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.

Mental Capital – Pulling the reins on your brain

Funds have limited financial capital that they can deploy based on their assets 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.

Institutional Investor | 8 Mistakes Series – Final Installment Released Today

The last installment of the "8 Mistakes Money Managers Make" series on Institutional Investor (www.InstitutionalInvestor.com) was released today. The series has been highlighted in their weekly electronic newsletter and posted on their homepage. The articles focus on poor position sizing's effect on portfolio risk and return. The root cause being a basic misunderstanding of an asset's impact on the portfolio and how it should be used to determine position size.

A link to the entire series can be found here or by visiting www.InstitutionalInvestor.com and clicking on the "8 Mistakes Money Managers Make" link under the "Asset Management" section.

 

Institutional Investor Article Series: 8 Mistakes Money Managers Make

Institutional Investor (www.institutionalinvestor.com) will feature a daily article series I authored beginning today. The series, “The 8 Mistakes Money Managers Make,” was highlighted in their weekly electronic newsletter today and posted on their homepage. The articles focus on poor position sizing's effect on portfolio risk and return. The root cause being a basic misunderstanding of an asset’s impact on the portfolio and how it should be used to determine position size.

The initial article, “Mistake #1: Discounting the Downside” is located under the “Asset Management” portion of the website and can be found here. Be sure to visit www.InstitutionalInvestor.com tomorrow for the solution to Mistake #2: The Good Stock Paradox.

Fundamental vs. Traditional Risk Management

When people mention "Risk Management" in investing the traditional metrics of volatility, correlation, Value at Risk, Beta, Sharpe ratio, etc. come to mind. But for fundamental shops (stock pickers) it is difficult to utilize risk management statistics to manage a portfolio. In fact, at my old shop, we would fire up the risk management software on the 30th of every month so we could put the data in our investor letter and that was about it.

The reason is because good fundamental portfolio managers understand that risk is not volatility, it is loss potential. Loss potential is measured by their fundamental research and should be the primary risk constraint. This is a piece that I wrote a while back discussing some of the differences between fundamental and traditional risk management.

I think the concepts are more important today as the number of experts decrying the use of traditional risk metrics grows.

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.

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!!!

Institutional Investor Magazine article: A Plea to Put Down the Mental Calculator

I recently wrote an article for Institutional Investor magazine (www.iimagazine.com) called "Capturing the Benefits of Risk-Adjusted Return." It was a plea to put down the mental calculator. You can read the article here.

Here is an excerpt from the article:

Hedge funds throw away half of their potential returns by not explicitly calculating risk-adjusted 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 risk-adjusted 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 risk-adjusted return and end up assuming undue risk.