Power of diversifiers

I love thought experiments. Imagine you can own either:

(A) 1,000 assets, each with an annual volatility of 10% and each 50% correlated to every other asset in the portfolio; or

(B) Just two assets, each with an annual volatility of 10% but with a correlation of zero to each other.

In both cases, the assets are equally weighted within the portfolios, so portfolio (A) has 0.1% invested in each asset whereas portfolio (B) has 50% invested in each asset.

Which, intuitively, would you say has lower volatility – portfolio (A) with 1,000 assets or portfolio (B) with just two?

The answer is actually (B). The volatility of (A) is 7.075%, whereas the volatility of (B) is fractionally lower at 7.071%. In fact, you'd need an infinite number of assets in portfolio (A) to get the volatility as low as in (B).

Despite working with models of investment risk on a regular basis, and working through the algebra that proves it, I find this result quite surprising. It shows how finding just one uncorrelated return source can be as beneficial as finding an endless source of returns that are moderately correlated to everything else.

Implicitly, what's happening is that all the assets in portfolio (A) share a common risk factor that can't be diversified away. The situation can be more complicated if one is concerned with matters such as fat tails and skew – more information would then be needed to determine the winner – but I'll leave that for another day.

Net performance

So what are the potential implications of this for portfolio construction?

One key takeaway is that it's important to cast a wide net and seek out different return sources. But another is that even if a diversification strategy appears visually impressive in a pie chart, that may not tell the whole story. After all, as illustrated below, the pie chart for portfolio (A) looks more compelling than the simplicity of (B)!

You need to be careful, though: an uncorrelated risk is no good if it doesn't come with a positive expected return. It's quite possible that high demand for such powerful diversifiers has already depressed their return prospects.

Diversifying market exposure by asset class and within asset classes, for example by region, is a great start but investors may also wish to hunt for other return sources. One useful source can be choosing to under-hedge a risk. For example, under-hedging the longevity risk of non-pensioners in a defined-benefit scheme boosts returns – if the insurance is 'expensive' – but the risk retained is generally uncorrelated to investment returns. Another source might be to under-hedge interest rate risk if you are negative on bonds, although you need to be careful not to go too far.

Similarly, 'active' sources of risk such as global macro trades and alternative risk premia are generally independent of market risk. This means that they only require relatively little faith in their existence to justify a role in a portfolio. If you would like to read more about this idea, we examined it in a post last year.

All these sources of return need to be sized appropriately relative to each other and combined in a way that helps investors meet their objectives. Models can help: they can test many different strategies; they can take into account correlations and more subtle interactions; and we can choose ones that strike a good balance across a range of short-term and long-term metrics.

Diversification isn't just important in portfolio construction, of course; it's useful in teams too. It's also surprisingly beneficial for individuals, as I've recently read about in David Epstein's fascinating book Range. Diverse perspectives can be just as important to problem solving as portfolio performance. Of course, in our line of work, the two are linked!