Monday, November 21, 2011

How Many Stocks Are Enough to be Diversified?

Most commentators agree that the stock portion of our portfolios should consist of many stocks in order to reduce volatility. Where they disagree is on how many stocks are needed to be adequately diversified. Over the years, the trend has been for the recommended minimum number of stocks to rise. I have an explanation for this trend.

In 2009 Tom Bradley wrote "While a portfolio of 20 stocks and a few government bonds were just fine for our parents a generation ago, it’s probably not enough today." Why would the minimum number of stocks we should own change over time?

With each stock you add to a portfolio, the volatility tends to decrease. However, the amount of benefit drops off as the number of stocks rises. Adding a second stock gives a big reduction in volatility, but adding a 101st stock doesn't reduce volatility much.

For indexers, there is no such thing as too much diversification as long as the cost of ownership (fund MERs) stays low. So, an index investor is happy to get the benefit of reduced volatility by owning all the stocks in an index.

Stock pickers see things differently. Suppose that they rank their stock picks from most to least confident. From the stock picker’s point of view, the expected return is highest for the first stock and decreases as we move down the list.

The expected compound return of a portfolio is a combination of the expected return minus a penalty for the amount of volatility. As the stock picker adds each stock on the list to a portfolio, volatility drops giving a boost to expected compound return. However, a lower confidence pick (with lower expected return) is diluting the expected return of the stocks already in the portfolio. One effect raises expected compound return and the other lowers it.

After some number of stock picks, the volatility benefit isn't enough to offset the dilution penalty of a lower confidence stock pick. It can be difficult to put exact numbers on these things, but this is the reason why a stock picker wants to own enough stocks, but not too many.

The better a stock picker is at outperforming the market, the fewer stocks he or she will buy before the dilution effect outweighs the volatility benefit. So, better stock pickers should want to own fewer stocks than weaker stock pickers.

Some commentators, including Benjamin Graham, have said that picking good stocks has been getting more difficult over the years. If this is true, then a given stock picker whose skill level remains constant will find that as the years pass, his or her returns in excess of the market averages erodes. This should lead to the optimal number of stocks to own to rise over time.

For index investors who don't believe they can beat the market net of costs, the optimal number of stocks to own is all of them.


  1. In the current climate there is no incentive to save the money. I recently did some calculations and the results are very much frustrating, to be brutally honest. Have a look yourself - they are all published.

    If you invest $ 40, 000 a year over 35 years, at modest inflation rate of 2% and administration fee of 1-2% you need stock market to perform at 4% just to preserve value of your money and higher to gain anything.

    This means that you are only preserving money you are investing at a very high risk. So it is just plain wisdom - is there a point to be frugal and try to save, if you ended up loosing money?

    Feeding financial industry or living your life in full now?

  2. @Financial Independence: You're not exactly on topic, but I understand your frustration. However, there is no need to pay 1-2% in fees if you take the time to understand index investing. I'd suggest reading Dan Bortolotti's book. See my review here.