Sunday, November 27, 2011

How much diversification is too much?

As an investor, should you put all of your money in one stock or should you spread your bets across many investments? If it is the latter, how many investments should you have in your portfolio? The debate is an old one and there are many views but they fall between two extremes. At one end is the advice that you get from a believer in efficient markets: be maximally diversfied, across asset classes, and within each asset class, across as many assets you can hold: the proverbial “market portfolio” includes every traded asset in the market, held in proportion to its market value. At the other is the “go all in” investor, who believes that if you find a significantly undervalued company, you should put all or most of your money in that company, rather than dilute your upside potential by spreading your bets.

Cuban versus Bogle
These arguments got media attention recently, largely because two high-profile investors took opposite positions. The first salvo was fired by Mark Cuban, who made his substantial fortune (estimated by Forbes to be $2.5 billion in 2011) as an entrepreneur who founded and sold for $ 6 billion by Yahoo!, at the peak of the dot com boom. Cuban's profile has increased since, largely from his ownership of the Dallas Mavericks, last year's winners of the NBA championship, and his intemperate outbursts, about referees, players and the NBA in general. With typical understatement, Cuban claimed that diversification is for idiots and that investors, unless they have access to information or deals, should hold cash, since hedge funds have such a tremendous advantage over them. In response, John Bogle, the father of the index fund business, countered that "the math (for diversification) has been proved over and over again. It's not just the first thing an investor should think about, but the second, the third and probably the fourth and the fifth thing investors should think about".

The limiting cases
So, should you diversify? And if so, how much should you diversify? The answers to these questions depend upon two factors: (a) how certain you feel about your assessment of  value for individual assets (or markets) and (b) how certain you are about the market price adjusting to that value within your specified time horizon.
·      At one limit, if you are absolutely certain about your assessment of value for an asset and that the market price will adjust to that value within your time horizon, you should put all of your money in that investment. Though this may seem like the impossible dream, there are two possible scenarios where it may play out:
o   Finite life securities (Options, Futures and Bonds): If you find an option trading for less than its exercise value: you should invest all of your money in buying as many options as you can and exercise those options to make a sure profit. In general, this is what falls under the umbrella of pure arbitrage  and it is feasible only with finite lived assets (such as options, futures and fixed incomes securities), where the maturity date provides a endpoint by which time the price adjustment has to occur.
o   A perfect tip: On a more cynical note, you can make guaranteed profits if you are the receipient of inside information about an upcoming news releases (earnings, acquisition), but only if there is no doubt about the price impact of the release (at least in terms of direction) and the timing of the news release. (Rumors don’t provide perfect information and most inside information has an element of uncertainty associated with it.) The problem, of course, is that you would be guilty of insider trading and may end up in jail... .
·      At the other limit, if you have no idea what assets are cheap and which ones are expensive (which is the efficient market proposition), you should be as diversified as you can get, given transactions costs. If you have no transactions costs, you should own a little piece of everything. After all, you gain nothing by holding back on diversification and your portfolio will be deliver less return per unit of risk taken.
Most active investors tend to fall between these two extremes. If you invest in equities, at least, it is inevitable that you have to diversify, for two reasons. The first is that you can never value an equity investment with certainty; the expected cash flows are estimates and risk adjustment is not always precise. The second is that even if your valuation is precise, there is no explicit date by which market prices have to adjust; there is no equivalent to a maturity date or an option expiration date for equities. A stock that is under or over priced can stay under or over priced for a long time, and even get more under or over priced.
There is one final point worth making. Note that how much you diversify will be based upon your perceptions of the quality of your valuations and the speed of market adjustment, but perceptions are not reality. In fact, psychologists have long noted (and behavioral economists have picked up the same theme) that human beings tend to have too much confidence in their own abilities and too little in the collective wisdom of the rest of the world. In other words, we tend to think our valuations are more precise than they really are and that the market adjustment will occur sooner than it really will.

How diversified should you be?
            Building on the theme that diversification should be attuned to the precision of your valuations and the speed of market adjustment, the degree to which you should diversify will depend upon how your investment strategy is structured, with an emphasis on the following dimensions:
a.     Uncertatinty about investment value: If your investment strategy requires you to buy mature companies that trade at low price earnings ratios, you may need to hold fewer stocks , than if it requires you to buy young, growth companies (where you are more uncertain about value). In fact, you can tie the margin of safety (referenced earlier in this chapter to how much you need to diversify; if you incorporate a higher margin of safety into your investing, you should feel more comfortable holding a less diversfied portfolio. As a general propostion, your response to more uncertainty should be more diversification, not less.
b.     Market catalysts: To make money, the market price has to adjust towards your estimated value. If you can provide a catalyst for the market adjustment (nudging or forcing the price towards value), you can hold fewer investments and be less diversifed than a completely passive investor who has no choice but to wait for the market adjustment to happen. Thus, you will need to hold fewer stocks as an activist investor than as an investor who picks stocks based upon a PE screen. Ironically, this would mean that the more inefficient you believe markets are, the more diversified you will need to be to allow for the unpredictability of market movements.
c.     Time horizon: To the extent that the price adjustment has to happen over your time horizon, having a longer time horizon should allow you to have a less diversified portfolio. As your liquidity needs rise, thus shortening your time horizon, you will have to become more diversifed in your holdings.
In summary, then, there is nothing irrational about holding just a few stocks in your portfolio, if they are mature companies and you have built in a healthy margin of safety, and/or you have the power to move markets. By the same token, it makes complete sense for other investors to spread their bets widely, if they are investing in young, growth companies, and are unclear about how and when the market price will adjust to value. So, the choice is not between diversification and active investing, since you can pick stocks and be diversified at the same time. It should be centering on  making the right decision on how much diversification works for you,.

Evidence from the field
            So, how diversified is the typical investor’s portfolo? And if it is relatively undiversified, is it undiversifed for the right reasons? And what is the payoff or cost to being undiversified? The evidence from many studies over the last decade or so is enlightening:
  1. Investors are thinly diversified: The typical investor is not well diversified across either asset classes, or within each asset classes, across assets. A study of 60,000 individual investor portfolios found that the median investor in this group (which was a representative sample of the typical active investor in the United States) held three stocks and that roughly 28% of all investors have portfolios composed of one stock. In a later study, the same authors find that not only do investors hold relatively few stocks but that these stocks tend to be highly correlated with each other (same sector or type of stock).
  2. Many are thinly diversified for the wrong reasons: While the lack of diversfication can be justified if you have good information or superior assessments of value, many of the undiversfied investors in this study failed to diversfy for the wrong reasons. On average, not only did younger, poorer less eductated investors diversify less, but they, as a group, tend to be over confident in their abilities to pick stocks. 
  3. And they pay a price for being thinly diversified: Not surprisingly, investors who fail to diversify because they are over confident or unfamiliar with their choices pay a price. On average, they earn about 2.40% less a year, on a risk adjusted basis, than their more diversified counterparts.
  4. But some undiversified investors are good stock pickers: On a hopeful note, there are clearly some active investors who hold back on diversification for the right reasons, i.e., because they have better assessments of value for stocks than the rest of the market and long time horizons. A study of 78,000 household portfolios finds that the among households wealthy enough to be diversified, those with more concentrated portfolios (holding one or two stocks) earn higher returns than those with more diversified portfolios (holding three or more stocks) by about, though they are also more volatile. The study goes on to note that the higher returns can be attributed to stock picking prowess and not to market timing or inside information.

Bottom line
Most investors are better off diversifying as much as they can, investing in mutual funds and exchange traded funds, rather than individual stocks. Many investors who choose not to diversify do so for the wrong reasons (ignorance, over confidence, inertia) and end up paying dearly for that mistake. Some investors with superior value assesssment skils, disciplined investment practices and long time horizons can generate superior profits from holding smaller, relatively undiversified portfolios. Even if you believe that  you are in that elite group, be careful to not fall prey to hubris, where you become over confident in your stock picking and market assessments and cut back on diversification too much. 


Ram said...

You say that the response to more uncertainty should be more diversification. Is that the reason why venture capitalists make so many investments?

Aswath Damodaran said...

Yes, and they have an added problem. Many of their investments don't make it. So, if you are a start-up VC and you put all your money on a few start ups, you are asking for trouble.

Procrastinatus said...

I just realised this is similar to the Knapsack problem.

Jason DaCruz said...

In number three of "Evidence from the Field," you note that less diversified portfolios earned 2.4% less on a risk adjusted basis. But these portfolios have much more risk - so is it possible that their absolute returns were higher? Or am I totally misinterpreting the meaning of 'risk adjusted'?

Aswath Damodaran said...

You are absolutely right. That is how you reconcile point three and four. Less diversified investors on average have higher average returns but get less returns per unit risk taken...

Shawn S said...

I generally agree with most of your points but I feel like you passed over the simplest point which is that the point of diversification is to address and eliminate the idiosyncratic element of the risk you are taking on. In other words, perhaps the best way to look at diversification is through the lens of the Sharpe ratio. If you are a passive investor, it is probably in your best interest to diversify, not because it will necessarily improve your returns (on an expected basis), but because it will reduce the volatility of those returns, effectively improving the Sharpe ratio. I will caveat this by saying though that if you are an active investor (and presumably know what you're doing), you either have some piece of information (hopefully legally) or are able to assemble available information such that you can generate a conclusion that isn't already reflected in the share price. As such, in some ways you now have a piece of information that is idiosyncratic, but this is not bad, because if you know what you're doing, this represents the source of alpha for all intents and purposes. At this point, there becomes a trade off in trying to diversify out the bad idiosyncratic risk (catastrophes, accounting irregularities, etc.), while retaining and exploiting the idiosyncratic element that you believe to be a driver of (hopefully, positive) returns. If anything, too much diversification will only serve to dilute your best ideas. Obviously this is not easy, and hard to quantify since it is hard to separate and categorize different types of "risk." Overall, there are plenty of investors who believe that it is possible to over-diversify (if you know what you're doing). Although Warren Buffett is now a buy and hold investor, when he was younger and was running an investment partnership that effectively operated as a hedge fund, he was completely fine with making certain positions in his portfolio represent up to 30% or 40% of the entire asset value. Obviously you increase your exposure to bad idiosyncratic risk, but in the event there is a clear misvaluation, and you have the time horizon to capitalize on it, it can be a great driver of returns.

Rohit Sarma said...

“After all, you gain nothing by holding back on diversification and your portfolio will be deliver less return per unit of risk taken.”
I take it as the professor meaning to say – By diversification you will be rewarded with more (expected) returns per unit risk. Is it always the case? Is there any statistical or empirical explanation to this! Shwan S also, in essence, talks about the same thing but in a more refined manner cast in terms of Sharpe Ratio.
“If you are a passive investor, it is probably in your best interest to diversify, not because it will necessarily improve your returns (on an expected basis), but because it will reduce the volatility of those returns, effectively improving the Sharpe ratio.”
Does diversification ALWAYS lead to an improvement in Share ratio? What about those instances where diversification not just reduces uncertainly but dilutes the expected return as well – Although it wouldn’t make any sense for an investor to go ahead with such an investment, more so if he is risk averse. My concern is directed at recognizing there diversification need not always guarantee us an improved Sharpe Ratio.

Aswath Damodaran said...

Shawn and CSLV,
If you bring nothing to the table (in terms of information or stock picking ability), Shawn is absolutely right. Diversification will always improve your risk/return tradeoff and deliver a better Sharpe ratio. It is just the law of large numbers at work. If you bring information or stock picking ability to the table, which is the basis for my argument, diversification may hurt you.

David F. said...

"Diversification is for idiots." I assume he is intending to say 'you are an idiot if you diversify.' However, the other way to read that line is 'if you are an idiot, you should diversify.' As in, if you don't have the time or understanding to do fundamental research on particular companies, you should allocate your investments to whole market portfolios (both stocks and bonds depending on risk tolerances). If, on the other hand, you are not an idiot and you do fundamental research and find companies that are under-valued, why would you want to dilute your portfolio with companies that you don't like or don't know anything about? Advising that people sit in cash instead of investing in mutual funds is an absurd statement. Over a 40-year period, an indexed equity mutual fund will likely outperform cash by leaps and bounds. (Even if the cash strategy involves toothpaste stockpiling.)

Yermek said...

if i will invest my own money i will rpefer to invest to the stock or bond at least in one sector. i can make precise valuation and be expert in or tow sectors so you can feel some changings there. if you will trust your money to the some funds, shit can happen. last crisis showed that analytics of such funds dont know the the asset they invested, i mean there were too much derivatives. if you are in one sector you will be very carefull and pay attention to small things that can affect the market. i think it is better not to diversify, for sure it is mcuh riskier but the probability is higher that you can escape on right time if you are there.

Anonymous said...

There are two aspects I miss in this blog:

(1) Portfolio weighting plays a dominant role in portfolio returns. For instance, the historical S&P500 returned 0%/year during the past dozen years with two maximum drawdowns of 55% when cap weighted at every tick. The current composition of the S&P500 practically mimics this performance over the past dozen years. However, equal weighting the same portfolios, weekly rebalanced, generated 14%/year during the past dozen years with the same risks of 55%. Hence, portfolios where capital is more evenly spread show a completely different dynamics than cap-weighted portfolios where capital tends to accumulate in stocks with the highest market value.

(2) Randomization rather than diversification of portfolios shows that the share prices are endowed more by chance than by anything else. Equal weighting of randomly selected portfolios with 50 to 5,000 stocks, weekly rebalanced, also generated 14%/year during the past dozen years with the same risks of 55%. So when your investment is not large enough to move markets and you have no special knowledge that can be considered price-sensitive, using chance (randomization) of your portfolios appears to be a more certain protection for underperformance and risks than any valuation method. Portfolios of random compositions can be Markov chained to increase performance. Randomness always has its instant pick order whatever the ordering parameter is (value, growth, momentum, etc.).

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Unknown said...
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Unknown said...

Aswath, can You comment on what Anonymous said about equal weighting ? I totally agree with the Anonymous on that matter, but in the book “Investment Valuation” in Chapter 3 “Models of Risk” you wrote that part of potential advantages of diversification is lost if investors are not using cap weighting (it was in the chapter notes and unfortunately I am not able to give you the exact quote or page number because I have a translated version of the book). Do you still agree with what You wrote in that book?