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Wednesday, 6 October 2010

Diworsification is Good for You

Mythic Investments

We all know that over-diversifying our stock portfolios is bad for our wealth. Even if our main aim is simply to avoid the problems of correlated stocks all falling together it’s well known that you can get most of the benefits of diversification from a portfolio of no more than fifteen companies. Anything else isn’t diversification it’s diworsification: it adds no benefit and costs us more.

Only, like so many well-known truths about stocks, this is a myth. Owning as few as fifteen stocks opens you up to all of the terrible things that happen to investors that take on too much risk. In the worst case everyone loses money and you get a socialist government. How bad is that?

Defined by Outliers

Consider two portfolios each of fifteen stocks. Each stock holding costs us a thousand dollars. After ten years all fifteen stocks in the first portfolio have doubled and are now worth two thousand bucks each. In the second fourteen of the stocks haven’t changed their price at all but the fifteenth holding has multiplied sixteen times and is now worth sixteen thousand dollars.

Both portfolios have precisely doubled in price. To a first approximation these two portfolios, chosen at random, will probably correlate to their underlying market which will also have roughly doubled. But how lucky did you need to be to pick up that sixteen bagger? Well, actually, you had about a one in six chance in a fifteen stock portfolio.

And, unfortunately, it’s the second portfolio with a host of very average performers and the odd standout success that’s more typical of the real markets. This, then, is the problem with fifteen stock portfolios: your chance of matching the market is a mathematical artefact of the modelling process. In reality five in six of us will be glumly looking for left-wing politicians under the bed.

Risk Revisted

The problem is that the fifteen stock portfolio is that bane of our imperfect lives, an outcome of a mathematical model, which aims to reduce the diversifiable risk in a portfolio by ensuring we select stocks which aren’t correlated with each other, the idea being that if one stock falls dramatically the others shouldn’t. This can’t eliminate the risk of systemic risk when everything crashes, but it does reduce the pain of individual stock collapses.

Trouble is that this is a world in which “risk” is equivalent to “volatility” and minimising risk in this way simply means ensuring that we get a smooth ride, with as few shuddering rises and falls in our portfolio value as possible. It says absolutely nothing about the one number most people investing in stocks for the long term really care about: the value of their portfolio when they come to liquidate it.

Terminal Wealth Dispersion

The range of possible final portfolio values is known as Terminal Wealth Dispersion and the trouble with the 15 stock portfolio model is that it doesn’t address this at all. This issue was raised back in the 1980’s by Meir Statman when the considered opinion was that 10 stocks were enough. Statman showed that to get sufficient diversification to justify the risk taken investors needed portfolios of over thirty and possibly over fifty randomly chosen stocks.

However, William Bernstein on his now sadly underused site, The Efficient Frontier, went even further than this in debunking the idea of limiting diversification, by arguing that even properly diversified portfolios suffered from this problem:
“To be blunt, if you think that you can do an adequate job of minimizing portfolio risk with 15 or 30 stocks, then you are imperiling your financial future and the future of those who depend on you. The reason is simple: There are critically important dimensions of portfolio risk beyond standard deviation. The most important is so-called Terminal Wealth Dispersion (TWD). In other words, it is quite possible (in fact, as we shall soon see, quite easy) to put together a 15-stock or 30-stock portfolio with a very low SD [Standard Deviation], but whose lousy returns will put you in the poorhouse.”
Superstocks and Mutual Funds

The issue is that the returns on the indexes that these models are based on – the S&P500 in the above article – are vastly weighted in favour of a few “superstocks” whose outperformance makes a huge difference to the overall success or failure of the approach. Bernstein suggests there’s only a one in six chance of owning one of these, if you pick your stocks to meet the conditions of the fifteen stock portfolio, but we can make up our own numbers based on our own experiences.

The same is true for mutual funds. Edward O'Neal showed (abstract only) that, although a single fund was sufficient to meet the requirements of the usual measures of risk, to achieve proper downside protection of terminal wealth requires many funds. In essence the range of potential final values was significantly reduced by holding multiple funds, no matter what the standard theory prescribes.

That it generally seems to come as a surprise to some investment professionals that investors are probably more concerned about their final destination in terms of “terminal wealth” – the value of the portfolio at the point they decide to liquidate it – than the volatility of the portfolio valuation along the way shouldn't really be a surprise. After all, there really isn’t any way of managing this effectively other than buying the market, aka index tracking, and that's not advice that tends to generate fees.

Alternative Investments

Andrew Clare and Nick Motson looked at this in terms of diversifying across asset classes in How Many Alternative Eggs Should You Put In Your Investment Basket? and, with that typically talent for understatement so typical of the British, came to a similar conclusion:
“These results have important implications for an investor seeking to invest in alternative asset classes. Although diversifying beyond 8 assets offers extremely marginal benefits in terms of time series standard deviation, if the investor wants more certainty that the risk level they expect is the one they actually experience … then they should diversify much more”.
Pity the poor investor struggling with the concepts of portfolio theory trying to make sense of this. After all, the world's experts tells us that diversification is a terrible way of generating excess returns: all you're doing is regressing to the average. Unfortunately most of us aren't smart enough to figure out how to pick winners most of the time.


Still, a couple of things are clear. Firstly, to have adequate diversification you need far more than 15 stocks, even assuming you choose them to have limited correlation. Unless you can figure out how to avoid excessive correlation then you should probably limit yourself to an index tracker.

Secondly, a major part of overall portfolio capital returns will be generated from just a few super-stocks. In the event you get lucky enough to hit one of these the last thing you should be doing is trading it away. Selling your winners is the last thing you should ever do. The fact is that in a world full of investors it is probable that some will outperform the market handsomely by nothing more than luck. The rest of us will probably need to make do with diworsification.

Related articles: Exploiting the Anomalies, Puke: Don't Invest in the Familiar, Recency: Hot Hands and the Gambler's Fallacy


  1. Blarg.

    I have nothing against selling winners.
    I also have nothing against selling losers.

    Paying attention to the price you paid rather than the current value is known as 'price anchoring', and is an investing fallacy.

    For instance, a core holding for me is DGS, which I first bought in 2008 at 43.71, then added more shares at a fantastic price of 23.5 later that same year. As of today, DGS closed at 51.58, but I'm not going to treat shares from my first purchase (18% gain) any different from those from my second purchase (219% gain).

  2. Paying attention to the price you paid rather than the current value is known as 'price anchoring', and is an investing fallacy.

    Indubitably. However, if you're skilled enough to make these judgements you won't be needing to diworsify. On the other hand Blarg is an alien language, so your message may be in code ... ;-)