Many of the investors I follow advocate concentration and run extremely concentrated portfolios. For example, Warren Buffett says that he operated mostly with five positions. From the other end of the spectrum, momentum trader Mark Minervini, who I have become interested in recently due to his quite stunning results and apparently quite straightforward and intuitive strategy, advocates a similarly concentrated portfolio.

I am happy with the performance of my strategy so far but I have begun to question whether perhaps I can do better through concentrating my portfolio on fewer investments.

To be fair, compared to the average fund manager or ‘sensible’ investor my portfolio is already pretty concentrated. I am 100% in equities, mostly small cap growth companies and currently have only 25 stocks, while I understand the average fund manager with a similar focus would be likely to have 50 plus stocks. But my portfolio is still considerably less concentrated than the sorts of portfolios advocated by some.

I currently follow fairly rigid rules for diversification – my desire to hold a certain number of stocks (currently 25) and to stagger my position sizes evenly dictates a lot of my decisions of which holdings to buy or top-up when I have funds available. I like following rules and structure. While I think this discipline is generally good for investing, in the case of diversification I haven’t really thought through carefully the rationale for the rules and it’s possible they might be costing me. If I’m honest, I also have to admit that part of the reason I like being quite diversified is that I don’t want to miss out on holding some of the great businesses I have identified on my watchlist – this seems like a pretty bad reason for diversification.

So what are the actual benefits and costs of diversification and what do they imply about the optimal level of portfolio concentration for me?

The benefits of diversification

I can think of two main benefits to diversification. The first is that diversification is a way to manage risk. Because we can’t predict the future, investing in any business involves taking on the risk that something goes wrong. Diversifying reduces the impact of any individual risk on the overall portfolio.

Diversification is a ‘free lunch’ in that it can allow you to reduce risk without compromising return. For example, if you believe that two different stocks are likely to appreciate by 50% you would expect the same return if you invested in one of them compared to if you invested in both of them. However, if you invest in both, the impact of one of them going wrong is less on your portfolio. This benefit only applies to idiosyncratic risks i.e. those that are specific to individual shares. Obviously diversification does not protect you from systematic risks which affect you whole portfolio, such as a general market downturn.

The second benefit of diversification is to manage liquidity risk. Diversification allows you to have smaller positions that are easier to sell quickly in the event that something goes wrong. There can be very big benefits to selling quickly after profit warnings so I believe there is a benefit to making sure positions don’t get too large. However, this benefit only really kicks in once your portfolio is fairly large – I don’t think it’s that relevant for me at the moment.

While reducing the impact of idiosyncratic risk is an important benefit:

• This benefit diminishes rapidly after a relatively small number of holdings
• Diversification can also mean that you end up investing in worse ideas with lower expected returns
• Diversification does nothing for systemic, market risk and may even be worse for it

Benefits of diversification diminish rapidly

After you’ve reached a certain number of holdings, the benefits of diversification reduce quite rapidly. Studies have shown that in practice the benefit of diversification, in terms of reducing variance, diminishes quickly after about 10 holdings and is more or less negligible after about 35.

To illustrate how the benefit of diversification diminishes in a somewhat oversimplified way, think about the impact of a really bad profit warning on one of your stocks. With a one stock portfolio this impact on portfolio value might be say 50%, while with 10 it would be 5%, with 25 it would be 2%, with 35 it would be 1.4% and with 50 is 1%. The difference in the impact gets smaller and smaller the larger the portfolio gets.

A useful way of think about optimal diversification is the Kelly criterion. This is a formula used to determine the optimal size of a series of bets, given a probability of winning and a win loss ratio (the size of a win relative to the size of a loss). The formula for the percentage of your portfolio you should allocate to each holding is given by:

Kelly % = W – [(1 – W) / R]

Where W is the winning probability and R is the win loss ratio.

For my portfolio, based on the last two years W is 43% and R is 2.2. This suggests I could optimally allocate my portfolio between about 6 shares. I wouldn’t use this directly, particularly as it’s based on the last couple of years where things have been going very well. I also think there is a psychological benefit to some diversification in that it allows you to sleep better at night. However, it does suggest that greater concentration wouldn’t hurt based on my current record. On the other hand, there are reasons why greater diversification might be hurting my returns…

Diworsification

Buffett has famously referred to ‘diworsification’ – the idea that investing in a greater number of stocks results in you investing in worse ideas. As well as diluting your expected returns, this can also result in you investing in companies where risks are greater. More concentration can also allow a more detailed focus on individual companies and better monitoring of them.

Many other investors I follow also think this, for example Terry Smith and Nick Train, though notions of what is is concentrated varies – between about 5 and 25 stocks.

Having got up to 25 holdings I feel I might be suffering from diworsification. I definitely have a lot more conviction in some positions than others. While I think there are quite severely diminishing returns to very detailed research, I feel I am exposing myself to more risk by investing in businesses I know less about or am a bit less confident in. I’ve also found that top slicing my best performers to preserve diversification has almost always had a negative effect on my returns.

The universe of shares I think are high quality enough to invest in (my watchlist and portfolio) only consists of 65 businesses at the moment. I think picking more than a third of them to actually invest in is probably too many. I guess that investing in only 10 to 20 % of them would be likely to serve me better – say 5-10 out of 50.

Concentration better for market risk?

In reality I am much more worried about the risk of a market downturn than about the risk of individual shares serving up a profit warning. Diversification does very little to protect me against this risk. In fact, I think greater concentration may allow better management of this risk. In a market downturn, greater concentration would allow a greater focus on shares that are ‘swimming against the tide’ and on defensive, low beta businesses which are less affected. And if there aren’t any businesses ‘swimming against the tide’, I’m now wondering whether a better strategy is to just hold cash until opportunities present themselves (even though I’ve previously said that I believe in being fully invested).

So what am I going to do?

I’m beginning to see a lot of benefits from running a more concentrated portfolio. I think the optimal portfolio size is substantially fewer than my current 25 and could be as low as 5-10.

However, I’m not going to change my portfolio drastically all at once. I’m going reduce my number of holdings bit by bit, waiting for sensible opportunities, to 20 holdings first and then think again. I can do this by:

• After selling a holding, reinvesting across existing holdings.
• When a new opportunity looks good, selling 2 existing holdings to finance it, rather than 1.
• When an existing holding looks worthy of increasing (e.g. because of good news or a share price breakout) I will look to sell a weaker holding to finance it.

I think all of this should boost my performance.

Also as my portfolio has fewer holdings I will also relax my maximum holding size rule up from 10% gradually. I also aim to become more flexible about where to reinvest across holdings rather than stick to a rigid staggering approach. In the future I might also relax my fully invested rule – I’m going to be a bit less adverse to sitting on cash if opportunities don’t look good.