Deciding how concentrated my portfolio should be is a question I’ve mulled over many times. I wrote about it in a previous post more than a year ago, where I decided that I would benefit from being more concentrated. Unfortunately, I think my reasoning then, while on the right lines, was a little half-baked. As a result, I still feel torn by the conflicting desires to either diversify into more of the attractive-looking opportunities on my watchlist, or to only concentrate on my very best ones. To build a more coherent approach I can confidently stick to, I think I need to go back to first principles. 

The core trade-off

From a statistical perspective, there are basically only two things investors should care about in constructing their portfolios: their likely portfolio return and the risk they need to take to achieve this return.

Risk can be thought of as the variance in the return you might expect from an investment.  The more variance there is, the more varied the range of returns you might get. Two investments may have the same expected return, but one is less risky if it is more likely to approximate this return within a narrow range, while the other is more risky if a much broader range of outcomes is possible.

Diversification is a ‘free lunch’, in that it can allow you to reduce some of the variance without compromising the return. For example, if you believe that two different stocks are equally likely to appreciate by 50% over a given period, you would expect the same return if you invested in one of them compared to investing in both. However, if you invest in both, the variance in the returns you would expect is reduced, as it is less likely that both would underperform your expectations. This can allow you to achieve your expected return with greater certainty.

It’s a bit more complicated than this in practice, as diversifying will often mean you have to buy some stocks in which you have lower conviction than others. This implies a trade-off between targeting a high expected return and reducing the variance of your returns. You can ‘optimally diversify’ by holding the number of stocks in your portfolio that best balances this trade-off. To do this you need to know: how do the costs and benefits of diversification vary with the number of stocks in your portfolio?

The cost of diversification: ‘diworsification’ compromises returns

How much diversification will cost you depends on how your degree of conviction varies across your potential investments. If you have high conviction in only a handful of investments, diversifying beyond them may imply significantly compromising your returns. On the other hand, if you follow a more systematic approach and have fairly equal conviction across a broad range of potential investments, diversification may not cost you that much at all.

I’d say that my strategy puts me nearer the systematic end of this of this spectrum. My level of conviction in potential investments does vary to some extent, but it’s hard to judge by how much. I think it’s likely that my expected return would benefit significantly from holding a very concentrated portfolio in a handful of my favourite investments. Beyond a certain point (I’d say about 10 stocks), my systematic approach means that additional diversification is probably not going to reduce my expected returns much until I held around 30 stocks.

The benefit of diversification: minimising return variance

The benefit of further diversification when starting from a small number of holdings is large. It certainly makes sense to hold more than one or two positions, even at the expense of some cost to your expected return. However, the benefit of further diversification diminishes fairly rapidly as the number of holdings increases, becoming pretty irrelevant after about 30 holdings.

The benefit from diversification is further limited by the fact that it only applies to uncorrelated idiosyncratic risks i.e. those that are specific to individual shares. Obviously diversification does not protect you from systematic risks which affect your whole portfolio, such as a general market downturn. In my case, as I focus particularly on a certain type of investment i.e. high quality, the benefits of diversification may be limited further.

The importance you should place on reducing the variance of your returns relative to the returns themselves is hard to judge. Provided that you are sufficiently diversified to avoid severe capital loss and are investing for the long term, it’s not obvious that you should care a great deal about the variance in your expected returns over a year or so. After several years this should balance out. However, you may have good reason to be more risk averse than this. This could be because of your circumstances, e.g. your age and how much you can afford to take losses, but is also partly a question of preference. I am fairly cautious by nature and am prepared to make some sacrifice to reduce stress and have greater certainty of a consistent decent return.

Dynamic risk management: what if we can change our minds?

The core diversification trade-off between risk and return is straightforward to understand, even if difficult to judge. Things get more complicated once you introduce the dimension of time. Over what time period should you be thinking about risk and return? What about the fact that you can change your mind and sell your investments at a later date if things don’t go to plan?

The typical investor should care less about temporary fluctuations in prices and more about the risk of a permanent loss of capital. Because of this, they should in principle be thinking about their portfolio’s expected returns and variance over a longer time period, perhaps their whole investing lifetime. However, this is also a question of the strategy you follow. While a true buy and hold investor should consider their whole lifetime, an investor that rebalances every year should only think about the likely variance over the next year.

The option to revise your decisions at any time time is a complementary way to reduce risk. You can choose to sell at any point if the prospects of an investment deteriorate. For example, you may sell if there is a profit warning or you may use stop losses, allowing you to take advantage of momentum. If you are at least partly effective in occasionally rotating your portfolio towards stocks with better prospects, you reduce the need for diversification to some extent. This doesn’t replace the benefit of diversification, though it does limit the risk you need to diversify to some extent.

Not just about numbers of stocks

Of course diversification is not just about numbers of stocks you hold, but also the relative weighting of each holding in your portfolio. If some positions are much bigger than others, your portfolio can still be highly concentrated even if you hold many stocks. As well as meaning you may be more concentrated than you think, this can provide useful flexibility.

You can measure portfolio concentration quite easily using a measure such as the Hirschman-Herfindal Index (HHI), more commonly used to measure market concentration in competition economics. Using this I can see that my current portfolio, which has 18 positions, has equivalent concentration to a portfolio with 14 equally weighted positions. If I went up to my maximum limit of 20% in my top four positions, and spread the remaining funds across the rest of my portfolio, the concentration would become roughly equivalent to an equally weighted portfolio with only six stocks, despite holding 18.

This shows that to diversify well you may want to limit the size of your largest positions as well as the overall number of stocks. I limit my maximum investment to 10% of my portfolio and will let a position grow to a maximum of 20%.

Behavioural effects

You are not a robot. Unfortunately, your emotions also have a hand on the controls. As in other aspects of investing, it makes sense to account for this when deciding your approach to diversification. There are several ways I think diversification can help:

• It can reduce the tendency to overtrade. As well as the greater stress caused by there being more at stake in each position, there is greater competition for attractive-looking candidate investments to take a place in your portfolio. This can lead to the pressure to trade more than is necessary and incur the related costs.
• Too few positions or positions that are too large in size can reduce your flexibility to run winners and add to positions before they get too large.
• Once your positions get sufficiently large, it can reduce liquidity risk i.e. increase your ability to sell out quickly when prospects are not looking good.

So how concentrated should I be?

I’m pleased that the process of writing this blog post has helped clarify my thinking about diversification for my portfolio.

It is clear that the extremes of holding fewer than five or more than about 25 stocks are not the best place to be. Within this, I think there is a strong case for me to hold a highly concentrated portfolio of 5-10 stocks, given my strategy also mitigates risk through focusing on high quality and applying stop losses. I’m tempted by this possible route to accelerate my returns. However, my mindset at the moment is too cautious. Perhaps this may change if I develop greater confidence in my approach over time. I also value the more behavioural benefits of diversification, in reducing incentives to overtrade and allowing greater flexibility. My preference is to achieve concentration by overweighting my largest positions when I have very high conviction in them, while holding a relatively large number of smaller positions.