical method, I still have a very low probability of finishing in the Top 3. This goes down even further if there are 1000 participants. 

What does all this mean? I'm sticking to small office pools or pools with Cinderella points (extra points for picking upsets) and I will not be offended when someone calls me a moron for picking every favorite.

2012 Blog Post:

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.

 

 

 

The Real Cost in Cost to Borrow

Alpha Theory has always incorporated the Cost to Borrow in the Risk-Adjusted Return calculation of shorts but recently we’ve improved our calculations and I’ve really been pounding the table to get clients to incorporate Cost to Borrow more formally in their decision process. For those unaware, the “Cost to Borrow” is the annualized expense charged to a manager for borrowing the shares of another investor to short in their own account. For many stocks the cost is fairly low (0-5%) but for other “Hard to Borrow” stocks, the cost can be 15-50%. “Hard to Borrow” stocks are expensive because lots of investors are suspect of the company’s prospects and want to short the shares. It is simple supply and demand.

What this means is that a 25% Cost to Borrow short would have to be down at least 25% by the end of the year to breakeven. But what if the investor believes the payback will be three months? Or, to complicate things, that there is an 80% chance the payback will be in three months and a 20% chance that the company will be able to work things out by the end of the year? Our new Cost to Borrow calculation adjusts returns by the duration and probabilities associated with the investment thesis. The concept is simple but not generally implemented. This is surprising since effectively accounting for Cost to Borrow is critical to running a good short book.

Ever since we began making a concerted effort to capture clients’ Cost to Borrow data I’ve seen how often it is being under-represented in client return expectations. Many times a client’s best short idea has a high Cost to Borrow because it is an obvious dud that others would like to short. Because of the manager’s high-conviction that the company will fail, he puts on large positions. The problem is that there may be other short ideas with slightly lower certainty or downside but also dramatically lower Costs to Borrow which make their effective return better than the high-conviction short. Now that Alpha Theory incorporates the Cost to Borrow into Risk-Adjusted Returns, clients are able to compare their short ideas on an apples-to-apples basis. Would you rather have a 40% Risk-Adjusted Return with a 30% Cost to Borrow (10% net Risk-Adjusted Return) or a 20% Risk-Adjusted Return with a 3% Cost to Borrow (17% net Risk-Adjusted Return). Of course this seems completely obvious but until it is spelled out and placed in front of the manager it is easy to let the conviction and absolute Risk/Reward sway them into oversizing the position. The message is straightforward, anyone that shorts Hard to Borrow equities should calculate a Risk-Adjusted Return adjusted for Cost to Borrow before making portfolio decisions.

What’s Up with Up/Down Ratio?

I had a couple of meetings yesterday and in each of them, the concept of Up/Down Ratio (Risk/Reward) popped up. Both portfolio managers calculated the ratio by taking the amount of potential upside for an investment and dividing it by their potential downside. For instance, let's say they were considering an investment in IBM. They would do research on IBM and determine their upside was 30% if they sold a few extra Watsons and would be down 10% if they didn't. The ratio is straightforward, 30%/10% or 3x. The portfolio managers in both meetings said they were looking for Up/Down of 2x or greater and would size positions accordingly to the size of the Up/Down. Sound familiar? Yes, it does sound like Alpha Theory.

Now let me start by saying that by calculating an Up/Down Ratio, these firms are asking important questions about risk and reward and giving the portfolio manager a powerful tool to more efficiently size positions. I can promise most firms are not this disciplined. But Up/Down is so close to great but suffers from two fundamental flaws: 1) Up/Down has scale issues and 2) it gives equal probability of risk and reward. To explain the scale issues, let's compare two other companies to IBM's 3x using the same measure. Homerun Company has an upside of 90% if their new drug is approved and down 30% if it isn't – Up/Down Ratio = 3x. On the other hand, Dull Company, is worth 9% more if it gets a new contract and 3% less if it doesn't – Up/Down Ratio = 3x. All three companies have an Up/Down Ratio of 3x but they're not created equal and they'll affect the portfolio differently. If we assume the upside has the same probability (50%) as downside (50%) then Homerun, IBM, and Dull have expected returns of 30%, 10%, and 1.5% respectively. That's not even close to being equal.

So if managers wanted to make a huge improvement on their Up/Down Ratios, they could just assume equal probabilities of Up and Down and calculate an expected return like I did. 30%, 10%, and 1.5% is more predictive and differentiating than 3x, 3x, and 3x. But they can do even more. By assuming 50/50 for Upside and Downside, they run into the next problem of Up/Down Ratios. Analysts have greater confidence in some bets than they do in others. That difference in confidence should be expressed in how positions are sized. For instance, if the analyst has high confidence in Dull Co., medium confidence in IBM, and low confidence in Homerun Co. we could express that conviction as 90/10, 70/30, and 50/50. This would change our expected returns to 7.8% (Dull Co.), 18% (IBM), and 30% (Homerun Co.) These are the measures that should be used to size positions because they express the research and conviction level while measuring the assets' expected impact on the portfolio (i.e. if I were to invest in each of these assets 100 times I would actually expect to get returns similar to the calculation).

With very little change these firms that are using Up/Down Ratios can convert to an expected return. At a minimum, firms with Up/Down can multiply their Up and Down by 50% to get over the scaling issue.  Ideally, firms can take it to the next level by using probabilities to factor in conviction level.

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.

5 Ways Analysts Benefit from Alpha Theory

I was having a conversation with a portfolio manager the other day who was talking about how much sense Alpha Theory made, but how he expected his analysts to hate the idea of having to build scenario analysis for all of their research. It reminded me of a piece I put together a while back when the same question came up, take a look at "5 Ways Analysts Benefit from Alpha Theory".

To Price Target or Not to Price Target…that is the question

The other day, I was doing what I spend much of my days doing – talking to a portfolio manager about Alpha Theory. He told me that Alpha Theory makes terrific sense for firms that calculate price targets, but that he didn’t believe in price targets. When I asked him why, he responded that there is a lot of instinct that price targets do not capture and it is his instinct that makes him successful. I explained that instinct and price targets are not mutually exclusive because price targets are estimates. Instead of estimating whether to buy or sell (pure instinct), you’re estimating reward and risk (price targets). To drive the point home, I asked him, “What are the 5 best ideas in your portfolio? Are they your 5 biggest positions?” He did not know. Is there any more proof needed?

Using price targets is not about being precise; it is about being directionally accurate. Price targets define why you are making the decisions you are making and do not require that you strip away the instinct that may be a primary component of your abilities. In fact, it is quite the opposite.  Because price targets are part science and part art, instinct plays a critical and indispensable role. This is especially true if you use probability weighted price targets because the art-to-science ratio is even higher. If you are already good at estimating price targets and probabilities, you will create a far superior portfolio if you discipline yourself to write them down. If you are not good at estimating price targets, well … you probably would not be successful anyway.

The only way to justifiably choose against the use of price targets is to take the position that instinctual decision making is not detrimentally affected by cognitive biases.  Before taking this position and relying solely on your instinct, however, it is an enlightening exercise to review a list of Cognitive Biases and consider whether any of them affect your decision making. Believers in the instinct assume (implicitly or explicitly) that instinct reflects logic. This assumption is compellingly supported by the studies of people like Gerd Gigerenzer, Daniel Goldstein, and Malcolm Gladwell.  Unfortunately, however, these studies become much less compelling when they are applied to investing. In this area, there is much more support for non-instinct based decision making. Behavioral Finance and Neuroeconomics research shows how logic based decision process is critical in achieving successful long-term results (see the work of, for example, Amos Tversky, Daniel Kahneman, Michael Mauboussin, Ron Howard, Jason Zweig, James Montier, and Matthew Lieberman).

To illustrate why price targets are critical, ask yourself this simple question, “Why did you buy this stock?” Your answer is probably some version of “I believe I can sell it for a higher price down the road.” If your decision is only about that one stock, that’s a great answer and you can responsibly stop the analysis right there. If, however, you have many stocks to choose from and you have capital that must be efficiently allocated between too much risk and too little return, then you have to consider each asset’s impact on the overall portfolio. To responsibly measure this impact, you must quantify the potential reward and its probability as well as the risk you are taking on and its probability, the combination of which is a risk-adjusted return. Instinct can, and perhaps, should be a primary component of these estimates, but it cannot responsibly stand alone.  Repeatable success requires disciplined price targets that explain the fitness of a decision within your portfolio.

EMPIRICAL EVIDENCE: YOU MUST USE RISK-ADJUSTED RETURN TO SIZE POSITIONS

Portfolio managers often ask me for empirical proof for why they need to calculate risk-adjusted return to size positions. Because I do not have empirical evidence, my argument is that risk-adjusted return is a precise measurement of an asset's impact on the portfolio and, to maximize overall returns, you must make your best ideas your biggest positions. Their concern is that they do not have confidence in their calculated risk-adjusted return or their ability to differentiate between the quality of investments in their portfolio.

I always make a few points in return:

1) If you can differentiate between an asset that deserves to be in the portfolio and an asset that should not, then there is clearly some differentiation between quality of assets in the portfolio.

2) Whether you calculate risk-adjusted return or not, you are estimating risk-reward when making investment decisions so you might as well calculate it to cut down on mistakes.

3) Monte Carlo simulations show risk-adjusted return as a superior method of portfolio construction when compared to other position sizing methodologies.

4) Probabilistic portfolio management is the competitive advantage of some of the smartest and most successful funds that I have spoken with.

All of the reasons mentioned above are compelling but a little academic support is nice. Below are four academic papers that show why it is critical to make your best ideas your largest positions and how not calculating your best idea can put you in a 6% return hole compared to your peers.

Excerpts (Once you click on the link, push download, then select the SSRN site):

"Best Ideas" – Randy Cohen, Christopher Polk, and Bernhard Silli (2009) – 1 to 4% improvement

We examine the performance of stocks that represent managers' "Best Ideas." We find that the stock that active managers display the most conviction towards ex-ante, outperforms the market, as well as the other stocks in those managers' portfolios, by approximately one to four percent per quarter depending on the benchmark employed. The results for managers' other high-conviction investments (e.g. top five stocks) are also strong. The other stocks managers hold do not exhibit significant outperformance. This leads us to two conclusions. First, the U.S. stock market does not appear to be efficiently priced, since even the typical active mutual fund manager is able to identify stocks that outperform by economically and statistically large amounts. Second, consistent with the view of Berk and Green (2004), the organization of the money management industry appears to make it optimal for managers to introduce stocks into their portfolio that are not outperformers. We argue that investors would benefit if managers held more concentrated portfolios.

When asked to talk about his portfolio, the typical investment manager will identify a position therein and proceed to describe the opportunity and the investment thesis with tremendous conviction and enthusiasm. Frequently the listener is overwhelmed by the persuasiveness of the passionate presentation. This leads to a natural follow-up question: how many investments make up the portfolio. Informed that the answer is, e.g., 150, the questioner will often wonder how anyone could possess such depth of knowledge and passion for so many disparate companies. Pressed to answer, investment managers have been known to sheepishly confess that their portfolio contains a few core high-conviction positions, the "best ideas", and then a large number of additional positions which may have less expected excess return but which serve to "round out" the portfolio.

This paper asks a related simple question. What if each mutual fund manager had only to pick a few stocks, their best ideas? Could they outperform under those circumstances? We document strong evidence that they could, as the best ideas of active managers generate up to an order of magnitude more alpha than their portfolio as whole, depending on the performance benchmark.

We argue that this presents powerful evidence that the typical mutual fund managers can, indeed, pick stocks. The poor overall performance of mutual fund managers in the past is not due to a lack of stock-picking ability, but rather to institutional factors that encourage them to overdiversify, i.e. pick more stocks than their best alpha-generating ideas.

"The Value of Active Mutual Fund Management" – Hsiu-Lang Chen, Narasimhan Jegadeesh, Russ Wermers (1999) – 2% improvement

When we examine mutual fund trades, we find that stocks that the funds actively buy have significantly higher returns than stocks that they actively sell. This return difference is roughly two percent during the one-year holding period following the trades, adjusted for the characteristics of the stocks that are traded.

We find that stocks that funds newly buy have significantly higher returns than stocks they newly sell. This is true for large stocks as well as small stocks, and for value stocks as well as growth stocks. The evidence that stocks actively traded by the funds outperform stocks that are passively held from prior periods suggests that mutual funds hold stocks longer than the horizon over which they can predict returns, possibly because of a preference to avoid high transaction costs or capital gains taxes.

Overall, our evidence is suggestive of the funds possessing superior stock-selection skills.

"Fund Managers Who Take Big Bets: Skilled or Overconfident" – Klass Baks, Jeffrey Busse, and Clifton Green (2006) – 4% improvement

We document a positive relation between mutual fund performance and managers' willingness to take big bets in a relatively small number of stocks. Focused managers outperform their more broadly diversified counterparts by approximately 30 basis points per month, or roughly 4% annualized. The results hold for mimicking portfolios based on fund holdings as well as when returns are measured net of expenses. Concentrated managers outperform precisely because their big bets outperform the top holdings of more diversified funds.

The findings lend support to the notion that the managers who tilt their portfolios toward their favorite stocks assess correctly the relative merits of stocks overall as well as within their portfolios. By contrast, funds whose portfolio weights more closely approximate a uniform distribution display less ability to correctly sort stocks within their portfolio according to future performance. Overall, our results suggest that concentrated fund managers do have some ability to correctly pick stocks.

Using a variety of performance measures, we find that concentrated fund managers outperform their diversified counterparts. This result lends support to the notion that the managers who are confident in their ability assess correctly the relative merits of stocks overall as well as within their portfolios. By contrast, funds whose portfolio weights more closely approximate a uniform distribution display less ability to correctly sort stocks within their portfolio according to future performance. Overall, our results suggest that focused fund managers do have some ability to correctly pick stocks.

"The Information Content of Revealed Beliefs in Portfolio Holdings"- Tyler Shumway, Maciej Szefler, and Kathy Yuan (2009) – 2 to 6% improvement

In this paper, we elicit heterogeneous fund manager beliefs on expected stock returns from funds' portfolio holdings at each quarter-end. Revealed beliefs are extracted by assuming that each fund manager aims to outperform a certain benchmark portfolio by choosing an optimal risk-return tradeoff. We then construct a measure of fund managers' forecasting ability—the belief accuracy index (BAI)—by correlating a manager's revealed beliefs on stock returns with the subsequently realized returns. We measure the differences in beliefs between funds with high BAI and all other funds, the belief difference index (BDI). Sorting stocks based on BDI, we find that the annualized return difference between the top and bottom decile is about two to six percent.

Knowing the Financial Spread - Investor Lessons from WhatIfSports.com

“Once The Star-Spangled Banner began to play, I’d tell myself, “Here you go.  Start pulling away, start computerizing.  You must think clearly and remove yourself”...It was like watching a game through a window.” – Bill Walsh, Head Coach of San Francisco 49ers and creator of the West-Coast offense

A buddy of mine who knows how much I love sports analysis, sent me a website called WhatIfSports.com that runs mock simulations of games 10,000 times to create a projected outcome. Now I have no idea about the efficacy of WhatIfSports's Monte Carlo simulation, but I love this kind of stuff as anyone that has spoken to me about the chance of the Tarheels winning the National Championship in basketball can attest (we’ll save that diatribe for another blog). So, I decided to see what the best way to profit from this simulation, assuming it was accurate. I pulled up Vegas odds and Whatif’s NFL week 8 projections to see if I could find any inconsistencies and did a quick analysis: 

Based on this, Vegas was pretty much dead on, but not perfect. How would I profit from these mis-priced games? I would definitely bet the under on the Falcons/Saints, because Vegas has the game total at 54 and WhatIfSports has the total at 45.  I would also pick the Rams getting 9.5 points over the Lions, when WhatIfSports has the Rams winning outright. I may also pick the Broncos and 49ers, but I would not be as confident and would certainly place a smaller bet on those games. This got me thinking about how this analysis applies to investing.

If I am evaluating a basket of stocks for potential investment, the Vegas Odds are the current stock price because they indicate what I can “buy” the bet for today and the WhatIfSports analysis is my proprietary research. I want to find the assets with the biggest differentials, Falcons/Saints under and Rams and make big bets on them. If I find other stocks with a reasonable difference between the market price and my calculation of value then I will place a bet on them as well, but not to the same degree as the large spreads.

If I’m an investor, how can I determine which assets should go in my portfolio and how to size them without calculating the risk-adjusted return of every investment? I must measure the difference between the market price and what I think the value is to determine the attractiveness of the bet. This concept seems so straightforward, yet most investors are willing to allow their mental calculator to be the final arbiter of portfolio inclusion and position size. That’s just like looking down the list of Vegas Odds and saying, “hmmm, I know the Saints score a lot and 45 isn’t that high, I think I’ll take the over.” First off, our brains are not very well designed to make those kinds of decisions, just read any book on behavioral finance or neureconomics. Second, even if you are right in your assessment that it is a good bet, how do you know exactly how good it is. Is it pretty good, really good, or freakin’ fantastic? Those differences affect how the position should be sized.

No doubt, calculating risk-adjusted return is harder than not calculating risk-adjusted return. But honestly, there are millions/billions of dollars at stake. How do you know what to bet if you don’t know your own spread?

So, wish me luck this Sunday and GO RAMS!!!

The Probability Problem

“The fundamental law of investing is the uncertainty of the future.” – Peter Bernstein, famed investor

 

I am offered two bets. In bet number one, I am paid $150 for every heads and pay $100 for every tails. My risk-adjusted return is 25%. In bet number two, I’m presented with a bag of poker chips that are only black or white. I’m paid $150 for each white chip I pull out and I have to pay $100 for every black chip I pull out. I don’t know the distribution of colors, so my probability assumption would be 50/50. Drawing poker chips also has a 25% risk-adjusted return. Would I be equally likely to make both bets? No, I prefer the coin-flip bet because I am more certain about the distribution of probabilities.

 

To try and balance this issue, let’s assume that we could, with reasonable certainty say the range with which our poker chip probabilities would fall. In this example we’ll assume that white chips are somewhere between 30% and 70% of the contents of the bag. This widened distribution takes into account my uncertainty regarding my probabilities. Unfortunately, if I plot out every payout between 30% and 70% probability of success, I get an average of 25%. I’m back at square one.

 

What about betting systems that constrain loss? If I use Optimal-F (Kelly) suggested bet size, I get 17% bet for the coin-flip, which is the same as the average of all of the Optimal-F bets between 30% and 70% probability. Alpha Theory optimal position sizes suffer the same issue with a position size equal for both coin-flips and poker chips.

 

Here is my simple solution until I understand a better Bayesian solution. I have a somewhat arbitrary Analysis Confidence rating. Let’s name them High, Medium, and Low. The coin-flip is definitely “High Confidence” because I am certain about my coin-flip probabilities. The poker chips are “Low Confidence” because I know nothing about their true distribution. But my knowledge about the poker chips is not static. The probabilities are epistemic because, as I draw more poker chips, my knowledge of the distribution of chips will improve. I will adjust my probabilities as I draw chips and change my Analysis Confidence from Low, to Medium, and eventually to High when I have a better grasp on the distribution of chips in the bag. To account for uncertainty, I’m going to cut my bets. If I have Low Analysis Confidence, I cut my suggested bet in half, if I have Medium I cut it by 25%, if it is High, I don’t cut my bet at all. This is certainly imperfect, but it does create the effect we are shooting for, less exposure when we have less certainty in our assumptions.

 

This, of course, applies to equity investing. You may have high certainty in your probabilities for one investment and only low certainty in another. They both may have the same Risk-Adjusted Return, but you are not willing to invest in them equally. Use the same Analysis Confidence constraint to adjust position size and apply a heuristic-based cut since probability theory does not have a better answer. Alpha Theory provides an Analysis Confidence setting for precisely this purpose to better refine position sizes beyond Risk-Adjusted Return.