Diversification is No Free Lunch

“There’s no such thing as a free lunch.” This well-known adage, popularized in economics by Nobel laureate Milton Friedman, communicates the idea that you never get something for nothing. The saying finds its origin in a former practice of American public houses, which would offer a ‘free lunch’ in order to attract clientele. These customers doubtless spent more than enough money on drinks to cover their ‘free lunch’. The saying is typically used in economics to emphasize the reality of opportunity cost. Opportunity cost is what one could have achieved by deploying scarce resources elsewhere.

In portfolio management, the opportunity cost of every dollar invested is the return we could have achieved if we’d invested it somewhere else. This is easy enough to measure after-the-fact (ex-post) – you should’ve just invested everything in the best performer! But before the fact (ex-ante) it is impossible to know which asset will perform the best. Ex-ante opportunity cost is more difficult to measure and must also account for differences in risk. This is why we diversify our investment portfolios. Diversification is a hedge against our ignorance of future outcomes. To the extent that you cannot clearly differentiate between the merits of several investment opportunities, it makes sense to hold all of them rather than just one.

Harry Markowitz, another Nobel laureate, challenged the no-free-lunch rule by saying that diversification is the only free lunch in investing. In essence he was saying that the opportunity cost of alternative investments cannot even be reasonably estimated ex-ante. Therefore the ex-ante opportunity cost of alternative investments is zero. Since the benefit of diversification is the spreading of risk, it would follow that this benefit is to be had at zero cost. If this is true, then indiscriminate diversification is the best investment strategy. But is it true?

Can we Measure Opportunity Cost ex-ante?

 For competing investments, opportunity cost is measured in terms of return potential and risk. Risk and return are ultimately driven by business quality and valuation. Differences in business quality and valuations are readily measurable, if not perfectly then certainly by broad brushstrokes. The problem is that higher quality businesses tend to trade at higher valuations, and vice versa. This means that for most investment alternatives, opportunity cost is difficult to measure. For most of the investment universe, Harry Markowitz was right. But ‘most’ of the investment universe is not ‘all’ of it. There are opportunities where one is able to find high quality businesses trading at low valuations. They just aren’t the norm. To the extent that really compelling investment alternatives do exist, but are scarce, the opportunity cost of diversification is actually enormous!

Picture it this way: The ideal investment portfolio has 3 desirable characteristics:

1) It consists of high quality businesses;

2) The shares of these businesses are well-priced;

3) The portfolio is highly diversified.

If it isn’t possible achieve (1) and (2) simultaneously, you may as well go all-in on (3) since diversification will cost you nothing – i.e. Markowitz. If (1) and (2) can be achieved in many cases, you can have (1), (2) and (3) without much opportunity cost. If (1) and (2) can be achieved scarcely, then you need weigh the opportunity cost of (3), because diversification is actually very expensive – i.e. “There’s no such thing as a free lunch.”

In our experience it is the third scenario that best describes reality, especially in recent years where market valuations have been generally high. This means that the opportunity cost of diversification has been high.

How do the Benefits of Diversification Compare?

 It’s one thing to say that the cost of diversification is high, but cost always has to be weighed against the benefit. So how do the benefits of diversification compare to the costs? Burton Malkiel, a strong proponent of diversification, demonstrated in his book A Random Walk Down Wall Street that by the time a portfolio reaches ~30 holdings (spread across different geographies/industries), virtually all the benefits of diversification (in terms of downside protection) have been achieved, with diminishing benefits for each additional holding. The only further advantage of holding more stocks is in tracking the benchmark index more closely. This isn’t desirable for the active investor.

What we see then is that diversification is actually very expensive with little benefit beyond a 30 stock portfolio. Consider then that most mutual funds hold well in excess of 100 stocks. This is not because they are concerned about downside risk. Rather they don’t want to be too different from the overall market. They are prioritizing their own career risk over their clients’ investment objectives. We addressed this in Dare to be Different. If you’re going to hold 100 stocks you may as well just follow Markowitz’ advice and go all the way. The results won’t differ by much.

How does this apply to us?

At Bellwood, we’ve always understood the danger of indiscriminate diversification and we’ve formulated our process to avoid this. For starters, we’ve emphasized the importance of covering a very broad opportunity set. The best way to ensure a diversified portfolio of well-priced, quality assets is to make sure you aren’t limited to a small opportunity set. A portfolio of 30 stocks chosen from a universe of 5 000 is likely to be vastly superior in terms of quality, price and diversification when compared to a portfolio of 20 stocks chosen from a universe of 500. Our process is geared towards addressing a very broad investment universe.

Further, we’ve worked on a maximum initial position size of 3%, which would result in an initial portfolio of 30-40 stocks. In practice, however, we’ve found that as prices fluctuate certain positions become smaller than 3%, while we’ve tended to trim the positions that have grown in excess of 3%, adding new positions along the way. This has resulted in the portfolio drifting from the initial 30-40 stocks to 40-50 stocks. Because of the scarcity of well-priced, high-quality securities this implies that over time we’ve inadvertently sacrificed a little either on price or quality in favour of greater diversification. This has probably cost us returns at the margin without meaningful benefit.

Going forward we’re going to cap our initial position sizes at 5%, with average position sizes still around 3%. This will result in slightly more concentrated portfolios which consistently remain around our target of 30-40 stocks. We believe this strikes the best balance between return potential and diversification.