How many shares should an investor hold?

Most of the investors in Free Capital  hold concentrated portfolios, sometimes of fewer than ten shares (Luke, Owen and Taylor). Others such as Eric, John Lee, Peter Gyllenhammar and Sushil hold up to 60 shares.  Who is right? How many is too many?

Many experienced investors advocate a small number of holdings. I used to think this was always good idea.  I still think this is probably right for a knowledgeable investor with a relatively small fund. But for an investor managing millions or tens of millions of pounds (like most people in the book), I'm not so sure.

If N  is my number of stocks to hold, I think the optimal N is a function of the following variables...

N  =  f { quality of knowledge about return dispersions (↓),

              £ size of portfolio (↑)

               volatility of shares (↑)

               capital gains tax rate (↓) }

 ...that is, a decreasing function of quality of knowledge and CGT rate, and an increasing function of the £ size of your portfolio and the volatllity of the candidate shares.

Let me explain....

Decreasing function of quality of knowledge about return dispersions  This point is fairly obvious. If you know with certainty which share in the market will give the best return over your time horizon, all your portfolio should be in that one share(*).  If you know nothing about the return dispersions the optimal portfolio is indexation.  In reality, most of use are somewhere in between.    Exceptional investors with exceptional quality of knowledge should hold a relatively concentrated portfolio. 

For example, most  years between 1977 and 2000, Warren Buffett appears to have held around one-third of his portfolio in his largest holding (usually a different holding in each successive year). I don’t hold one-third of my portfolio in one share, because I’m not that good.

(* Side-note This “obvious” point may not be mathematically correct.  See information theory: if transaction costs are zero, a constantly rebalanced universal portfolio must asymptotically out-perform the best-performing share in the market.  Of course, in practice transaction costs are never zero.  But the point illustrates that the question  discussed in this post is quite subtle; observations which are "obvious" are not necessarily correct.)

Increasing function of £ size of portfolio With a small portfolio, liquidity is not a constraint.  If you know with certainty which share will give the best return over a time horizon, you can put all your money in that one share and sell at the end of the time horizon.  With a larger portfolio, liquidity becomes a constraint. Even with perfect knowledge, you can no longer "buy at the bottom and sell at the top."

 With a larger portfolio, a larger number of holdings becomes optimal –  not because it “spreads risk”, but because it increases liquidity, and so increases options to change your mind as prices and your expectations change.

 For example, if I invest £50,000 in each of my 10 best smallcap ideas, I can sell any which rise to be fully valued. If I invest £500,000 in my single best smallcap idea, and it rises to be fully valued, I probably won’t be able to sell all of it anywhere near that price (who is going to buy?).  Even with perfect knowledge dispersion of returns, it’s attractive to invest some in the 2nd, 3rd, 4th… best ideas, and thus create options to sell shares when they go up, and buy when they go down.

 Increasing function of the volatility of candidate shares If the candidate shares are highly volatile, it becomes attractive to switch frequently, buying individual shares when they are low and selling when they are high (volatilty pumping). To do this, you need liquidity, that is you need to restrict your size in any one share, to ensure you can “buy at the bottom and sell at the top."  For given £ size of portfolio, smaller size in any one share implies a larger number of shares.

Decreasing function of the CGT rate If the CGT rate is high, the tax penalty on turnover is high, so the optimal portfolio probably has low turnover.  You should pick only shares which you are happy to hold for 10 or 20 years (I call these “diamonds” – see last post); this probably means very few shares indeed, and these shares are difficult to identify (ie the chance of "false positive" errors is high). 

 On the other hand if the tax rate is zero, there is no need to attempt the difficult and error-prone search for a very few 20-year diamonds.  You can instead buy “flower bulbs” (see last post), which are always more plentiful than diamonds, and much easier to recognise.  Flower bulbs can only be bought in small size, because you need to be able to sell easily and promptly when the flower blooms.  For a given £ size of portfolio, smaller size for individual shares implies a larger number of holdings.

Some further practical considerations are given in the next post.

Guy Thomas Sunday 20 February 2011 at 12:57 am | | Default

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