Over the past 60 years, a rich history of quantitative research has emerged aimed at the investing community. None has had as much influence as the concept of portfolio optimisation.
According to research, portfolios do better when optimised for low risk and high returns. This has prompted the growth of passive index funds, because the idiosyncratic risks of individual stocks aren’t compensated enough, limiting the alpha that stock pickers can generate.
More recently, the idea of smart beta has become fashionable. If you divide the universe of stocks by factors such as size, momentum or value and optimise your exposure, you can outperform the index and demonstrate this using a backtest. Analytics provided by MSCI Barra or Bloomberg make this as easy as pushing a button. Today, hundreds of billions of investment dollars are being allocated to smart beta products.
In reality, the theory behind this fashion is shakier than many investors realise. When applied naively to input data, optimisation models can lead to extreme or unstable trading strategies.
To demonstrate this, the quant Thomas Smith has devised a simple framework, in a new paper published by Risky Finance . Smith’s model uses a small portfolio of just two assets, but that is enough to illustrate the problem, with the bonus of being easy to understand.
In his paper, Smith shows that the optimal portfolio (expressed as a pair of weightings for the assets), depends on just two numbers: the correlation between the assets and the ratio of their Sharpe ratios (called the Sharpe ratio ratio or SRR). He then shows that just a small change in these two parameters can flip a trading strategy from a long-short spread trade to long only and back again.
As an example consider an investor that owns just two assets, ETFs that track stocks and bonds. Chart 1 shows the relative weightings over time. The correlation is negative and SRR are fairly stable over time so this portfolio behaves predictably, providing diversification in line with orthodox theory.
Dynamic optimisation doesn’t add that much here (it probably underperforms a portfolio with a fixed allocation to stocks and bonds) but it doesn’t do that much harm either.
Now consider the second portfolio that tries to optimise two families of US stocks, in the form of a large-cap and small-cap ETF. The correlation is now positive and close to one. As the chart shows, a small variation in the SRR between these assets is enough to flip the portfolio from being a spread trade to long-long. But the fundamentals are not enough to justify such a radical change.
The lesson Smith invites us to learn from this exercise is to treat optimisers with caution, especially when dealing with highly correlated assets. A successful backtest may hide the fundamental instability lurking inside, leading to extreme behaviour when correlations change.
To paraphrase Smith’s fellow quant Emanuel Derman, it’s a case of ‘models behaving badly’ which deserves attention when hundreds of billions are allocated to it.