Diversification does two things. One it potentially reduces the risk in your account. Two it enables you to sleep at night. So whilst I am going to use a lot more words in this article the bottom line is that there is a correct answer for how many shares you should hold, but what that answer is, is very personal to the individual involved.
If you had, (through the science of time travel), a copy of the share index in 3 months time today, how many shares would you buy? To maximise returns the answer would be one. It would be the share with the greatest return over that period. If two shares had the same top return over that period it would still only be one as this would minimise dealing costs and therefore maximise your return.
In reality many people even with the future prices in black and white would buy more than one, perhaps two ,three, five etc, or indeed hold back some cash despite knowing that each extra share had a trading cost and the cash had an opportunity cost, just in case the information was not correct or they had misunderstood or because they cannot make 100% bets. In short many if not most people would not profit maximise but would attempt to hedge their perceived risk of total failure.
Mathmatically diversification works like this.
1 holding 100% risk in each holding – presuming equally weighted
2 holdings 50% risk
3 holdings 33% risk
4 holdings 25% risk
5 holdings 20% risk
6 holdings 16.67% risk
7 holdings 14.3% risk
8 holdings 12.5% risk
9 holdings 11.11% risk
10 holdings 10% risk
15 holdings 6.67% risk
20 holdings 5% risk
21 holdings 4.76% risk
22 holdings 4.54% risk
Broadly speaking once you are past 20 each individual holding doesn’t add much to the level of diversification. I don’t intend to go into it here but somewhere in the 35 – 60 range (depending on the research you follow) you get into a portfolio that equates to buying the market in its returns. If you are doing this you might as well buy an ETF and save yourself the worry of an individual share. This numeric approach even with equal weighting is also dependant on there being some diversity in the sector the shares come from. Ten big oil majors, BP, Shell, Exxon, etc, with 5 small oil companies, GKP, Amerisur, etc and 5 oil service companies, Oceaneering, Haliburton, Fred Olsen is not a diversified portfolio. Not even if you have 40 holdings. When the oil price tanks your portfolio will tank.
But a 20 holding is not inherently the best as there are the following points to also consider;
1 – Each holding costs money to create. If you have big bucks then the transaction costs don’t matter so much but for most of us they need to be considered.
2 – Many successful investors advocate a philosophy of limiting your holdings to ideas that you really understand and believe in. The broad concept being that you limit your risk not by having a multitude of shares but by only putting money into ideas where you have a high certainty you are right.
3 – Coupled with this it is very time consuming to stay on top of a 20 holding portfolio. Doubly so for a 40. As such almost inherent within the discussion the more holdings you have the harder you have to work or the lower your real understanding. Add to this the fact that if you follow a business you would also like to follow its competitors and comparators. A 20 share portfolio could either fill your life or lead to a lot of short cuts and file skimming.
4 – The more you diversify the lower the risk that any one share will destroy you but equally the lower that any one share will make you wealthy. If you hold 20 positions and one falls to 0, you have 95% of your starting portfolio. Equally if you hold 20 equal positions and one doubles you only have 105% of your starting position. And whilst it is not often that a share collapses to zero it also is not often that a share doubles in value.
5 – Many investors do have all sort of behavioural biases and need to set their portfolio to reflect this. For instance I know one person who is incredibly adverse to letting a good idea go so he has a portfolio of well over 40 holdings. He certainly understands the maths but having the holdings in his portfolio allows him to sleep as he is not agonising that he has missed the opportunity.
6 - It is also worth considering whether you want some market diversification. If you buy companies listed in the UK you will tend to get a greater correlation than if you buy some in the UK, some in Europe and some in the US, Latin America, Asia etc. But this can often be misunderstood. You can in the UK buy companies that sell largely abroad such as Diageo. But this will usually trend more in line with the UK than a US drinks company given the substantial UK shareholders and the fact that these reacts to the UK market. On the other side the US business may be less correlated but you have taken on FX risk.
At the end of the day there are brilliant investors with policies of 10 of 10% (Pabrai). There are others that run 25 holdings of 4%. Still others that have no overall holdings limit but want only to put money into ideas where they set either a minimum or maximum value or %. Or others that hold a multitude of holdings but at unequal weights. Many of the UK’s bigger hedge fund managers have wide holdings but weighted to a smaller bundle. If you were a cynic you might wonder of this was (a) because if they just bought and held their 10 best they would have trouble justifying their fees and (b) if they only held 10 or so would they need so many staff for research, marketing, sales, etc.
At the end of the day the correct number to hold for most of us is somewhere between 5 and 35 and these numbers are fairly arbitrary. Because the correct number is the number that allows you to sleep soundly at night understanding the risk that a small portfolio brings and the costs and behavioural biases a large one demonstrates.