A few weeks ago, at lunch with our very first Western investor, I was asked how many stocks we really needed to construct a diversified portfolio. Without hesitation I said 50 or 60 – less than the 100 or so we run in practice, but substantially more than her estimate of around 20.

Having given my opinion, it occurred to me that I should really try to find a logical argument to back it up, because the idea that effective diversification can be achieved with 20 stocks has good academic support. It is clearly reasonable for passive portfolios to attempt to replicate a cap-weighted index; in a cap-weighted index the largest 20 stocks should contain a substantial part of the total market cap, so it sounds reasonable that with a bit of attention to sector and factor exposure a decent tracking performance can be achieved.

This article will explain why the same argument does not hold for a return-seeking portfolio. To do so I will consider something I’ve come to think is an under-used concept, and its profound influence on the realities of return-seeking portfolios, particularly long/short. The analysis will also suggest that some commonly held beliefs about the relationship between the fashionable concepts of Focus and Conviction have a relationship to portfolio size and that is more complex than is usually assumed, and which cannot be fully understood without considering Investment Timescale.

How big are winners?

First, as a gentle warm-up, let’s have a think about how timescale impacts the economics of trading. Let’s imagine three managers, who each generate an un-leveraged net return of 12% a year. The only difference between these managers is where their ‘edge’ comes from, which is, respectively, from predicting stock performance over 1 month, 1 quarter and 1 year. These should also be their average holding periods.

“The influence of portfolio size on the amount of analysis that can be done is not as great as is often suggested.”

Since we are making 12% in a year, the monthly trader must on average earn 1% on every position, the quarterly trader 3%, and the annual trader 12%. It doesn’t matter whether we hold 10 positions or 100, the average return per position is simply determined by turnover. By the way, remember that these figures are for unleveraged portfolios. A manager with 200% gross positions would be averaging only half these returns per position. This is a very simple calculation, but I think the results are interesting and maybe counter-intuitive. Most managers I’ve heard, and we aren’t very different, prefer to talk about their big winners – the +50% returns. Ask us about Point sometime, ten-baggers make great stories. However, this simple analysis of trade timescale shows that these events cannot be very typical. They do not represent how the money is usually made.

Since the average return must be so much smaller than the headline success stories suggest, it is well worth understanding why. A few big losers (likely with a concentrated portfolio)? Lots of small losers (likely with tight stoplosses)? Smaller returns on his larger positions (likely with core)? Or just ridiculous implementation costs (likely if the manager runs $2 billion in illiquid stocks)? There are no right or wrong answers, but the questions are worthwhile because they help to build up a picture of the investment process. Long/short investing is a game of small edges, and the shorter the timescale the smaller the edge.

The differing scales of returns associated with different timescales hints that this may be a source of diversification for hedge fund investors, and simple simulations show thisto be the case.

Analysis quality

Another area in which timescale has a strong influence is in the nature and amount of analysis that can be put into a portfolio. Every stock-picker worthy of the name is proud of the quality of their analysis, and the ability to Focus analytic attention is a popular argument used to support Focused portfolios. If you have only N good ideas then you should hold about N positions because there is little point either padding with dull stocks or wasting good ideas, but the Focus argument goes beyond this. A manager, the story goes, can spend five times as long tracking each stock in a 20-stock portfolio as he could in a 100-stock portfolio.

This argument is clearly correct as far as it goes, but it stops when the manager has to replace his 20 positions with new ones and has to audition many candidates to find them. Then it doesn’t really matter whether he is highly selective and just buys la crème de la crème or, like us is a pushover who will buy anything he expects to go up. If the manager has to look at 200 new stocks it will take much the same time whether he eventually decides to buy 20 or 100 of them.

So, the influence of portfolio size on the amount of analysis that can be done is not as great as is often suggested. Smaller portfolios do make it easier to track the positions you already own, but do not much affect the amount of work required to find new names. For some kinds of trade, tracking positions is extremely important. For activists putting expertise and/or the boot into the management of a company over a substantial period, it doesn’t pay to be spread too thin because further expertise/kicks will be required on a regular basis. However, for the typical portfolio investor I suspect that finding new positions is at least as important.

This gives Timescale a direct impact on the search process: if you have to audition 200 new stocks every month, then you have to work 12 times as hard as the manager who auditions 200 a year. In a high turnover fund it is difficult to do deep analysis on many new positions. If two funds apply an equal level of analytic skill and effort, the one that trades on a shorter timescale cannot audition as many new stocks. It must either hold fewer positions than the longer timescale one or else it must be less selective about the positions it takes.

These ideas on average return and analysis quality match well. Managers with a longer timescale have to make higher average returns from each of their picks, but in compensation also have more time to carry out the analysis that is required.

Focus and Conviction: the conventional view

As my comments about analysis quality suggest, I’m sceptical about the current fashion for Focused portfolios. I illustrated some of their potential shortcomings in a MARhedge article “Lack of Focus” last year and this analysis is going to develop that theme using the concept of timescale.

However, we first need to pin down what is meant by Focus and Conviction. They are great buzzwords, but I am not certain that everyone agrees on what they mean.

Conviction relates to the mental state of the manager. Is he making bets because he believes them to be money-making propositions, or just because he cannot think of anything better to do? Conviction is important, because it is part of what investors are buying when they hire an active manager, and the search for high-Conviction managers seems to be a major part of the interest in Focus.

Unfortunately, Focus is used to indicate three distinct ideas. “Focused Portfolio” and “Small Portfolio” are often used interchangeably suggesting that it is just a numeric concept — twenty stocks is Focused, fifty isn’t. Let’s call this Numeric Focus. However, stock-counting approach to Focus arises because attention and analytic effort are assumed to be more focused on the small portfolio, permitting better analysis. Let’s call this Analytic Focus.

Finally, once you have done your Focused analysis and picked your stocks, it makes sense to take a significant amount of risk on them. Let’s call this Risk Focus.

Fig.1 suggests that under the conventional view these four concepts are essentially interchangeable. Small Portfolios are always Focused, their managers all have High Conviction. All are in antithesis to diversified portfolios, and Timescale does not enter the picture.

But how realistic is this?

Problems with the conventional view

* Conviction does not imply returns
It should be clear that Conviction is not enough for good performance. As Graham said, and Buffett recently reminded us, belief is not enough for profits, you also have to be right. Conviction tends to be very expensive when attached to a mistaken belief – anyone remember the TMT bubble? Some Conviction is necessary, but more is not always better.

* Small Portfolios do not imply Conviction
Any manager who uses tight stoplosses clearly doesn’t have much Conviction: his belief in the quality of his analysis is in fact so low that he allows it to be overruled by small movements in price.

* Small Portfolios do not imply Analytic Focus
Remember the influence of Timescale? We saw that short timescales suit small portfolios, because there just isn’t enough time in a month for a manager to do a really deep job on auditioning many new candidates. If you run a short-timescale fund then it makes sense to run fewer positions, but don’t pretend it means you know them better. It doesn’t. It is simply a sensible reaction to being on a high-turnover treadmill that doesn’t allow time for deep analysis on more than a few names.

* Small Portfolios do not imply Risk Focus
Remember the influence of Timescale? A short-term manager is actually taking modest risk on each position. He is in for a few percent. Over time a long-term investor takes on as much or more risk per position for the same position size.

Focus in reality

It is clear that in fact these concepts are related but distinct. It is also clear that timescale is intimately involved in their relationships. In my view these relationships are better represented by Fig.2, which introduces ‘The Forgotten Dimension.’

The figure shows the range from Focus to Diversification as a function of two influences, Timescale and Portfolio Size, which have a similar – almost interchangeable – influence. Numeric Focus, associated with holding few positions, becomes just one of the drivers of Analytic and Risk Focus, with Investment Timescale taking an equal role.

“One of the minor advantages of taking a long-term investment approach is that it allows us to have some fun.”

And Conviction? Well, as befits a concept relating to the mental state of hedge fund managers it is shown in vivid and exciting colour, but its exact position is strangely elusive. Probably Conviction hides mainly in the same general area as Focus, so if you seek conviction, do not seek it in the top right of the chart. but beyond that, Conviction may lurk in the heart of any manager who renounces stoplosses.

Diversification in Two Dimensions

To pin down exactly how Timescale can play such a similar role to portfolio size, let’s take another look at our monthly and yearly traders. Consider the yearly trader who places a single bet for the year. He has 12% riding on a single roll of the dice.

The monthly manager makes 12 separate trades a year – 12 rolls of the dice, with 1% riding on each roll. Lucky chap. He is diversified in time: if May is horrible, June may still be good. Or July. Remember he just has to average 1% on each position, and at the end of each month he will be in something new. Repeating 12 times over will get him his 12%.

But of course, he pays a price for all this risk-reducing diversification. We saw earlier that he has much reduced analysis time. Comparing him to the annual trader and looking along the time dimension the monthly trader has lost Focus and gained Diversification. He is making more trades, which reduces his Risk Focus, and he can devote less Analytic Focus to each. Now imagine that the yearly manager wishes to reduce his level of Focus to match that of the monthly manager, so he diversifies across 12 positions but still runs each of them for a year. Like the monthly trader he has to find 12 new positions each year, and gets to roll the dice 12 times, so he has achieved the same level of Risk Focus and the same level of Analytic Focus as the monthly trader who runs one position at a time. This is not intuitive, so I’ll say it again. A longer-term trader has more Focus across time, so he needs to diversify across more positions to achieve the same overall level of Focus. Timescale is the dimension missing from the dogma that active portfolios must be small. It is fair for investors to demand some Conviction from an active manager which suggests running Focused portfolios, which suggests they should be small or long term. Provided the role of Timescale is not forgotten I believe it. But believers who conclude that Conviction portfolios must always be small are simply wrong, because low-turnover portfolios can be Focused as well.

Five years ago, when Peter Tasker and I were first on the road introducing Zensen to a sceptical world, he came up with a beautiful way to explain the situation. Arcus, he said, needed to run more positions in order to allow us to be more aggressive in our stock-picking. We don’t use stoplosses, we are not scared of holding deeply unpopular, complex, risky stocks for a long time, and we are always betting that the market is wrong. Qualitatively, we have always known that we need a lot of diversification to permit us to follow this aggressive approach but it has taken me five years to tie numbers to this concept.

Our long timescale means we have the analytic time to do a decent analytic job on a large number of stocks. It also means that we have given up substantial time diversification, so we need more positions than a shorter-term manager. That is why Timescale is the critical missing dimension of the Focus debate. The question of how many stocks a manager should hold to achieve the correct balance between Focus and Diversification cannot be answered without considering the timescale over which he makes money. Or, to look at it in a more practical way, at last I can stop apologising for running so many positions, and go on the attack.

Hey, you short-term so-called ‘Focused’ manager, how come you are so massively over-diversified in time?

Robert Macrae, CFA, is the managing director of Arcus Investment. He has spent 14 years applying engineering concepts such as robustness, reliability and problem-solving to value investment.