Modern Portfolio Theory Stacked the Deck

I have often made the case to clients that diversification and volatility are portfolio management distractions. Not because they are uniformly irrelevant, but because industry dogma gives them a status well above their merit. Our industry uses diversification and volatility as yardsticks of comparison, so funds are naturally incentivized to alter their behavior to maximize their performance based on these measures. If a potential investor gauges a fund’s performance using return per unit of volatility, Value-at-Risk, Beta, tracking error, and diversification – guess what happens? You get lots of fund managers building portfolios with too many positions and avoiding volatility. Not surprising then that our industry has been increasingly dominated by high diversity / low volatility funds since the advent of Modern Portfolio Theory (average fund has 140 positions – study by Pollet and Wilson).

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).

About Cameron Hight

Cameron Hight, CFA, is an investment industry veteran with experience from both buy and sell-side firms, including CIBC, DLJ, Lehman Brothers and Afton Capital. He is currently the Founder and President of Alpha Theory™, a Portfolio Management Platform designed to give fundamental money managers the ability to create their own repeatable discipline to organize the complex process of portfolio management.
This entry was posted in Not Categorized. Bookmark the permalink.

Leave a Reply