Low Volatility and Beta 1.0 Portfolios

A low volatility portfolio targets the lowest volatility, or beta stocks. I have found that using a 3-4 factor model to minimize variance generates the lowest volatility portfolios, but the advantage to this approach is 2-4% annualized volatility, and given most investors do not understand factor analysis, merely taking the lowest volatility or beta stocks, generates a decent approximation while retaining a great deal more intelligibility. The alternative I proposed yesterday was the beta 1.0 portfolio. The difference low volatility and beta 1.0 approaches is shown below:


Beta 1.0 merely takes those stocks with betas nearest to 1.0. That is, every 6 month I estimated betas for every US stock listed that had a sufficiently high market cap (about 2500 stocks), and monitored the return, putting merged or delisted stocks back into the index. Data are from CRSP, Compustat, and Bloomberg, and when constructed over the past, they include dead companies, so this is a survivorship free dataset. Prior to 1997, I used monthly returns, after that, daily returns in estimating betas. The beta 1.0 portfolio has had a portfolio beta very near 1.0 in real time (about 1.05). The low beta portfolio merely took the lowest 100 beta stocks (dark blue obs) every six months, doing the same thing.

The differences in their mean returns is as follows:

US Returns Since 1962

	Beta1.0	Low Beta	S&P500
Avg. Ann.Geo. Return	11.4%	10.4%	9.3%
Ann StDev	17.4%	13.1%	15.1%
Beta	1.04	0.58;

If people cared primarily about beta, a proposition still dominating Business Schools, they should invest in low volatility or low beta portfolios. You can get a much lower 'risk' at about the same return, perhaps even a little higher. Merely cutting out the high volatility stocks generates a better return too, which is why low volatility portfolios, such as Robeco's, should be attractive to institutional investors trying to maximize a Sharpe ratio.

Note the Beta 1.0 stocks have a slightly higher return than the low beta stocks (and a slightly higher volatility). This is not really surprising, in the the perverse volatility effect is generallly that high volatility or beta stocks underperform massively. From low to mid beta, you actually get a modest return improvement.


Above we see the histogram of relative returns, and the relative return distribution is in fact fatter for the low beta portfolio compared to the beta 1.0 portfolio. 'Low risk' is risky if you are benchmarking against the index. This was especially pronounced in the tech bubble of 2000 (below), when high beta stocks greatly outperformed, and anyone incidentally plying a low beta stocks probably lost their jobs (unless they were Warren Buffet, who survived tech underperformance).


The bottom line is that if you are concerned about relative performance then the Beta 1.0 portfolio is a smart alternative to the low volatility approach, which has as its greatest advantage avoiding those lousy lottery-ticket stocks that over the long run have proven disastrous across every major equity market.

Now you might say, 'what kind of idiot measures risk relative to the S&P?" Don't I only care about my consumption, my wealth? I would say, most people care more about relative returns than absolute returns. CAPM pioneer Bill Sharpe consults for pension funds evaluating asset managers and states his first objective in is that ‘I want a product to be defined relative to a benchmark’ (see Tanous). Fund Manager Kenneth Fisher‘s book The Only Three Questions that Count, in the index next to Risk, it has ’see Benchmarking.’ When asked about the nature of risk in small stocks, Eugene Fama noted that in the 1980‘s, “small stocks were in a depression”, and Merton Miller noted the underperformance of the Dimensional Fund Advisors small-cap portfolio against the S&P500 for 6 years in a row was evidence of its risk. But smaller stocks actually had comparable total returns, and higher returns relative to the risk-free rate, in the 1980‘s compared to the 1970‘s. It was only relative to their benchmark (the S&P500, large cap stocks) that they had ‘poor‘ returns’ highlighting that even Fama and Miller’s practical intuition on risk is purely relative, and these are champions of the standard model. Needless to say, other people, especially fund managers, are keenly aware of their year and life-to-date performance relative to the S&P500.

It seems reasonable to presume that for investment professionals and academics, risk is a variation in return relative to a benchmark. This fact has several important implications for investing optimally, whether you act that way or not.