Low-Risk Stocks Outperform High-Risk Stocks

. July 10, 2014

Have you heard the saying, "Low risk, low return?" Stocks that go up and down less than the market have low risk (low beta) and should offer lower returns than high-beta stocks. This is the common-sense relationship between risk and return predicted by the capital asset pricing model (CAPM), which most professionals would use to manage your money.

The truth may surprise you.

Real-world data contradict CAPM's predictions. A paper titled Country and Sector Drive Low-Volatility Investing in Global Equity Markets finds that a portfolio of low-risk stocks formed from the cap-weighted MSCI World Index has a return that is higher than that of the index itself.

From 1978 to 1996, the low-risk portfolio had a return of 18.5% (Sharpe ratio 0.98), while the index had a return of only 15.0% (Sharpe ratio 0.56). From 1997 to 2012, the low-risk portfolio had a return of 9.6% (Sharpe ratio 0.74), while the index had a return of only 5.5% (Sharpe ratio 0.17).

It's worth pointing out that it's easy to beat the cap-weighted index, despite what some experts say. Even picking stocks randomly will do it. But one of the few things worse than a cap-weighted index is a portfolio made up of high-risk, high-beta stocks. (See Equal-Weight Benchmarking, p. 3.)

The chart below, taken from the paper, explains why the low-risk strategy works.
Beta and Up/Down Capture by Min Vol Strategy
The low-risk portfolio, represented by the tan bars in the chart, has a beta of 51%, meaning that when the index goes up or down, it should move 51% as much as the index does. "Low risk, low return," right?

But the chart shows that this isn't actually what happens. When the index goes up, the low-risk portfolio goes up more than its beta says it should, as reflected in the upside capture of 64%. The return is 1.25 times what it's "supposed" to be.

When the index goes down, the low-risk portfolio goes down less than its beta says it should, as reflected in the downside capture of 32%. The loss is only 0.63 times as large as it's "supposed" to be.

The low-risk portfolio outperforms the index over a long period of time because it outperforms its beta in both up and down markets.

(The blue bars in the chart shows that the low-risk strategy also works if you group the stocks by country and sector first and then build a portfolio based on the lowest-risk country/sector combinations. The paper describes this in more detail.)

A spate of articles has come out recently saying that low-risk portfolios haven't worked in the past few years, since their return has been lower than the market's return. To evaluate these criticisms, look at the beta of a low-risk portfolio. If its beta is 50%, it is half as risky as the market, and it should only provide half the return (assuming interest rates are near zero). If its return is higher than half of the market's return, the portfolio is doing what it's supposed to.

Low-risk stocks do better than stocks as a whole because their return is only slightly lower in bull markets and is much better than average in bear markets.

Some people use leverage, borrowing money at a low rate, to be able to buy a larger amount of a low-risk portfolio, making its beta equal to that of the index. Since the low-risk portfolio already has a higher long-term return than the index does, leverage increases that return even more.

Common Sense is Not Common True

If you need more evidence, look at the chart below, taken from a paper titled The Volatility Effect: Lower Risk Without Lower Return. The chart has a line moving upward from left to right showing a low return for low-risk (low beta) stocks. The line was drawn using predictions from CAPM.
Theoretical relation between beta and return
There's nothing in the chart that would surprise most financial professionals. The problem is that I cheated.

It's not actually the chart taken from the paper. I erased the real-world data before showing it to you.

Here's the real chart:
Empirical versus theoretical relation between beta and return
The data points don't fit the line at all. In fact, they seem to trend in the opposite direction. Low-risk, low beta portfolios have higher returns than high-risk, high beta portfolios.

A paper titled Betting Against Beta shows that low-risk assets outperform their betas for U.S. stocks, 20 international markets, the Treasury bond market, the corporate bond market, and the futures markets.

The paper hypothesizes that low-risk works because of mutual fund managers. They try to outperform the market, but they're not allowed to use leverage, so they buy high-risk stocks instead. This drives up the price of high-risk stocks, causing a drag on returns, while leaving low-risk stocks underpriced.

The authors of the paper look at actual portfolios to test their hypothesis:

We study the equity portfolios of mutual funds and individual investors, which are likely to be constrained. Consistent with the model, we find that these investors hold portfolios with average betas above 1. On the other side of the market, we find that leveraged buyout (LBO) funds acquire firms with average betas below 1 and apply leverage. Similarly, looking at the holdings of Berkshire Hathaway, we see that Warren Buffett bets against beta by buying low-beta stocks and applying leverage.
Mutual funds hold risky, high-beta stocks. Warren Buffett, on the other hand, buys low-risk, low-beta stocks and applies leverage, accessing money at favorable terms so he can buy more.

People think leverage is risky, but risk depends on what the leverage is buying. The data suggest that using leverage to buy low-risk stocks is a better idea than buying high-risk stocks without leverage. An alternative, sort of like using leverage, is to change a portfolio over to low-risk stocks and to use more of the portfolio than normal for stocks and less for bonds.

Another way to invest in low risk, discussed in a paper titled Capitalizing on the Greatest Anomaly in Finance with Mutual Funds, is to buy funds with low betas.

There are also specially-designed low-risk exchange-traded funds that can be bought and sold like individual stocks. They have favorably low expense ratios. However, retirement accounts typically have limited choices that may not include these funds.

Be Brave

What we've discussed may make financial professionals uncomfortable. The low-risk, high-return phenomenon has been known since the 1970's, but people are still taught the capital asset pricing model in school, and they still use it to manage money.

Strategies with academic research behind them, like low-risk investing, value, and momentum, get ignored in favor of passive investing. Beating the market is said to be hard, despite evidence that a cap-weighted market index like the S&P 500 historically has been beaten by picking stocks randomly.

If you challenge the capital asset pricing model, you challenge what people were taught in school. You challenge what they do for a living. You challenge their worldview.

Think different. Be brave.

Cheap Stocks Outperform Expensive Stocks

. July 2, 2014

Here's a recent article testing growth ("expensive") stocks and value ("cheap") stocks. The test finds that, very consistently, value has higher returns and lower volatility risk than growth. The U.S. stock market is currently on the expensive side, and stock markets outside the U.S., especially emerging markets, are on the cheap side.

A chart taken from the article:
Growth vs. value: Compound annual growth rate

There is a lot of academic evidence suggesting that value stocks should be offered as a benchmark to follow. The evidence is so strong that most academic studies actually use value as a control.

One of the problems with cap-weighting (for example, the S&P 500 index is cap-weighted) is that cap-weighting gives more weight to stocks that have gone up in price and gotten more expensive. This is probably the reason that cap-weighting underperforms almost every other method of indexing - even an indexing method that picks stocks randomly.

Click through to read the entire article: Never Buy Expensive Stocks. Period.

One can't even simulate a scenario where a diversified portfolio of 30 expensive stocks can beat the worst performing portfolio of 30 cheap stocks. Why investors allocate to expensive, or "growth," stocks is beyond me.

Picking Stocks Randomly Beats the Market

. July 1, 2014

Is it a good thing to put your money "in the market?" That depends on what you mean. Most people will steer you toward cap-weighted funds (the S&P 500, for example, is a cap-weighted index). Research suggests that of all the ways to balance stocks in a portfolio, cap-weighting is one of the worst.

Article in plain English: Index Monkeys Beat Cap-Weighting 

Researchers have found that equity indices constructed randomly by 'monkeys' would produce higher risk-adjusted returns than an equivalent market capitalisation-weighted index over the last 40 years.

White paper: Equal-Weighted Benchmarking: Raising the Monkey Bars 
Given the disappointing performance of active managers, it is particularly surprising how many alternatively weighted indices outperformed the cap-weighted S&P 500.... A more comprehensive critique conducted by the Cass Business School showed that “...equity indices constructed randomly by 'monkeys' would have produced higher risk-adjusted returns than an equivalent market capitalization-weighted index over the last 40 years. A study based on monthly U.S. share data from 1968 to 2011 found nearly all 10 million indices weighted by chance delivered vastly superior returns.” This counterintuitive and remarkable result deserves specific emphasis. According to these results, in the period from 1969 to 2011, if you had picked stocks at random, there is a 99.9% chance you would have beaten the market.

Facebook Page on Quantitative Trading

. June 26, 2014

Over the past few years, I've gravitated toward multi-strategy thinking. What strategies tend to do well when momentum underperforms for a few years? What strategies have a low correlation with momentum that can help diversify it?

The strategies have been debated in academic papers for decades, so they're not hard to find. Integrating them into a portfolio is more of a challenge.

The obvious way to combine strategies is to use leverage: for example, to reduce the market risk of a momentum strategy as much as possible, to do the same thing with a value strategy, and then to borrow money at a low rate in order to get exposure to both. There is a risk that momentum and value will both underperform at the same time and that the leverage will end up hurting the portfolio. Now imagine managing the risk of four or eight strategies integrated in the same way.

I've chosen not to go with the obvious method, but instead to pick from a universe of exchange-traded funds using a quantitative method to select funds based on multiple strategies. The tradeoff is the increased amount of information I have to process to actually put on a trade. Most people would say that this is more trouble than it's worth.

So far, I've hesitated to post about anything other than trend-following momentum using moving averages other than on the resources page. Most people aren't obsessed with trading, and information overload might cause them to give up on it completely.

That's why I've been posting the information overload links to a Facebook page for the past three years. If you really are obsessed, check it out: