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Alpha Theory Blog - News and Insights

14 posts categorized "Institutional Investor"

July 05, 2018

More Evidence of Manager Skill – Concentration Manifesto Continued

In preparation for a webinar we hosted about the Concentration Manifesto on June 21st we had a client question using batting average (win percentage) as a way of measuring skill. Their contention was that high batting averages do not always result in great returns, because a low hit rate with high asymmetry (lots of upside with little downside) can be even more profitable than predictable low returners.

 

Screen Shot 2018-07-05 at 12.25.30 PM

 

To analyze that point, we looked at the Return on Invested Capital (ROIC) by the same buckets we analyzed batting average.

 

Chart2

 

You can see that there is a similar correlation. Assets that are sized the largest had the highest return on invested capital. Said another way, the Top 5 positions went up an average of 12.1% while the portfolio as a whole went up 8.4% (for shorts, went down 8.4%).  That’s 50% better!

Chart3

 

We then analyzed the distribution of returns by bucket.

 

Again, you can see a predictive quality in manager position sizing. Stocks that have smaller positions have a wider distribution of returns (and more downside). The smallest positions had the most upside, but what we see in the data is that managers can forecast more volatile positions and size accordingly.

 

To finish the point, I’ll pull up a chart from the original Concentration Manifesto where we use our clients’ forecasted returns (Expected Return) and created two portfolios. One with the 20 best forecasted returns and then the rest. In the graph below, you can see that managers can forecast which assets will have the best returns. This shows skill not associated just with positions sizing, but on forecasting price return.

Chart4

 

There is very little question that our clients demonstrate skill. There is also very little question that they have mitigated a substantial portion of their skill by having too many positions.

 

May 03, 2018

Positive Skew…Part 2 – Maybe It’s Not So Bad for Active Managers After All

In my last post, I discussed the negative impact of positive skew for active managers. Basically, that more than 50% of all stocks in a given market underperform the average because there are stocks that go up more than 100% but no stocks that go down more than 100%. This means that if you pick a random portfolio of stocks from the market, you have a greater than 50% chance of underperforming the market because most portfolios will not hold those few stocks that went up more than 100%.

 

Because of the popularity of the last post and TV appearance, we spent time digging further into the data to answer questions posed by readers and viewers. We noticed that there was a tendency for the returns between the average stock return and the index return to be different.

 

And that is the problem with using the average stock return as the hurdle for funds. Investors are not measured against the average stock return, they’re measured against the benchmark, typically the S&P 500. Most indexes are market cap weighted, meaning that the index return and the average stock return are generally different.

 

In the example below, we’ve taken the current S&P 500 constituents and calculated their return since the beginning of 2012 and compared that to an average return (Equal Weighted) and the actual return of the S&P 500. The S&P 500 over that period was up 136% vs 175% for the average stock (this isn’t a perfect analysis because the constituents in the portfolio changed over that time but it is an approximation).

 

Positive Skew-part2

 

The graph above shows the distribution of individual stock returns over that period. You can see the outliers that pull the average stock return (red line) up to a point where 63% of individual securities underperform the average of 176%. But the S&P 500 was up 136% (green line) over that period so only 51% of stocks underperformed the benchmark. Pretty much a coin flip.

 

We brought positive skew up with Andrew Wellington at Lyrical Asset Management. They have done some great analysis comparing the top 1000 stocks by market cap in the US to the S&P 500 each year going back to 1998.

 

Chart2

Source: FactSet and Lyrical Asset Management

 

As you can see in the chart above, the average stock beating the S&P 500 index is a coin flip. For the past 20 years, the likelihood of any individual stock beating the S&P 500 in any given year is 50.2%. If I build random portfolios using the Top 1000 stocks in the US, there is a high likelihood that the portfolio return will be close to the S&P 500 return.

 

Some years are clearly better than others. ’98 and ’99 were horrible stock picking years. If you didn’t own the few stocks that had meteoric rises, you had a high likelihood of underperforming the S&P 500. ’01 and ’02 were good stock picking years. Over 60% of stocks beat the index.

 

What this means, is that any given fund’s batting average should be compared to the batting average of the universe of stocks compared to the benchmark. A 54% batting average in ’98 is heroic, in ’03, 54% is just inline. Take a look at 2017. It was the 3rd hardest stock picking environment in the last 20 years using this metric.

 

But what about other indices? Thankfully, our friend Julien Messias from Quantology Capital Management has done the analysis (1999-2014) comparing the S&P 500 and Russell 2000. Below are thoughts from Julien on the topic:

 

The Russell 2000 components returns exhibit a much more leptokurtic distribution (fat-tailed) than S&P 500, meaning that you have a huge part of the index’s components suffering from huge loss (or even bankruptcies), with an average of more than 60% of the components underperforming the index performance and 2% of the components with huge performance (more than 500% per year). The performance of the index is therefore pulled up by those latter 2%.

Assuming a stock-picker operates at random to choose its investment within the index universe, this means that his performance should be closer to the median performance of the components, than to the index performance itself. Therefore, given that the median performance is almost always lower than the index performance (see chart below), an investor in Russell 2000 securities is very likely to underperform and very unlikely to outperform.

The S&P 500 distribution is much more mean-centered, with very shallow/thin tails, meaning that the average stock picker is much more likely to generate a performance close to the index performance (graph from Lyrical AM) and less likely to underperform.

 

Chart3

Source: Quantology CM

 

The Russell 2000 index more apparently displays the impacts of positive skew because it is less impacted by a contribution of a few very large companies. AAPL, MSFT, GOOG, AMZN make up 12.2% of the S&P 500 while the Russell 2000’s top 4 positions make up 1.7% of the index. The result is that the average of all stocks in the Russell 2000 is much closer to the Russell 2000 index return than the average of all stocks in the S&P 500 (recall the large difference from the 2012 to 2018 analysis that showed the S&P 500 return was 136% vs 175% average of all stocks).

 

This means that the index chosen as the benchmark for your fund has a profound impact on your ability to beat it. More specifically, the probability of beating the S&P 500 with a random portfolio is 50%, for the Russell 2000, it’s 42%.

 

There has been quite a bit of press regarding positive skew. It’s a great conversation but, for the average fund that is measured against the S&P 500, the impact is overblown. Almost every investor is compared against a benchmark. I recommend that you dig a layer into your benchmark and measure its positive skew, the likelihood of beating the average stock return, the likelihood of beating the index return, and compare your hit rate against the hit rate each year to know how difficult or easy it was for you on any given year.

 

Quantology Capital Management Russell 2000 and S&P 500 Analysis:

 ­ Screen Shot 2018-05-03 at 10.03.58 AM Screen Shot 2018-05-03 at 10.05.52 AM

Does not include management fees

Data is cleaned from index turnover, with updates every year

April 06, 2018

Positive Skew is Negative for Active Managers

 

Let’s play a game. In this game, there are 10 random poker chips in a bag. 9 of these chips will give you a return between -8% and +8% on the money that you bet. The 10th coin will give you a 100% return. The distribution of returns for this game has a positive skew.

 

Screen Shot 2018-04-06 at 9.29.11 AM
 

If offered to put money down on this proposition you would take it because you would expect a 10% return if you could play the game over and over.

 

Now let’s add a wrinkle. Your goal isn’t just to make a positive return, you have to beat the bag. The bag puts 10% of their money on each chip and pulls them all. Voila, a 10% return. One last wrinkle, you can only pick one chip at a time.

 

How many times out of 10 would you beat the bag? Only 1 in 10. 90% of the time you would lose to the bag. It doesn’t matter if we expand the number of chips as long as the bag maintains the same positive skew (we could increase the to 100 chips and you get to pick 10, 100 chips and you pick 1000, etc.)

 

By now, you’ve probably guessed that the bag is the market, the chips are stocks, and you are, well, you. This is the game we play when trying to beat an index. True, you can be better than the market at figuring out the good chips but given that initial conditions for a random game means you lose 9 out of 10 times, it’s really hard to beat the market. Add fees and the likelihood of beating the market goes down even further.

 

Positive Skewness has gotten a decent amount of press over the past year because of the championing of JB Heaton who wrote a paper1 researching the impacts of positive skew on manager underperformance. Heaton’s paper is similar to research from Dr. Richard Shockley in 19982. See below for an article written by Bloomberg News on the topic.

 

Picture1

Source: Bloomberg News (“Lopsided Stocks and the Math Explaining Active Manager Futility” by Oliver Renick)

 

Given that many of the conversations active managers have today revolve around active versus passive, “positive skew” should be top of mind. This is my push to increase awareness.

 

Given that active managers can’t change market skew, what should we do? We could measure skill in a different way. Let’s say I want to measure a manager skill. If I take all of the stocks of the markets they’re investing in and then randomly build 100,000 portfolios with the same number of securities as the manager. I can then plot where that manager falls on the distribution and give them a Z-Score for how far away from the norm they are. I could do the same thing for hedge funds by randomly buying and selling securities in the same universe as the investor.

 

I’m not saying that this excuses active managers from underperforming passive strategies, but it should at least be a more realistic assessment of their skill. My hope is that positive skew becomes just as common an explanation as fees when discussing active manager underperformance. Only by knowing the causes, will we be able to make changes that allow active managers to outperform.

 

 “Why Indexing Works” by JB Heaton, Nicholas Polson, and Jan Witte

2  “Why Active Managers Underperform the S&P 500: The Impact of Size and Skewness” published in the inaugural issue of the Journal of Private Portfolio Management. One of the original authors of the study is Richard Shockley.

Related paper: “Do stocks outperform treasury bills?” Hendrik Bessembinder of Arizona State University

 

March 12, 2018

Capital Allocators Podcast with Ted Seides: Moneyball for Managers

 

Learn how to enhance your investment results in this great podcast from Ted Seides and his guests, Clare Flynn Levy from Essentia Analytics and Cameron Hight from Alpha Theory.

This conversation covers the founding of these two respective businesses, the mistakes portfolio managers commonly make, the tools they employ to help managers improve, and the challenges they face in broader adoption of these modern tools. The good news is the clients of Essentia Analytics and Alpha Theory have demonstrated improvement in their results after employing these techniques. If you ask Clare and Cameron, you may develop a whole new appreciation about the potential for active management going forward.

 

LevyHight-FINAL

 

By creating a disciplined, real-time process based on a decision algorithm with roots in actuarial science, physics, and poker, Alpha Theory takes the guessing out of position sizing and allows managers to focus on what they do best – picking stocks.

In this podcast, you will learn how Alpha Theory allows Portfolio Managers convert their implicit assumptions into an explicit decision-making process. 

 

To learn how this method could be applicable to your decision-making process:

 

LISTEN NOW

 


 

 

March 02, 2018

Size-Based Batting - A Different Perspective on Stock Selection

 

How do you determine if an investor is a good stock picker? One commonly used measure is to count the number of positions that make money (winners) divided by the total number of positions. This metric is commonly called a Batting Average, analogizing stock picking with baseball hit-rates.

The problem with Batting Average is that several inconsequential positions that lose money can really bring down the total. We saw this with our clients. They have historically outperformed other funds (every year for the past six) but have a batting average, adjusted for the move in the bench, of only 51%.

We decided to take a different approach and measure the total exposure of positions that made money versus the total gross exposure of the fund. For instance, if 60% of a fund made money on an alpha-adjusted basis and the fund was 120% gross exposed, then the fund had a Sized-Based Batting Average of 50% (60/120).

Our clients had a Sized-Based Batting Average of 54% versus the non-sized based average of 51%. That means that our clients were good at selecting investments and at sizing them, but they were harming their overall returns with small losing investments.

Alpha-Adjusted Batting Average1

 

Screen Shot 2018-03-02 at 10.09.00 AM

 

In the table above, Size-Based Batting, while not perfectly consistent, is generally better from year-to-year for our clients (exceptions being 2012 and 2015).

We’ve performed other analyses that have proved this point, specifically that our clients’ positions under 1% dramatically underperform the rest of the portfolio, but Sized-Based Batting presents a compelling way to highlight the “small position” issue (see the “Concentration Manifesto” for other issues with small positions).

In our profession, it is incredibly difficult to detangle skill from luck and, as cathartic as it would just rely on returns, returns are actually negatively correlated with next year’s returns for most funds (i.e. funds that outperform in year N have a higher likelihood underperforming in year N+1 – there are multiple research sources that analyze mean reversion in funds, here is one).

Sized-Based Batting is a nice addition to the allocator’s tool bag for finding managers with stock picking skill. In much the same way, managers should use Sized-Based Batting as a way to highlight their strengths and compare it to traditional Batting Average as a way to potentially point out weaknesses.

 

1 S&P 500 for US securities and MSCI WEI for non-US securities

2 Why is “All Time” so low compared to each year? Reason #1: There are many more observations in the more recent years which skew the overall results to be more similar to the more recent years. Reason #2: There were many assets that were losers over “All Time” while being winners for multiple years (small win in 2015, a small win in 2016, big loss in 2017 = 2 winning period vs 1 losing but a loser in the All-Time bucket).

 

 

February 07, 2018

Alpha Theory Case Study: Top Performing Funds of 2017

Alpha Theory’s clients have historically outperformed (see 2017 Year in Review from last month), but 2017 was special as our most active client was also the 2nd best performing equity fund. We have worked with them since their launch, and their focus on discipline and process is a testament to how to build a fund. If you would like to learn more about the client, their challenges, their solution, and the data supporting their process, check out the Case Study.

 

DOWNLOAD NOW

 

 

January 05, 2018

2017 Year in Review

 

Alpha Theory’s product helps investment managers reduce emotion and guesswork in position sizing. The result is reduced errors and improved returns. For six consecutive years, Alpha Theory clients have outperformed their peers (see table below – we use the benchmark of Major Equity Hedge Index because 86% of Alpha Theory clients are hedge funds). Our clients have consistently outperformed their competitors, more than doubling their returns over the period.

 

Graph1

*Totals are not including 2017 data

In 2017, our average client generated 18.9% returns and, when it is released, I anticipate that we’ll beat the Hedge Index again. These results are consistent with other blog posts we’ve written highlighting our clients in 3rd party rankings: Reuters / WSJ / Novus.

 

NEW 13-F ANALYSIS

This year, we expanded our analysis through a new 13-F dataset with all publicly filing funds. The upside of using this dataset is it enables us to compare results against every reporting fund in 2017. The downside is it only includes the US equity long positions. The results indicate that once again, Alpha Theory clients outperform their peers.

The average Alpha Theory client performance in 2017 (13-F data) was 27.6% vs 19.9% for all others (3013 total funds with over 20 positions). That’s almost one full standard deviation higher (8.8% standard deviation) than the mean and has a Z-Score of 2.03 (statistically significant above the 95% confidence level).

Even more interesting was the individual performance results of our clients, one Alpha Theory client was the 2nd best performing fund in 2017 (this client thanked us more than once for our contribution to their success) and four clients landed in the top 40 performers.  We also had six of the top 100, and 10 of the top 200. Statistically, we’d anticipate less than 1% in all categories because Alpha Theory clients are less than 1% of all funds. Instead, as in previous periods, there is a concentration of Alpha Theory clients amongst the top performers.

Graph2

Simply put, Alpha Theory clients outperform their peers. The traits these firms share are discipline, intellectual honesty, and process focused. They gravitate to Alpha Theory because it is their tool kit to implement and measure that process.

 

PROCESS EQUALS PERFORMANCE

Alpha Theory clients use process to reduce the impacts from emotion and guesswork as they make position sizing decisions. Alpha Theory highlights when good ideas coincide with largest position sizes in the portfolio. This rules engine codifies a discipline that:

1. Centralizes price targets and archives them in a database

2. Provides notifications of price target updates and anomalies

3. Calculates probability-weighted returns (PWR) for assets and the portfolio as a whole.

4. Enhances returns

5. Mitigates portfolio risk 

6. Saves time

7. Adds precision and rigor to sizing process

8. Real time incorporation of market and individual asset moves into sizing decisions.

DISCIPLINED USAGE REDUCES RESEARCH SLIPPAGE

Alpha Theory’s research not only suggests that adoption of the application by itself leads to improved performance, but actual usage intensity further enhances results.

Usage intensity is determined by:

1. Percent of Positions with Research

2. Correlation with Optimal Position Size

3. Login Frequency

 

Graph3

1.Measured as the annualized ROIC where data was available, for a sample of 48 clients, 12 for each quartile

 

OPTIMAL POSITION SIZING REDUCES RESEARCH SLIPPAGE

Comparing clients’ actual versus optimal returns shows:

HIGHER TOTAL RETURNS
ROIC is 4.5% higher.

IMPROVED BATTING AVERAGE
Batting Average is 8% higher. Explanation: many of the assets that don’t have price targets or have negative PWRs are held by the fund but recommended as 0% positions by AT. Those positions underperform and allow AT’s batting average to prevail.

 Graph4

1.Measured as the average full year return for clients where full year data was available, adjusted for differences in exposure, net of trading costs

2.Before trading costs

 

ALPHA THEORY CLIENTS OUTPERFORM NON-CLIENTS
Alpha Theory clients have outperformed Major Equity Hedge Indices every year since Alpha Theory started collecting historical data. While our clients are a self-selecting cohort who believe in process and discipline; process orientation goes hand-in-hand with Alpha Theory software that serves as a disciplining mechanism to align best risk/reward ideas with rankings in the portfolio.

 Graph5

PRICE TARGETING REDUCES RESEARCH SLIPPAGE

Alpha Theory has further found that ROIC for assets with price targets is 5.6% higher than for those without price targets. Some investors chafe at price targets because they smack of “false precision.” These investors are missing the point because the key to price targets is not their absolute validity but their explicit nature which allows for objective conversation of the assumptions that went into them.  Said another way, the requirements of calculating a price target and the questions that targets foster are central to any good process.

Graph6*Long-only as many short positions are hedges and have no price targets

 

December 15, 2017

Superforecasting for Investors: Part 2

Alpha Theory hosted a book club on December 6th with portfolio managers, analysts, and allocators coming together to discuss “Superforecasting” by Phil Tetlock. We were lucky enough to have a Superforecaster, Warren Hatch, moderate and perform forecasting exercises with the group. We spent 2 hours together and only scratched the surface on applying Superforecasting to investing.

 

Here are a few key takeaways:

1. COMMON ATTRIBUTES OF SUPERFORECASTERS:

INTELLIGENCE: Above average but genius isn’t required

QUANTITATIVE: Not only understand math but apply it to everyday life

FOXES, NOT HEDGEHOGS: Speak in terms of possibilities, not absolutes

INTELLECTUALLY HUMBLE: Understand the limits of their knowledge

SYSTEM 2 DRIVEN: Use the logic-driven instead of instinct-driven portion of their brain

DO NOT BELIEVE IN FATALISM: Life is not preordained

CONSTANTLY REFINE: Make frequent small updates to their forecast based on new information (but not afraid to make big changes when warranted)

COUNTERFACTUALS: Believe that history is one of many possible paths that could have occurred

OUTSIDE VIEW: Incorporate the internal and external views

GROWTH MINDSET: CONSTANTLY SEARCH FOR WAYS TO IMPROVE THEIR FORECASTING PROCESS

 

2. IDENTIFYING TALENT: There are identifiable attributes that can be used in hiring and have a profound impact on forecasting skill

 

Active Open Mindedness*

   image from alphatheory.typepad.com

Fluid Intelligence*

image from alphatheory.typepad.com

 

* At a prior book club, we measured participants and the results showed they had the attributes of Superforecasters with high Active Open-Mindedness (3.99 out of 5) and high Fluid Intelligence (8 out of 10 – this is the highest score that the Good Judgment  folks have seen).

Active Open Mindedness (i) and Fluid Intelligence (a) are two measurable traits that managers can use to select talent. In the chart below, the improvement impact of the definable attributes equates to about 40% of their forecasting skill over standard forecasts.

image from alphatheory.typepad.com

3. DEVIL’S ADVOCATE: Firms should appoint a Devil’s Advocate for each investment to expand critical thinking (someone to ask the question, “I see your downside is $40. How is that if the 52-Week Low is $22 and the trough multiple would put it at $25?”)

 

4. OUTSIDE VIEW: Firms should require an Outside View for every investment idea (“While everyone I’ve spoken to says this deal will close, only 20% of deals with one party under SEC investigation close.”)

 

5. REFINEMENT: New information should always be incorporated in forecast (think Bayesian).

 

6. TEAMS MAKE BETTER FORECASTS: Team dialog generally improves forecasting accuracy.

 

7. FORECAST CULTURE: Firms should embrace “forecast” as part of their vernacular and conversations should revolve around how information impacts the forecast.

 

8. MEASURE TO BE BETTER: We all forecast, but we rarely measure. That fact needs to change if we really want to improve.

 

9. CLUSTERING: Break complex topics into individual components that are better able to be forecast and use the combination of the smaller forecasts to forecast the more complex. (ie. Will AAPL break $200 is a complex forecast that can be broken down into Will iPhone X ship more than 400m units? / Will Samsung’s technology outpace Apple’s? / etc.)

 

10. INDEXING: Individual clustering questions can be weighted to come up with a forecast for the complex topic instead of using simple equal weighting.

 

11. DIVERSITY OF FORECASTS MATTER: Forecasts made from similar perspectives are less accurate than those made from multiple perspectives (see Boosting below).

 

12. BOOSTING: If you have three forecasters with different perspectives that all arrive at a 70% probability of an event occurring then the actual probability is greater than 70%.

 

13. GISTING: We didn’t get to spend much time here, but the idea is that complex subjects, reports, presentations, etc. can be distilled down into gists that the team votes on and refines into supergist. Full understanding is never just quantitative or qualitative. Superforecasting is quantitative. Supergisting attempts to provide the qualitative piece. 

 

14. HYBRID FORECASTING COMPETITION: IARPA, the defense agency that sponsored the forecasting tournament that launch the Superforecasters (Good Judgment) is sponsoring a new Man+Machine Forecasting Tournament. For those interested in Forecasting and Machine Learning, this is your spot: https://www.iarpa.gov/index.php/research-programs/hfc

 

September 14, 2017

Asset Manager Reliance on Human Judgement vs Machine

Asset management is the industry most reliant on human judgement according to a recent Price Waterhouse study on Data Analytics.

 

Screen Shot 2017-09-14 at 10.14.59 AM

 

Asset managers rely on human judgement 3x more than the next industry. For an industry with some of the best and brightest, we seem to be far behind. There is no expectation that this will happen overnight, but at a bare minimum we need to be experimenting with ways to enhance our judgement with machines.

Alpha Theory has been doing just that for over 10 years and our clients have outperformed the average hedge fund by over 2x. Getting started is not hard. Adopting “machine” does not require a wholesale change as all of our clients operate with Man + Machine. What it does require is an acceptance that Man alone is generally inferior to Man + Machine and a cultural embrace of the “machine” as an enhancement to the daily judgements we all make.

The reliance on human judgement will fall over time for asset managers. Do not be the last the change.

 

 

April 17, 2017

Investor Bias Seen in Data

By Cameron Hight and Justin Harris

 

Alpha Theory’s Analytics Department studies clients’ historical data to provide useful insights. Over time, we have identified patterns that point to certain investor biases. Typically, biases are highlighted by deviations between actual and optimal position sizes. Said another way, biases occur when managers size positions different than what the risk-reward would suggest.

 

Here are a few examples:

 

1. NOT ADJUSTING POSITION SIZE AFTER A BIG PRICE MOVE: One of the most common biases we see in the data, is that after large positive price changes, managers are less likely to cut exposure, even though the probability-weighted return has diminished due to the move. The potential damage from this willful ignorance is compounded by a much larger position with a lower expected return. The typical behavior of investors is to let winners run, however, we’ve found that to be sub-optimal for fundamental funds.

The first step to alleviating this bias is to force re-underwriting names when they reach an unacceptable PWR. If the new assumptions justify the size, then all is good. If not, then the manager knows there is some bias that is causing them to stay in the position. Forcing re-underwriting at critical levels ensures that checks and balances are in place so that profits are kept and not lost on reversals.

 

2. NOT SIZING UP GOOD PROBABILITY-WEIGHTED RETURN WHEN INITIATING A POSITION: When analysts input price targets into Alpha Theory, and a manager decides to act on that information, what we’ve seen in the data is a tendency to build a position over time. We’ve found, on average, this is detrimental to returns. Slowly scaling into a high conviction and high probability weighted return name causes investors to miss some of the return potential.

 

3. UNDISCIPLINED APPROACH: Our data has shown that managers who are more disciplined (i.e. have more of their portfolio with price target coverage and size closer to optimal position sizing) tend to outperform those who don’t. Unfortunately, running complex sizing algorithms through our heads is not something we do well. What we see in the data is that positions without explicit price targets underperform. Be it hubris or any other number of reasons, it’s almost always detrimental to returns.

 

4. DIVERSIFYING: Our research shows that the largest positions in client portfolios outperform smaller names by a big margin, mostly because the batting average on top holdings is high. Most clients nullify this benefit by taking on many more names in the portfolio at much lower probability-weighted returns. We’ve done research which shows that concentrated portfolios outperform diversified portfolios by 2.2% on an alpha basis (run as a Monte Carlo study using batting averages calculated for various portions of client portfolios 2011-2016). The cost of diversification is a loss of alpha without a commensurate improvement in risk protection.

 

For 2016 returns, if clients sized using the suggested Optimal Position Size, they would have been better off by 5.1%. Clearly we recognize that not every position was able to be sized optimally, but even if half of that difference could have been captured, there was a lot of money left on the table. The biases above highlight why some of the difference occurs. It’s hard to beat an unemotional version of yourself, especially when we’re not psychologically built for the game.