Scott Vincent of Green River Asset Management published an article titled “Is Portfolio Theory Harming Your Portfolio?” In it, he describes how Modern Portfolio Theory (Efficient Frontier – Markowitz, CAPM – Sharpe, and Efficient Market Hypothesis – Fama) has changed the shape of the investment industry from stock picking funds to super-diversified quantitative or quasi-quantitative funds. Volatility gained acceptance as the standard measure of risk for one primary reason, it was measurable (see answers to questions 2 and 10 in “Great Investor Mentality Quiz”). But being measurable doesn’t make it right. In “Is Portfolio Theory Harming Your Portfolio?”, Vincent explains:

Amazingly enough, there’s not much empirical “proof” as to why we should use variance as a measure of risk, yet it plays a critical role in almost all large financial transactions. It seems that academicians needed a way to quantify risk to fit mathematical models and they grabbed variance, not because it described risk very well, but because it was the best quantitative option available. But just because it is convenient, and it carries a certain intuitive appeal, doesn’t make it right.

If volatility is not a very good proxy for risk then are our historical judgments of active managers wrong? Yes. Do we need to change the way that we judge managers? Yes. In fact, there are half a dozen “risks” that are more important than volatility. I’m often surprised by investors that care more about volatility than leverage. I certainly believe the latter is more indicative of potential risk (i.e. Asian Financial Crisis, Mexican Financial Crisis, Russian Financial Crisis, S&L, Junk Bond, Sub-Prime Mortgage, et. al. – see article comparing Sub-prime and Junk Bond). Volatility can be tough to stomach, but potential downside loss is true risk. As Vincent says (concept described in “Eight Mistakes Money Managers Make” presentation):

Risk is often in the eye of the beholder. While “quants” (who rely heavily on MPT) might view a stock that has fallen in value by 50 percent over a short period of time as quite risky (i.e. it has a high beta), others might view the investment as extremely safe, offering an almost guaranteed return. Perhaps the stock trades well below the cash on its books and the company is likely to generate cash going forward. This latter group of investors might even view volatility as a positive; not something that they need to be paid more to accept.

Recognize that there is more than one measure of risk and that volatility is not a synonym for risk. Risk is a combination of downside potential, liquidity, time horizon, sector exposure, leverage, market correlation, and volatility (and probably several more). Just like a pilot cannot look at one gauge to fly the plane, a portfolio manager cannot look at one measure of risk to manage a portfolio.

Another major point of “Is Portfolio Theory Harming….” is that diversification is not only over-rated, but it becomes corrosive at a certain point:

The appeal to diversification, according to quantitative finance, is the idea that it allows us to enjoy the average of all the returns from the assets in a portfolio, while lowering our risk to a level below the average of the combined volatilities. But since we can’t call volatility risk and we can’t reliably predict volatilities or correlations, then how can we compile diversified portfolios and claim they are on some sort of efficient frontier? These super-diversified portfolios may be inefficient — it may be possible to earn higher rates of return with less risk. It may be that by combining a group of securities hand-selected for their limited downside and high potential return, the skilled active manager with a relatively concentrated portfolio has greater potential to offer lower risk and higher returns than a fully diversified portfolio.

Even if we were to make volatility reduction paramount, the case for extreme diversification does not hold true. A study by Fisher and Lorie concludes that, “Roughly 40 percent of achievable reduction is obtained by holding two stocks; 80 percent, by holding eight stocks; 90 percent by holding 16 stocks.” Other studies by authors such as William F. Sharpe, Henry A. Latane’ and Donald L. Tuttle make similar statements.* Needless to say, it is hard to argue that 100 positions is necessary for volatility reduction.

But honestly, the more damning case against super-diversification is time:

A fund manager’s job is to identify assets that are priced “inefficiently,” where the market has ostensibly made an error and a stock is available at a level that allows for relatively little risk versus expected return. But finding inefficiencies and maintaining a portfolio is difficult work and requires resources (a manager’s time and brain power, among the most important of these). Resources are not unlimited (most importantly a manager’s time). Therefore, the amount of resources devoted to each specific investment varies inversely with the amount of investments owned in the portfolio. The more positions added to the portfolio, the less likely a manager is to capture these difficult-to-find inefficiencies because he/she has less time and other resources available to do so.

I have used the concept of “mental capital” for years with clients. I ask the client how many hours a month it takes an analyst to cover an investment. For example, let’s say 10 hours. Then we’ll also assume that the analyst has other ideas that are being considered for the portfolio and for each existing investment, they spend another 5 hours working on new ideas. That works out to 15 hours for each portfolio position. If we assume each analyst works about 150 hours a month (excludes time staring at the P&L and filling out March Madness pools), that means each analyst can cover about 10 names with 10 on the watchlist. That means a fund with a team of four can reasonably cover 40 names. But a majority of funds end up with 80 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. If it does not matter, get rid of it because it is a drain on mental capital.

All of these facts lead to the question, how do low diversity / high volatility portfolios perform? In fact, fairly well, granted that we do not have a good way to “risk adjust” portfolio returns given that we are no longer using volatility. However, Vincent highlights, “Multiple studies indicate that funds which are more actively managed, or more concentrated, outperform indexes and do so with persistence (Kacperczyk, Sialm and Zheng (2005), Cohen, Polk, Silli (2010), Bakks, Busse, and Greene (2006), Wermers (2003), and Brands, Brown, Gallagher (2003), Cremers and Petajisto (2007)). While we need to acknowledge that because we can’t measure risk, these studies, like any empirical work, need to be taken with a grain of salt. It is nonetheless interesting that if we compare the studies that focus on teasing apart the influence of more active, concentrated management, to the broad all-inclusive studies, there’s a large change in the signal received.”

Funds with the highest Active Share [most active management] outperform their benchmarks both before and after expenses, while funds with the lowest Active Share underperform after expenses …. The best performers are concentrated stock pickers ….We also find strong evidence for performance persistence for the funds with the highest Active Share, even after controlling for momentum. From an investor’s point of view, funds with the highest Active Share, smallest assets, and best one-year performance seem very attractive, outperforming their benchmarks by 6.5% per year net of fees and expenses. – Cremers and Petajisto (2007)

Basically, volatility is a distraction, diversification is a drag, and active concentrated management is a superior method of investing. That is music to the ears of Graham & Dodd’er out there. In a world where the dogma is against you, hold fast that the truth (i.e. common sense) is on your side.

Finally, I have saved my favorite quote of Mr. Vincent’s for last because it describes Alpha Theory perfectly, “The degree of concentration in a fund should reflect the confidence a manager has in the inefficiencies found, and the weight of those investments should reflect the probability of success as well as the level of asymmetry present in the prospective return profiles of the assets.” Right on Mr. Vincent, write on.

*If volatility reduction was the game, then holding 8 positions would get you almost home. But that would mean that the average position size would be 12.5%. I believe that diversification can be approached from another angle that involves downside tolerance. Start by asking, what is the maximum position size I am willing to take? Let’s say it is 6% of fund value. And if the minimum position size is 1% and position sizes are scaled linearly then a 100% gross exposure fund would have about 29 positions (6% max position size – 1% min position size = 5% / 2 = 2.5% midpoint + 1% min position size = 3.5% average position size – 100% gross exposure / 3.5% average position size ≈ 29 positions).

Now what does this mean for investors? We can assume that most investors have reasonable impulse control or they would have never made into or through college (personally, my impulse control went on sabbatical a few times during college). But there are still situations where the Id has to be tamed and the elephant kept in check. So what is an investor’s marshmallow moment? How about when an investment’s value increases beyond our expectations and our emotion tells us that “this thing has legs.” Our impulse is to scoop that marshmallow up and enjoy the ride as our investment trades even higher. The more difficult decision is to sell because the asset has met expectations. How about putting an idea, that a buddy told us about, in the portfolio before we do our full due diligence? How about holding onto that 40 basis point position, even though we know it has very little impact on portfolio performance and is a distraction from other research efforts?

Impulses and delayed gratification come in various forms. When it comes to fatty foods and narcotics, we may be rock solid, but when it comes to financial decisions, make sure you aren’t scooping up one marshmallow today at the expense of two tomorrow.

“If you listen to the press or read missives from investment firms, you might conclude that dividends play a prime role in capital accumulation. In fact, well-known strategists have pointed out that dividends have accounted for 90 percent of equity returns over the past century. This statistic is potentially very misleading and warrants further examination. Here’s the ending without the plot: price appreciation is the only source of investment returns that increases accumulated capital over time.

The cause of the confusion is that analysts do not distinguish between the equity rate of return and the capital accumulation rate. Depending on the choices of the shareholder, the rates can be very different. Understanding the distinction is essential for assessing past results and for thinking about satisfying future financial obligations.”

My contention has always been simple, “dividends do not create value.” It was my belief that for non-taxable accounts, dividends are fairly neutral, but Mr. Mauboussin makes a compelling case that dividends may even be a drag in non-taxable accounts because most of us do not actually reinvest the full dividend back into the equity. His analysis is thought provoking and definitely worth a read, The Real Role of Dividends in Building Wealth as are most of his writings which can be found on the Legg Mason website.

I wrote an article last month about why 50% of upside is not as good as 50% of downside is bad (see article here– Recap: A $100 million fund that rises 50% then falls 50% the following year will be left with $75 million. This asymmetry highlights the critical importance of understanding downside in portfolio management). I subsequently went out to lunch with a friend who is the marketing person from a fundamental long/short fund. We were discussing how some investors ding them for underperforming the market when the market rises and fail to give them credit for their positive relative performance in down-markets because they still lost money. This made me think of our previous example of the fund that started with $100 million and ended with $75 million. What if I just said that hedge funds only participated in 80% of that move, or 60% of the move, how would that change the results?

This example shows that, at 80% capture of upside and downside, the loss is decreased to 16%. At 60%, this example shows a 9% loss. But this is an extreme example where loss is equal to gain, what if we dampened the loss to 30%?

This next example is interesting because we now have positive overall returns and we find that the best Capture (you can think of the Capture as amount of bankroll bet because betting a percentage equal to the capture would create the same return) is somewhere around 60%. Actually, the optimal bet is at 67% which I explain how to derive in my previous article on the Kelly Criterion. My friend also told me that his fund captures 63% of market upside and only 23% of market downside and that the Credit Suisse Long/Short Equity Index captures 62% of upside and 37% of downside. I thought it would be interesting to take market (S&P 500) historical returns and see how they would compare to just being long the S&P 500 given the favorable upside/downside capture of the Credit Suisse Long/Short Equity Index. This analysis does not use actual hedge funds results, but instead implied returns using the capture rates compared to the S&P 500. The results are interesting:

Over the past 15 years, hedge funds have outperformed the S&P 500 due to the simple fact that they have smaller drawdowns. This leaves more capital to benefit in up markets even if the upswings are to a lesser degree. Even over longer periods of time where the S&P outperforms hedge funds, the hedge fund returns are subject to a lower standard deviation.

Hedge funds are generally considered risky investments. But I believe the opposite is actually true for fundamental long/short funds that do not use excessive leverage. As the results bear out, hedge funds are better protectors of capital and are not damaged to the same degree as long-only strategies during down markets. The asymmetry of returns in compounding investments is a true “feather in the cap” for hedge fund investments and does not get the credit it deserves from some hedge fund investors. In fact, I believe the up 50%/down 50% example should be a component of every hedge fund manager’s marketing documents. It highlights the true benefits of capital preservation for compounding investments inherent in hedge funds. If you would like Alpha Theory to help your fund analyze the impact of up-down capture in your portfolio and help you customize your presentation to investors, please contact us at info@alphatheory.com.

If a $100 million dollar fund is up 50% one year and down 50% the next, do you still have a $100 million dollar fund? No, the fund has been reduced to $75 million or a 25% loss. I use this question in almost every conversation with an investment manager to highlight the importance of downside.

And the order of the sequence doesn’t matter. We could have lost 50% first and then gained 50% and the ultimate result would be identical. So, why does loss have a disproportionate impact? This simple illustration highlights the asymmetry of returns in compounding portfolios. This means that returns come in sequence not simultaneously. So any loss creates a smaller bankroll with which to make subsequent bets. Gains on the other hand, although they do increase your bet potential, lack the impact of a commensurate amount of loss (this is why the Kelly Criterion makes sense). The reason is simple. In our original example, the $50 million gain from a 50% profit is only 33% of the overall $150 million in the fund. But, the $75 million loss associated with going down 50% represents a full 50% of the $150 million fund total. The 25% loss associated with this example is the empirical proof of Buffett’s very famous quote that served as the prelude to this article.

So if loss and gain are not created equal, then what is more important to define in portfolio construction? How much you can make or lose? Clearly, understanding loss is the foundation of all sound portfolio management. Just ask any manager fighting to get back to their high-water mark (a manager down 25% in ’08 has to have returns of 33% to get back to pre-2008 levels).

The message is short and sweet. Spend the time to estimate an explicit downside before an asset is allowed into the portfolio because downside risk is the true swing factor in portfolio management. Additionally, if a firm only calculates a single value based on the thesis coming to fruition there is an implicit assumption of a 100% probability of that thesis coming true. Finally, mandating a discrete downside calculation allows the research team to expand their investment mind and encourages the search for the devil’s advocate. This subtle shift moves a firm away from a process where the focus is typically finding evidence to support their thesis (http://en.wikipedia.org/wiki/Confirmation_bias) to a process that searches for complete information.

I’ve had hundreds of conversations with fund managers, analysts, traders, etc. about the warts of their investment process. And, as simple as it is, if given the ability to make only one change inside of a fund, calculating a downside would be it (try out our calculator to measure the impact of downside).

As a fundamental investor, these kinds of comments make me very happy because it gives me insight into the primary reason that investments can become mispriced. There are billions upon trillions of dollars that are being actively managed with this trading mentality which means they have profound impacts on many underlying assets. So when I see my great long idea trade down 5% for no apparent reason, I can make the assumption that it is not 100% guaranteed that someone knows something that I do not. It may just be a different investing philosophy (momentum / technical in this case) influencing the price. That being said, I should always question my thesis in a never-ending quest for the Devil’s Advocate’s point of view, but I should also appreciate that stocks move irrationally over short-to-intermediate periods of time and I hope to remain solvent for the long-term to benefit from a more rational valuation.

Here’s a big thanks to all non-fundamental investors, without whom, I would rarely be able to find investable opportunities.

I’ve often been asked by portfolio managers, why I think it is important to force analysts to come up with a discrete probability. Closing the gap between my meaning of “likely”, “probably”, “possibly”, “almost certainly”, “maybe”, “slim chance”, etc. and your interpretation is a critical reason.

There are numerous studies that find that one person’s intentions generally (look, another probability expression) don’t match their interpretation. These studies show that many times the gaps are so vast to make the words meaningless.

As a portfolio manager, the most important goal is to accurately capture the economic impact of an asset in your portfolio and size the position based on that impact. Without an accurate assessment of probability, that task is rendered ineffective.

There is a considerable amount of literature on the subject and I’ve chosen a few that prove my point. There are studies that show that certain probability expressions on average have similar meaning. However, the variance between individuals was great and we are talking about interpersonal relationships where the expression of probability can have a huge impact.

Check out the studies for proof that Probably is not a Probability.

“How probable is probable? A numerical translation of verbal probability expressions”, Ruth Beyth-Marom, March 1982

“Adolescents’ and adults’ understanding of probability expressions”, Michael Biehl, May 2000

Cost and Time to Build – Alpha Theory is the culmination of over 20 man-years and millions of dollars in design and development. For many funds, the money variable in the equation gets a small weighting, but the time is another matter. A few dedicated resources will be required to steward the process but do not forget that the portfolio manager and analysts will continuously be involved with design and testing. Their time is precious and their mental capital is better allocated on analysis, not software building.

It’s Complicated! – We all have smart people on our teams so yes you can figure out many of the challenges but there is also a possibility that some of these hurdles may render the system ineffective. Let’s go through a few challenges:

+Time Horizon. How do you deal with short dated returns versus long dated returns? You can’t use text book annualization because they produce wildly inaccurate return profiles over very short timeframes. Additionally, how do you handle losses in short time periods? Let’s ask a question, would you rather lose 20% in 2 days or 2 years. The gut reaction is 2 years, but that’s incorrect because you would rather get the loss behind you. I’ll ask it another way, would you rather have $0.80 two days from now or $0.80 two years from now. Dealing with these challenges in determining returns is complicated and a challenge that Alpha Theory has solved for you.

+Portfolio and Sector Exposure. Do you care about total portfolio gross and net exposure? How about sector exposures? If so, then let’s take a portfolio with constraints of 200% gross/40% net, global region exposure maximums of 50% gross/30% net, and industry exposure maximums of 40% gross / 20% net. Assume you have lots of good ideas and your portfolio of research exceeds many of these constraints. How do you construct a portfolio that maximizes risk-adjusted return while paying heed to each of these constraints? The answer requires an optimization function. To do this in Excel you either need to buy incremental software or create kludge Solver functions. The optimization function is inherent in Alpha Theory.

+Extreme Loss Constraints. Not all returns are created equal. The width of the distribution has a dramatic impact on the long-term geometric return of the portfolio for two assets with the same arithmetic risk-adjusted return. For example, assume you could only make one bet over and over for the rest of your career but they both had a 20% risk-adjusted return. Bet #1 has a 100% chance of going up 20% each year. Bet #2 has a 50% chance of going up 90% or 50% chance of losing 50% each year. Each bet has a 20% expected return but which one do you prefer and how should it change your position size? Well if we assume that we have $1 today and we make each bet sequentially 10 times in a row we would end up with $6.20 from choosing Bet #1 and $0.77 from choosing Bet #2. This explains the potentially damaging effects of wide-distribution returns and why Kelly Criterion is the optimal method of choosing bet size. Alpha Theory includes this dynamic in position sizing and continues to research new ways to improve the long-term geometric return of the portfolio.

+Other Complications. Alpha Theory has spent exhaustive time investigating improvements to representing research and constraints in the form of position size, including market correlation, liquidity, loss constraints, analysis confidence, market-implied expectations, differences between longs and shorts, and many more factors that go into position sizing. These are challenges that every homegrown solution will have to traverse. Any cost-benefit analysis of growing your own solution must include these intricacies.

Collaborative Environment – To foster an effective solution the system must encourage multiple users. Excel is a closed environment that generally allows one user at a time and in not conducive to personalized views. An analyst, a portfolio manager, and a risk manager will all look at the system differently and be tasked with different elements of maintenance. They need their own customized views that highlight the variables to which they need to manage. Alpha Theory is an open architecture which allows multiple users simultaneous access to the system at any time and any geography. Excel is not built to allow this level of collaboration and synchronization and will falter as the organization tries to create a holistic solution.

Three Dimensions – Excel is two-dimensional which makes it difficult to have much variance in research structure. For instance, one analyst wants to describe the distribution of returns in a simple Bull and Bear case, but another has a more complex representation which has a Bull and Bear case but also a possibility of Black Swan and takeout. These are real scenarios that should be encouraged in the research process. Alpha Theory’s multi-dimensional platform allows analysts the flexibility to describe their research in ways that best represent the true byproduct of their research.

History – To maintain a history of research in Excel, firms will keep snapshots of the system going back in time. This is kludge way to retrace the firm’s investment process. Alpha Theory keeps a record of change made by analysts and portfolio managers and can show a consolidated history of changes.

Maintenance – Once the first version is complete the second version should be under way. A system is a constantly evolving organism that requires constant feeding and training to keep up with the demands and challenges of the firm. There will need to be dedicated resources for the system and the portfolio manager and analysts’ time will be sucked into continuous testing and design, just as with the initial build.

Return on Investment – Alpha Theory points out inefficiencies in the portfolio where the firm’s research and constraints do not match their position sizing. For most firms this can represent the largest source of lost return and unnecessary risk. If Alpha Theory points out a couple of inefficiencies per month it will return hundreds of basis points of incremental alpha over the course of the year versus the 1 or 2 basis points of cost for a medium sized fund (even lower cost for larger funds). Even without pointing out a single mis-sized position, Alpha Theory improves the investment process by allowing analyst to describe research in the form of distributions that the portfolio manager can use to make portfolio decisions. No matter how you measure it, the ROI is wildly positive.

Continuous Innovation – Alpha Theory releases updates to the product on a quarterly basis with improvements that continually enhance a firm’s ability to manage the investment process. These enhancements come from internal development and input from partners and clients. Alpha Theory spends 100% of its time dedicated to this concept. An internally developed product would have to focus dramatic energy to keep pace with Alpha Theory’s development and industry-driven ideas.

By the way, the risk manager at the beginning of this post decided to go and build his own version of Alpha Theory (probably because I did not have this article in my hip pocket). However, after a few months, he hired us as a consultant to help him get over a few of the challenges above. Finally, after a year he decided to scrap the whole process and use Alpha Theory. Now granted, we added several features between our initial conversation and when they finally implemented Alpha Theory, but the moral is to proceed with caution if you plan to build your own Alpha Theory.