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:

Play the Lotto Like a Trader

. April 2, 2012

Good odds look better than they actually are. A $540 million jackpot isn't worth $540 million if they pay it out over decades, once you take inflation and unearned interest into account. Calculate the odds based on today's lump sum payout. It will always be less than the advertised jackpot.

Photo by Mike Fleming
And then there are taxes. You'll lose nearly half of the lump sum payout to the government unless you can find a way to defer or eliminate being taxed on your winnings.

And then there's the law of diminishing returns. Dollar for dollar, $1000 spent on lottery tickets is a house payment that will keep some people from foreclosure. $1000 after you already have $100,000 cash is less precious. An extra $1000 after you have $540 million is peanuts.

Would you buy $1000 in lottery tickets to have an 11% chance to win $10,000? How about $1 million in lottery tickets to have an 11% chance to win $10 million?

Some of us would go for the first option, though I honestly don't see why after taxes and deferred payments are taken into account. Almost no one would go for the second: $1 million in your pocket today is not worth risking to have $10 million, which will not really be worth ten times as much to you.

When it comes to money, slow and steady wins the race.

More here: Is the $540 Million Lottery a Good Bet?

A Free Education

. December 5, 2011

Reading as a form of self-education becomes more important the older a person gets. After college, reading becomes the primary form of self-education.

One of the best ways for a job applicant to elevate himself to the #1 position is to maintain a blog with book reviews and articles on topics related to the field the person wants to work in.

Getting good grades in college shows that the applicant has read in his field, but maintaining the blog shows that it is likely that he will continue to read widely and educate himself. It's an education with no tuition for the employee and no cost to the employer: a win for both.

Since one of the keys to self-funding is to earn more and spend less, preferably in a career where you can find fulfillment through service, it makes sense to make the most of your opportunities when applying for jobs.

Great Reads: A Flood of Trading Links

. November 15, 2011

Don't say I didn't warn you.

Trading and Investing

The Ivy Portfolio vs. Ivy League endowments last year. (Mebane Faber)
Trend-following indicators reduce downside volatility. (MarketSci)
When momentum is poor, sell out. (Research Puzzle
Ideas about volatility-adjusted relative strength. (CXO Advisory)
Individual stocks mean-revert from month to month; industries trend. (SSRN)
Anomalies like momentum and value to go in and out of style. (CXO Advisory)
Selling puts or calls according to trend. (CXO Advisory)
Managed futures can save your tail. (Steven Koomar)
Investors allocate to the wrong asset class at the wrong time. (Mebane Faber)

A Softer World: 703
Software and brokers for options trading. (Condor Options)
Yes, bonds can be volatile instruments. Surprised? (ETF Replay)
Investing lessons from a pianist. (Marc Faber)
How to explain short selling to your mother. (BC Lund)
Are you a deranged trader? (Surly Trader)

In complex transactions involving a lot of people, be cynical. (Aleph)
"Never, ever take counterparty risk." (Reformed Broker)

It may be cheaper to buy ETF's than mutual funds. (Mebane Faber)
"Funds of funds face a huge hurdle because of the high fees." (Mebane Faber)
Can active managers add value when everything is correlated? (ETF Replay)
Commodity indices behave like mostly energy. (MarketSci)
Asset classes are becoming more correlated. (MarketSci)

Some of hedge funds' returns come from liquidity risk. (CXO Advisory)
Be careful about shorting that VXX. (MarketSci)
The state of short-term mean reversion. (MarketSci)
What happens to P/E ratios when rates and inflation change? (Mebane Faber)

Average market performance on the last day of the quarter. (MarketSci)
Average market performance on the first day of the quarter. (MarketSci)
The stock market tends to be strong in the fourth quarter. (MarketSci)
Dividend payers: less volatility and a significantly higher return. (SurlyTrader) 

Affordable Living

If you were a millionaire, would you act like one? (Reformed Broker)

An emergency fund can indirectly provide a good return on the money. (Aleph)
How to extend the life of laptop batteries. (Education Tech News)
Affordable ways to create gifts for men. (She So Crafty)


Blogging is like working out. (The Basis Point)
How to find a job in finance. (Aleph)

Man Links

The importance of trusting men in your circle. (The Art of Manliness)
Are you a spectator or a doer? (The Art of Manliness)
Leaders lead people through fear. (Donald Miller)

Stop living for the approval of women. People-pleaser. (Art of Manliness)
Don't live for your mother's approval, either. (Art of Manliness)
Men, stick to your guns. (Art of Manliness)

How to improve your posture. (Art of Manliness)
The power of morning and evening routines. (Art of Manliness)
How to be the perfect party guest. (Art of Manliness)
Ten cheap date ideas she'll actually love. (Art of Manliness)

Marriage and Family

The personality types that make the best matches. (Personality Page)

Society and Worldview

Churches, are you sure you want your young adults back? (Immerse Journal)

Hypothesis: the efficient market hypothesis led to the financial crisis. (Aleph)

It costs 2% to 5% of GDP to file taxes. Not pay, just to file. (Dan Dascalescu)
Washington, D.C. is booming. What recession? (Reformed Broker)

The Facebook Gross National Happiness indicator. (Facebook)
Welcome to the genomic revolution. (YouTube)

Christian Living

How to stop worrying. (Max Lucado: part 1 and part 2)
"God understood Elijah's weary despair, and he let him sleep." (CCEL)


Get rid of line breaks that bother you when you copy from the Web. (Text Fixer)


Why go to college? (SurlyTrader)
Watch out! (Signs of Danger)

Scary church signs. (Ed Stetzer)
How different Christian denominations see each other. (Ed Stetzer)

How to win at Monopoly: buy the orange properties. (BBC)

Penguins attack: