How many shares do I need to hold to be adequately diversified?

Chris,

We seem to be at crossed purposes here.

Characterizing portfolios is traditionally the work of securities databases and painstaking fundamental analysis. We know models aren't reality, and that outcomes certainly differ (especially in the short term) from the results predicted by models. But much of investing is about creating structure based on a logical and empirical "fit" with historical experience.

I am describing a three factor model that narrows the variables that describe investment returns in any stock portfolio—the variables that investors should focus on managing. These are the “risk factors” I was referring to and they do not necessarily relate just to standard deviation which is one of your core criticisms.

The factors are “market” Stocks minus t-bills, small cap minus large and value minus growth

The three-factor model reads a time series of returns, measuring the sensitivity to each factor and assigning a percent to the common movement.

Investors can tilt their portfolios for a higher expected return than the market by increasing their exposure to the small or value risk factors or both.
But they don’t need to hold a concentrated portfolio to achieve this. By overweighting either or both the size and value premiums investors have a higher expected return than the market portfolio but it is still possible to achieve this and hold thousands of securities.

Equally , if you present a concentrated portfolio of “winning stocks” it is possible to compare this portfolio with the risk factors and determine how much of the variation in returns can be explained by exposure to these common risk factors.

Hence my point is that if you did better than the market portfolio you probably took more risk by which I mean you probably had more exposure to small stocks, value stocks or both. These are compensated risk factors – compensation for higher risk which you cannot get rid of through diversification.

But if you only held 25 stocks you also had uncompensated risk, risk you were not rewarded for taking because you could have diversified it away simply by holding more securities.
 
Marc, you always make excellent points, but we really are at a crossroad here. I simply do not believe that you can measurably quantify risk or even generalise what is risk. Yes, my portfolio did better than the market in the last ten years because I generally stick with value stocks. But in my subjective evaluation, especially in the last 4 years, I bieve I have been taking on less risk by selecting the value stocks that I did.
Another example would be that in my opinion having less than 20% allocated to precious metals is a big risk as is investing in pretty much any government debt. But these very actions would be looked at as very risky by most people; I just happen to disagree.
 
Chris said:
Marc, you always make excellent points, but we really are at a crossroad here. I simply do not believe that you can measurably quantify risk or even generalise what is risk. Yes, my portfolio did better than the market in the last ten years because I generally stick with value stocks. But in my subjective evaluation, especially in the last 4 years, I bieve I have been taking on less risk by selecting the value stocks that I did.
Another example would be that in my opinion having less than 20% allocated to precious metals is a big risk as is investing in pretty much any government debt. But these very actions would be looked at as very risky by most people; I just happen to disagree.
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Chris I think the models that the financial industry has developed over the past 50 years or so for the measurement of risk, asset allocation and the like are in need of a serious rethink. I question whether we can truely measure and magage risk in the first place in our portfolios. Certainly not in the way that a large swave of the financial industry think.

Howard Marks coceptualises excellently on these subject in his book 'the most important thing'.

Personally I believe that behavioural economics will come significantly to the fore in the future for the remodelling of risk.
 
I would go beyond Ringledman in terms of the need for a fundamental re-think ....it is of financial theory not just the models. Marc makes lots of good points but is still grounded in EMH.

The frailities of human behaviour (and probably the excessive power and greed of Wall Street) trump the theory.

As for the original question,25 stocks would diversify away an awful lot of market risk.I am unwilling to say how much because I don't believe in any of the models.
 
It is reasonable to posit that diversifiable risk will not be rewarded by the market. A simple model - market risk is 20%, individual stock risk is 30% i.e. an excess 10% idiosyncratic risk which brings no reward. Using the square root rule we would get the excess risk on 10 stocks as c.3%, 25 stocks 2%, 100 stocks 1%, 10,000 stocks 10 bp. If there are any nagative factors to more diversification, e.g. costs for an individual's portfolio, it can be seen that diversification will quickly give diminishing returns.

The real fly in the ointment in all this is exchange rate risk. Exchange rate risk (as oppposed to currency risk) is a zero sum game and hence is not rewarded by the market. Marc's argument would seem to be that one grand global portfolio is suitable for all investors. This is clearly not borne out in practice, there being a huge divergence between the typical US, UK, Japanese, German etc. investors.

A portfolio of 11,000 stocks must surely bring in a large chunk of "unrewarded" euro exchange rate risk.
 
Here's an interesting statistic

During the bull market of the 1990s 22% of all US stocks (that's a total of 2,397 companies that were in existence for the whole decade) lost money. Not in real terms in absolute terms they were worth less at the end of 10 years than at the beginning.

How do you avoid the risk that over a fifth of all US stocks can go down?
Over this same period Japan went down dramatically. How do you avoid the risk of buying the wrong countries?

Surely the answer here is diversification broadly across asset classes and countries.
 
Don’t overdiversify
While portfolio diversification can improve your investment performance, it does have limits and is not without drawbacks. Research suggests that 90 per cent of diversification benefits can be obtained in most markets with a portfolio of just over 20 stocks.
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I disagree strongly with this claim and have been meaning to say something on it for a while. I believe a more extreme version used to be in the Guide? Recommending the top 10 Irish stocks?

The problem with the analysis which "proves" that you only need 10 or 20 stocks to achieve 97% (or whatever) of the diversification benefit is that it based on comparing volatility of the basket of 10 (or 20) stocks with that of the entire market over a year. The demonstration may be convincing but is does not constitute validation for the 10 or 20 stocks claim when combined with a "buy and hold" recommendation.

Simply because volatility is does not "scale" with time. If your holding period is 10 years for your top ten stocks, then the excess volatility (i.e. risk) over that of the entire market grows considerably. The only way to get the theoretical "protection" would be to re-balance your portfolio every year.

And the longer the period, the worse it gets. Imagine if you put your wealth into the biggest 10 Irish stocks in 1983 with a buy and hold plan for 30 years. Your portfolio would likely be in a sorry state at this stage. Unfortunately the Irish Stock Exchange website provides painfully poor access to their data, so I cannot demonstrate this directly but intuitively, it's clear that a bunch of the Irish companies from 1983 in your portfolio would have gone bust or been taken over for a pittance, etc.

Another take on the subject is here http://www.efficientfrontier.com/ef/900/15st.htm. This article also provides some interesting history on the development of what he calls the "15-stock diversification myth". (This guy's articles are excellent by the way it's well worth browsing through his archive.) To summarize roughly; 3 quarters of randomly selected 15 stock portfolios under-perform the US stock market over a 10 year period.

I could understand why holding a limited basket of individual stocks might have seemed like the most effective way of gaining exposure to stock market returns in the past. But since you can get diversification almost for free now in the form of ETFs, it is very poor advice to recommend not availing of cheap and easy diversification. I have simply no idea what "drawbacks" Terry Smith could be referring to.

From my experience, ETFs are less hassle to buy and hold; they automatically re-balance and collect all the dividends for you. Dealing with the corporate actions of 15 or 20 stocks is a pain in comparison. And the big index ETFs have some of the smallest spreads (which is a tax on investment) in the equity markets.

If you want equity like returns and assuming predicting the future is not possible, you should concentrate on reducing fees and volatility. The simplest way of reducing volatility is to increase diversification. As far as I can see, you can never have enough of diversification particularly if it is almost free like it is with ETFs.
 
Hi Marc. I think we are in complete agreement about diversification. What is surprising is that this opinion seems to be in a minority here.

I've searched that thread for the downsides to "too much diversification" and I can find very few actual specifics on what these supposed downsides are.

First of all, the discussion about EMH (and related) is a complete red herring or at least a completely separate argument. You either believe in passively exposing yourself to the equity markets or you don't. If you fundamentally believe that you can do better with your own research, then holding the top 10, 100 or 10000 stocks are all equally poor investment strategies. In other words, if you are a stock picker/market timer, then the entire argument (of how many stocks you should passively hold) is irrelevant to you.

Many express the the belief that extra diversification is unnecessary - e.g.
...it is unnecessary overkill.
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Which simply expresses the belief that there is little value in more diversification without explaining what the "downside" is.

Some question whether there is an efficient mechanism to achieve such diversification but in fact as you point out, there are cheap and very simple ways of achieving diversification across thousands of global stocks. For example, I have shifted all my equity exposure into the Vanguard VT ETF. This is certainly easier than holding 10 individual stocks: I now only have a single dividend to deal with, I get free and automatic re-balancing and tracking my "equity portfolio" is trivial.


Another argument demonstrates a lack of understanding of the properties of volatility and correlation:
I find it hard to believe that correlation wouldn't become an issue with 11,000 shares
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Unless the stock you add to your portfolio is 100% correlated with a stock you already hold, you can only reduce the risk of your portfolio. And if it is 100% correlated, you do not increase the volatility of your portfolio assuming proper balancing.


One issue which was raised is that of exchange rate risk. This might deserve a thread of its own.
A portfolio of 11,000 stocks must surely bring in a large chunk of "unrewarded" euro exchange rate risk.
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I had long worried about exchange rate risk as it commonly given as a reason to avoid investing globally (or at least limit your global exposure). However when I tried to measure this risk, I could not find it. For example, take the Standard and Poors 500 as a proxy for the US market (because the data is so readily available - e.g. from yahoo finance) for the last ten years. The closing prices in USD actually have MORE volatility than the same closing prices expressed in EUR. In addition the returns are slightly lower denominated in EUR. So in fact, for a Eurozone investor holding the S&P500 for the last years was a lower risk (and lower reward) proposition than it was for a US resident. This example doesn't constitute a general proof, but for me it is relevant given how important I believe having exposure to the US equity markets is.

And I sure am glad that I ignored the 10 Irish stocks recommendation when I first started to put money into equities (buying index ETFs instead although I was poorly balanced globally).
 
Just how many angels can dance on the head of a pin.

Either buy the market, through an EFT or be a stock picker.

If you are a stock picker you will probably loose money, but if you have time, ability and luck you might do well.

On average you cannot beat the market, but we all believe that we are better than average.
 
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