The Minimum Variance Misnomer

Markowitz’s original plan was that the choice of assets for a portfolio was a one time event.  You work out the historic variance and return for your chosen assets and weigh such assets in your portfolio to provide the highest possible return for the lowest variance (or “volatility”). Volatility is uncomfortable and usually entails steep increases of value as well as disastrous crashes. High variance is what you get if you invest 100% in a stock index.

The trouble is of course that historic returns are often not a useful guide to future returns. Historic volatility may be a little more stable and predictable.

So, many people have proposed that you work out the minimum variance portfolio on a periodic basis. Based perhaps on the last three months performance and volatility. This way you can account for changes in markets.

So let’s take a look at the Lazy Portfolio and rebalance it monthly to achieve a “minimum variance” portfolio for the following month.  Gold, long term treasuries, short term bills, and the S&P 500 stock index. The test is constrained: no shorts are allowed and the portfolio must sum to one (IE fully invested, no cash, no leverage)

Stat                 Minimum Variance    Benchmark
-------------------  ------------------  -----------
Start                1989-01-04          1989-01-04
End                  2016-12-20          2016-12-20
Risk-free rate       0.00%               0.00%

Total Return         1089.56%            1395.44%
Daily Sharpe         1.34                0.63
CAGR                 9.26%               10.16%
Max Drawdown         -13.46%             -55.25%

The stats look wonderful and so does the chart (apart from the past year or so):


But the catch becomes apparent when you look at an area chart of the assets over time:


It turns out that the MINVAR used in this way is more of a trend following approach. It is true that the system turns to bonds and gold in a crisis but do you really want to be 100% exposed to stocks on occasion?

It may well be that based on the data, a 100% allocation to the S&P 500 would, on occasion, have produced the highest return for the lowest volatility. But the market can turn on a sixpence.

This is not, surely, what MINVAR should be about?  The cautious investor might want to consider a different approach. Or perhaps imposing further constraints so that no one asset accounts for more than x% of the portfolio. But then that’s no longer the MINVAR approach.

As usual, many questions and few answers.




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