January 2, 2017

Are Commodities Still a Good Portfolio Diversifier?

Overfitting the data is a serious problem when constructing financial models. One way to guard against this is to have lots of data. This can help you determine if your results are robust by seeing how they hold up over different time periods.

But this assumes the underlying market dynamics remain stable over time. That is not always the case. Gogi Gerwal gives a good example of how you may be misled by extrapolating past results to the future. In his blog post, “Should We Consider Gold?” Gogi showed that adding gold to the Global Equities Momentum (GEM) model increased its annual return from 18% to 21%.

Source: SharpeReturns.ca

Gogi then pointed out that from 1971 to 1981 gold’s price went up 18-fold when the U.S. let the price rise to market levels. If we remove this period of unnatural price appreciation from the back test, GEM without gold has a higher return and less volatility.

This is an example of aggregation bias. By combining events that are different into one set of data, your results may look good. But appearances can be deceiving. Different market forces at work on different parts of the data means you should consider the periods separately. As momentum investors, we become sensitive to changing market conditions.

Commodity futures are another area where people may be misled using aggregated data. Here is a  long-term perspective on commodity performance versus stocks and bonds:

The blue line represents a traditional 60/40 balanced stock and bond portfolio. The green line is the popular S&P Goldman Sachs Commodity Index (GSCI) of commodity futures contracts. S&P GSCI had strong but erratic performance until mid-2008 when it collapsed.

There has been a strong disconnect in commodity index performance before and after 2008. We should see if the more recent performance is a normal variation or if it signals a change in market dynamics. This is important to know because many institutional investors use commodities to diversify their investment holdings. The Chartered Financial Analyst (CFA) curriculum recommends a 10% commodities allocation to a typical stock and bond portfolio.

Commodities Diversification

The idea of diversifying stocks and bonds with commodities first began with Gorton and Rouwenhorst (2005) in their paper, "Facts and Fantasies about Commodity Futures." They showed that from 1959 through 2004, a collateralized basket of 36 commodity futures had equity-like returns of 11.2% per year, while being negatively correlated to stocks. This meant a combination of commodities and equities could have large diversification benefits. In a 2006 report called "Strategic Asset Allocation and Commodities" commissioned by PIMCO, Ibbotson Associates also issued a report showing that commodities could be a valuable addition to traditional stock and bond portfolios.

Growth of Commodities

Following these two studies, institutional interest in passive, long-only commodity exposure skyrocketed. Goldman Sachs, PIMCO, and others aggressively marketed commodity index products. Many pension funds entered the market. Long positions in commodity indices went from $6 billion in 1999 to $256 billion by mid-2008. Annualized growth among the S&P GSCI commodities averaged 31% during the 2004-2006 period. This rate was nearly triple that of 2001-2003. Market participation by non-commercial traders tripled from 15% in 1990 to 42% in 2012. [1]

Despite poor performance since 2008, demand for commodities has remained strong. Commodity investments more than doubled from roughly $170 billion in July 2007 to $410 billion in February 2013. According to Bhardwaj, Gorton, and Rouwenhorst (2014) in their paper, "Facts and Fantasies About Commodity Futures Ten Years Later" open interest of the average commodity contract has more than doubled since 2004. Endowments, pension funds, hedge funds, and the public have all joined the bandwagon by adding commodity index futures to their portfolios. Following good performance in the 1980s and 1990s, speculative demand for commodities has also grown in the managed futures industry. Barclays Hedge reported that the amount in managed futures went from $50.9 billion in 2007 to $325 billion in 2014.
Financialization of Commodities

Increased participation of fund managers, pension plans and other financial investors created what some call the financialization of commodities. Under financialization, commodities are influenced by the aggregate risk appetite for financial assets and the investment behavior of commodity index investors. These investors have less commodity specific knowledge and a different attitude than commercial interests.

Financial investors enter or exit trades based on their perception of the macroeconomic situation, rather than on market specific fundamental factors. Increases in the supply of price insurance by financial investors has lowered the price hedgers pay for protection.

Financial investors improve the sharing of commodity price risk. Financial investors also channel volatility from outside markets to the commodity markets.

Source: Zaremba (2015), "Is Financialization Killing Commodity Investments?"

Increased Correlations

Financialization has also had an impact on the correlation of commodities to other assets. In their paper, "Financialization, Crisis and Commodity Correlation Dynamics," Silvennoinen and Thorp (2009) report on the conditional volatility and correlation dynamics of commodity futures from May 1990 until July 2009. They found increasing integration between the commodity and financial markets. Hedge fund managers were timing their futures exposure for hedging purposes.

Financialization means that returns from both commodity futures and stocks decrease in volatile markets. During the 2008 financial crises, the correlation between stocks and commodities shot up to over 0.80. Increasing correlation during times of financial stress diminishes the diversification value of commodities. Cheung and Miu (2010) also show in their paper "Diversification Benefits of Commodity Futures," that commodities are not a good diversifier in bearish equity environments. Bhardwaj et al. say that correlations increase in periods of market turmoil. Commodities are often acquired for their hedge-type protection during bear markets in stocks. But we see here that this kind of protection may no longer exist.

Commodities now may also be more correlated in general with other assets. The table below from Bhardwaj et al. shows the one-year correlation of commodity futures with stocks went from -0.10 in July 1959 through Dec 2004. to 0.60 from Jan 2005 through Dec 2014.

In their paper "Correlation in Commodity Futures and Equity Markets Around the World: Long-Run Trend and Short-Run Fluctuation," Li, Zhang, and Du (2011) looked at dynamic conditional correlations (DCC) from 2000 through 2010 between 45 country equity markets and the S&P GSCI index.  DCC preserves trends without smoothing fluctuations. Using DCC, the authors concluded, “… we are able to decisively disapprove the assertion that, despite recent history, commodities still provide portfolio diversification. Whether from the long-run or short-run perspective, the diversification value of the commodity futures index has, in general, vanished.” Li et al. attribute this to an increase in the integration between commodity futures and equity markets, and an increasing number of investors holding both commodity futures and equities.

Commodities may now also be more correlated to each other and to commodity indices, as we see from the Bhardwaj et al. study:.

In an interesting paper called "The Strategic and Tactical Value of Commodity Futures," Erb and Harvey (2006) show that the average annualized excess return for individual commodity futures from 1945 through 2004 was near zero. Portfolio returns of more than 10% came from mean reversion profits through portfolio rebalancing. Since correlations were so low back then, the diversification premium was enormous.

Lower Profits

If Erb and Harvey are correct and intra-commodity correlations are higher now due to financialization, then we should see lower commodity portfolio returns.  We should also see higher volatility. This is because commodities are bought and sold at the same time by financial investors rather than fluctuating independently based on their individual fundamentals.

There may be another reason why commodity futures returns are lower now. To see why, we need to understand how the futures markets work. Alpha Architect had a good overview of that last week.

In brief, there are three components of commodity futures return. They are the return from holding Treasury bills as collateral, spot return from changes in commodity prices, and the yield associated with rolling over futures contracts.

Importance of Roll Yield

According to Campbell & Company (2014) in "Deconstructing Futures Returns: The Role of Roll Yield", the cumulative impact of roll yield can be significant. In some cases, it is similar in size to the entire gain or loss an investor experiences over the lifetime of a trade. Erb and Harvey (2006) reported that from December 1982 to May 2004, roll returns explained 91% of the expected long-run cross sectional variation of commodity futures excess return. According to Anson (1998) in "Spot Returns, Roll Yield, and Diversification with Commodity Futures," roll yield provided most of commodity investments’ total excess return between 1982 and 1997. The S&P GSCI average annual roll yield then was 6.1%, while the average spot return was -.08%.

What happened to roll yield since financialization of commodities began? In the chart below, the difference between the commodities return and the commodity futures return is the roll yield.
Bhardwaj et al. show that the much of the reduction in commodity futures return in recent years is due to a lower collateral returns. But excess futures returns (futures returns less U.S. Treasury bill returns), have declined from 5.23% annually in 1959 through 2004 to 3.67% in 2005 through 2014 on an equal weight  portfolio. This is a 30% reduction in roll yield (risk premium). What is also important is the 26% increase in standard deviation from 12.1% in the earlier period to 15.23% in yhe later one. Return, volatility, and correlation are all are used in determining optimal portfolios.
Here is an explanation for why the risk premium has diminished. Hedgers can be on either side of a commodity market. When raw material prices go up, consumers still need to heat their homes, drive to work, and feed their families. Builders still need to buy lumber. There are no good substitutes for these things. This means the price elasticity of demand is generally low for commodity end products. Commercial interests who need to buy commodities can often pass price increases on to consumers rather than hedge future supply costs in the futures markets.

But the situation is different for commodity producers, such as farmers, mining and energy producers. They need to accept whatever the market prices is once their products are produced. To avoid the risk of not being able to cover their production costs, producers will hedge their price risk. They do this by selling futures contracts ahead of production that guarantees them a known selling price. Hedgers are willing to pay a premium to lay off this price risk. They offer speculators who take the other sides of their trades a positive return. More speculative activity now means less risk premium and lower roll yields.

In "Systematic Risk, Hedging Pressure, and Risk Premiums in Futures Markets," Bessembinder (1992) found that from 1967 through 1989, the average return of 16 non-financial futures was influenced by the degree of net hedging. Commodities in which hedgers were net short had positive excess returns for speculators to capture. When long-only financial investors entered these markets in force, the risk premiums they received from hedgers had to be spread out among many more participants.

The reduction in risk premium also helps explain the declining performance of commodity trading advisors (CTAs) in recent years. There has been less hedger premium available to them as well. In their paper, "Fooling Some of the People All of the Time: The Inefficient Performance and Persistence of Commodity Trading Advisors," Bhardwaj, Gorton, and Rouwenhorst (2013) reported that CTA excess returns over U.S. Treasury bills averaged only 1.8% from 1994 through 2102. This is not statistically different from zero.

Optimal Portfolios

With the trend toward higher correlations, higher volatility, and lower risk premiums, we should look again to see if commodity futures can still add value to a stock and bond portfolio. Besdies Bhardwaj et al. (2014), there have been three other academic studies addressing this question over the past five years. They all use more data from outside the financialization period than from within it. So their results are not overly biased toward recent events.

The first study was "Should Investors Include Commodities in Their Portfolios After All? New Evidence," by Daskalaki and Skiadopolous (2011). They looked at the S&P GSCI and DJ-UBSCI (now Bloomberg Commodity Index) from 1989 through 2009. Only one-quarter of their 20- year sample period was post-financialization. The authors did a portfolio spanning analysis. This shows what happens to the efficient frontier of optimal portfolios when you add more assets. They found that when you take higher order moments of the portfolio return distribution into account, commodities were not beneficial. When using rolling returns to construct out-of-sample data, the authors discovered that commodities were not beneficial even to mean variance investors.

The second study was "On the Correlation between Commodity and Equity Returns: Implications for Portfolio Allocation," by Lombardi and Ravazzolo (2013) of the Bank for International Settlements. They applied time-varying DCC correlations to the S&P GSCI and the MSCI Global Equities indices from 1980 through 2012. Again, only one-quarter of the data was post-financialization. These authors found the inclusion of commodities boosted returns for horizons of 2 to 4 weeks but at a cost of substantially higher volatility. They concluded that the idea of including commodities in one’s portfolio as a hedging device is not grounded.

The final study was "Portfolio Diversification with Commodities in Times of Financialization,"
by Zaremba (2015). He used spanning tests on the JP Morgan Commodity Curve Index data combined with stocks and bonds from 1991 through 2012. His conclusion was also that including commodity futures in a traditional stock and bond portfolio was no longer reasonable.

Front Running

There are a few more things that commodity index investors should be aware of. The first is a study by Mou (2011) called "Limits to Arbitrage and Commodity Index Investment: Front-Running the Goldman Roll." Mou examined the costs to investors of front running. This occurs when hedge funds or others buy the next month futures contracts just ahead of their usual rollover dates. Front runners then unwind their positions after prices have been pushed higher by index managers who bought the new contracts. Mou estimated that front running the S&P GSCI from January 2000 to March 2010 cost S&P GSCI index investors 3.6% in annual return. The popular S&P GSCI and Bloomberg commodity indices both use fixed rollover dates. Front running takes a toll on the performance of both indices, as well as on any funds using those indices.

Index Versus Fund Performance

One should also consider the costs associated with being in commodity index funds. I calculated the difference between index and fund returns since the start of the two oldest commodity index exchange-traded funds. The iShares S&P GSCI Commodity Indexed Trust (GSG) underperformed its index by 87 basis points per year. The iPath Bloomberg Commodity Total Return ETN (DJP) underperformed its index by 106 basis points. The annual expense ratio of both funds is 75 basis points. This accounts for some, but not all, of the difference in performance between the funds and the indices. None of the above portfolio optimization studies take these significant costs into account.

Weight of Evidence

Despite public information about lower roll yields, changing correlations, front running costs, and index expenses, researchers like Levine, Ooi, and Richardson (2016) are still positive about using commodity index futures as a portfolio diversifier. Their paper, "Commodities for the Long Run," does not discuss financialization. Instead, it uses a large amount of data to point out that commodity returns are sensitive to business cycle changes and the rate of inflation.

Here is a chart from Bhardwaj et al. (2014) showing returns of an equal-weighted commodity futures portfolio decade by decade. Both before and after inflation, we see that the latest decade is the only one where futures returns are below spot returns. In fact, they are substantially below. Something different is going on now after financialization of the commodity markets.

Even more telling is the following table from the Levine et al. paper itself:

Inside the red box are Sharpe ratios of the last two 20-year periods for portfolios with 90% of their assets in a 60/40 blend of stocks and bonds and 10% in commodities. (Allocating 10% of investment capital to commodity futures became widespread after the Gorton and Rouwenhorst paper in 2005.)
Portfolio Sharpe ratios take correlations, volatilities, and returns into account. The Sharpe ratios here are all about the same for the past 40 years. Thus, there has been no advantage in adding commodities to a balanced stock and bond portfolio. If you take front-running and commodity index fund expenses into account, an allocation to commodities would be even less desirable than a portfolio without them.

Aggregation Bias

Levine et al. say that their data extending back to 1877 implies that commodity futures add value to a diversified portfolio. Even if that is true, the nature of the commodity markets has changed significantly since the mid-2000s due to financialization. This means that data before financialization may not have as much relevancy. The Levine et al. optimal allocation to stocks, bonds, and commodities based on data from 1877 may not be the best one to use.

The three portfolio studies above, as well as the Levine et al. results over the past 40 years, may be a more accurate view of what to expect in the future. All four show that including commodities in a stock and bond portfolio is no longer beneficial.

Next Up

The reason I am discussing aggregation bias with commodities is two-fold. First, there are still many advisors and investors using commodities as a diversifier. They may want to reconsider that decision in light of the contrary evidence now.
The second reason has to do with factor-based investing. Factors have been growing in popularity and are expected to grow even more over the next few years. Yet they have many of the same issues as commodities with regard to aggregation bias, market impact, declining risk premia, front running, and unaccounted costs. This post has been an introduction to these issues. My next post will look at them in more detail in the light of factor-based investing.

[1] The CFTC does not always categorize hedgers and speculators correctly into commercial and non-commercial interests in their Commitments of Traders (COT) reports. The percentage of non-commercials mentioned here and elsewhere should be used with caution.

November 30, 2016

Common Mistakes of Momentum Investors

Like most investors, those using momentum are often guilty of chasing performance. In fact, momentum requires that we do this. But it should be done in a disciplined and systematic way. Performance chasing should not be due to myopia, irrational loss aversion, or other psychological biases.

Behavioral Challenges

It is not always easy adhering to a disciplined approach. If you are not vigilant, emotions can get the better of you. Even Daniel Kahneman, the father of behavioral economics, admits to being influenced by behavioral heuristics.

We may forget our strategy’s long-term expected outperformance when we experience uncomfortable drawdowns. The survival instinct kicks in strongly then. Recency bias can make us feel the drawdown will never end.

We may also have to deal with regret aversion when our portfolio underperforms. This will happen sooner or later. No strategy outperforms all the time. Occasional benchmark underperformance is the price we pay for possible protection from severe bear markets.

Those who look at performance frequently do not do as well as those who are less concerned with short-term performance. When someone asks me how my models are doing this year, I know they do not have a good understanding of momentum being a long-term approach.  Last May a dual momentum investor sent me an email saying his wife’s account in REITs was outperforming his momentum account. He then closed his account and invested in REITS himself. Since then, REITs have declined more than 10%, while momentum has gone up almost the same amount. This scenario has happened more frequently than you might think.

It is important to keep the big picture in mind. We should wait at least a full bull and bear market cycle before evaluating the performance of a dual momentum strategy. Do your homework so you understand whatever investment approach you select. Then relax, and enjoy the journey.

Accepting Lower Risk Premia
The other serious mistake momentum and other investors make is not understanding the real goal of investing. We should invest in a way that offers us the highest expected return while limiting our risk exposure. Limiting downside exposure is important so we do not panic under stress and do stupid things.
The stock market has had two bear markets over the past 20 years. Each time stocks lost more than half their value. Because of this, investors have been extra cautious. Many have tried to use broad diversification to reduce their portfolios' drawdown exposure.

If you select non-correlated assets, you can achieve some reduction in volatility and drawdown. But your expected return is the weighted average return of all your assets. That is where the problem lies. Assets with lower expected returns will reduce your portfolio's return.
Bonds have done well over the past 15 years. But longer term, their real return is less than one-third the real return of stocks. Given how low interest rates are now, there is not much room for bonds to appreciate further. In fact, current interest rates predict low bond returns in the years ahead.
Bonds are also not as low-risk as you might think. Since 1900, the worst real return drawdown was 73% for stocks and 68% for bonds. As we see below, stocks and bonds can sometimes have severe drawdowns simultaneously.

Bonds not only create a drag on our performance. They also may not reduce our risk exposure when we most need them to do so.

Some advisors recommend alternative assets, like commodities, with little or no expected real return. This is because such assets are generally (but not always) less correlated to equities. They can therefore reduce portfolio volatility. But the addition of low-return alternative assets can create an even more serious drag on portfolio performance.

What momentum investors should remember is absolute momentum does a much better job of reducing drawdown. Because of this, trend following absolute momentum lets us keep more of our assets in equities where we can receive more risk-premium.

Using Stocks and Sectors

My first research paper released in 2011 analyzed equity momentum with individual stocks, sectors, style attributes, and regions. I showed that momentum works best when applied to geographically diversified equity indices. Last year Geczy and Samonov (2015) applied momentum to stocks, stock sectors, geographic equity indices, bonds, commodities, and currencies. They also found equity indices performed best. This is without considering the issues of scalability and trading costs associated with individual stocks. (See my last blog post for more on this). Yet most articles about momentum and most momentum funds still use stocks instead of stock indices.  Broadly diversified, low cost stock indices do not get the respect they deserve.

Some momentum investors still adhere to the old paradigm of extensive diversification. They hold more assets than they need for optimal portfolio growth. I posted an article and mentioned on my website’s FAQ page that the long-run performance of sector rotation is not as good as momentum with broad stock indices. But I still get plenty of emails asking me about sector rotation and the use of other higher risk or lower return assets.
Preference for Complexity

Investors and advisors seem to prefer complexity over simplicity. Many must believe that elaborate models and more diversified portfolios perform better than simpler approaches. My research shows this is not the case. I tried adding factor-based indices and additional asset classes to my dual momentum models. My models worked best using just broad-based indices for U.S. stocks, non-U.S. stocks, and short or intermediate bonds.

Advisors may prefer complexity to justify their fees. It could be challenging to charge fees for putting clients in an S&P 500 index fund. Robo-advisors are the latest slice and dice diversification strategy for those who think more is  better.

Non-Optimal Portfolio Construction
Some portfolios suffer because investors rely on well-known measures like the Sharpe ratio for selecting assets. The Sharpe ratio divides excess returns by the standard deviation of those returns. It is an efficiency measure telling you how much return you might expect per unit of volatility. But unless returns are normally distributed (they almost never are), the Sharpe ratio is not a good indicator of tail risk. Nor is it a good indicator of the amount of wealth you might accumulate or your chance of future investment success.[1]

Wiecki et al. (2016) looked at 818 algorithmic trading strategies at Quantopian, a research boutique. Using data from 2010 through 2015, they found that the Sharpe ratio offered little value in predicting out-of-sample performance.  This was also true of similar metrics such as the information ratio, Sortino ratio, and Calmar ratio.

You can increase the Sharpe ratio of most portfolios by simply adding more bonds. But your expected rate of return and accumulated wealth will in most cases suffer.

Here is an example showing the performance of the S&P 500 index compared to a balanced portfolio with 60% in the S&P 500 index and 40% in the Barclays Capital U.S. aggregate bond index. The data is from the start of the bond index in January 1976 until November 2016. It represents a possible 40 year holding period of someone saving for retirement.

S&P 500 60/40
CAGR 11.6% 10.4%
Standard Deviation 14.8% 9.6%
Sharpe Ratio 0.43 0.49
Worst Drawdown -50.9% -32.5%
$10,000 Grows to  $781,760 $507,070
Results are hypothetical, are NOT an indicator of future results, and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Please see our Disclaimer page for more information.

The difference in annual return of 1.2% gives a 54% increase in ending wealth over this 40 year span. Which portfolio would you rather have? In this example, the most desirable portfolio may depend on your on your risk tolerance. The 60/40 portfolio has a less painful worst drawdown.

Here are the results adding the simple Global Equities Momentum (GEM) model featured in my book and in an earlier blog post. GEM uses relative momentum to switch between U.S. and non-U.S. stock indices, and absolute momentum to switch into aggregate bonds when stocks are weak. GEM’s single parameter, the look back period, was discovered in 1937. GEM uses a combination of relative and absolute momentum. Both have shown good results on over 200 years of back data.[2] 

S&P 500 60/40 GEM
CAGR 11.6% 10.4% 17.1%
Standard Deviation 14.8% 9.6% 12.5%
Sharpe Ratio 0.43 0.49 0.87
Worst Drawdown -50.9% -32.5% -17.8%
$10,000 Grows to  $781,760 $507,070 $5,416,080
Results are hypothetical, are NOT an indicator of future results, and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Please see our Disclaimer page for more information.

Which portfolio would you now choose? How difficult would it be for you to live with GEM?[3]

When I analyze investment opportunities, my primary criteria are a high CAGR combined with a tolerable level of risk exposure. CAGR represents the geometric growth rate of one’s capital.[4]  It takes volatility into account. If two strategies have the same average return, the one with lower volatility will have a higher CAGR.

But like the Sharpe ratio, CAGR does not measure tail risk. Extreme downside exposure can cause you to exit positions prematurely screaming in pain or cursing your investment advisor. That is why I also consider drawdown.

Worst drawdown is only a single point in time, but it can give you a pretty good idea about tail risk. I also examine the distribution of returns and look at all the other drawdowns. Keep in mind that your worst drawdown may lie ahead still. Having a simple, robust approach that performs well over a long period may reduce that risk.


It is important to remain focused on what is important – accumulating wealth while  protecting yourself from severe bear markets. Once you have a good investment strategy, you need to be patient so it can do its work for you. Warren Buffett said the stock market is a mechanism for transferring wealth from the impatient to the patient. This applies to momentum as well as other investors.

[1] See Levy (2016).
[2]  See Geczy and Samonov (2015).
[3]  I also have an enhanced version of GEM that I license to a few investment professionals.
[4]  For econ geeks, CAGR is consistent with logarithmic utility. The Sharpe ratio represents quadratic utility, unless returns are normally distributed. See Friedman and Sandow (2004) and Levy (2016).

October 17, 2016

Book Review of Quantitative Momentum

I have been looking forward to Wes Gray and Jack Vogel's new book, Quantitative Momentum.

It is the only book besides my own Dual Momentum that relies on academic research to develop systematic momentum strategies. My book uses a macro approach of applying momentum to indices and asset classes. Wes and Jack (W&J) take the more common approach and apply momentum to individual stocks.

W&J begin their book with an excellent question. Since there is ample research showing momentum to be a superior investment approach over the past 200 years, why isn’t everyone using it?

W&J do a good job explaining the behavioral biases that keep many investors away from momentum. W&J also discuss marketplace constraints like advisor career risk when momentum underperforms its benchmark.

In Chapter 1 W&J give a short history of trend based and fundamental analysis based investing. They show that both approaches can work.

In Chapter 2 W&J discuss irrational traders who can dislocate prices from their fundamental values. In the case of value, investors overreact in the short-run to bad news. In the case of momentum, investors under react to good news.

Investment managers are hired to exploit long-run profit opportunities, but their performance is judged by investors looking at short-term results. Advisors who continue to focus on longer-term opportunities, like value or momentum, may get fired. This is one reason why anomalies like momentum do not get arbitraged away.

In one of the key points of the book, W&J discuss the importance of sustainable investors as well as sustainable alpha. Gregg Fisher once said, “We don’t have people with investment problems. We have investments with people problems.” Investors often lack the requisite patience to stay with their chosen strategies during periods of benchmark under performance.
To better prepare investors for challenging times ahead, W&J highlight the risks associated with value and momentum investing. They point to Julian Robertson’s Tiger Funds that lost almost all their clients by sticking to their value model in the late 1990s. Value underperformed the market in 5 out of 6 years, sometimes by double digits. W&J make this interesting statement, “True value investing is almost impossible.”

What can investors do about this? W&J point out that momentum is largely uncorrelated with value. This means an investment in momentum can make value investing more tolerable. Momentum and value are largely uncorrelated only when their market risk is hedged. Long-only momentum and value are correlated to the market and to each other. All three can simultaneously experience large bear market losses.

As I show in my blog post, “Factor Investing: Buyer Beware,” value investing in actual practice has not shown any significant advantage over the market. If investors have no reason to hold value stocks, momentum loses some of its attractiveness as a diversification strategy.

In Chapter 3 W&J give a brief history of momentum and the important psychological challenges facing momentum investors. W&J show that momentum, like value, can underperform over long periods. They point to a 5-year stretch when momentum underperformed the broad market by 15%. Staying the course during times like that can be a challenge for any investor.

In Chapter 4 W&J demonstrate that a 50/50 allocation to value and momentum can reduce the tracking error of separate value and momentum portfolios during extended periods of relative poor performance. What may also be worth noting is the decline over time of both value and momentum premia. Their chart below is consistent with Bhattacharya et al. (2012) and Hwang & Rubesam (2013) who find that stock momentum premium and profits have disappeared since the 1990s.
In Chapter 5 W&J show that frequently rebalanced, concentrated momentum portfolios perform best.

Stock momentum is a high turnover strategy, and many momentum stocks are volatile with wide bid-ask spreads. There is bound to be price impact from trading in momentum stocks. This is especially true for frequently rebalanced, concentrated momentum portfolios.

W&J say that concentrated portfolio/higher rebalance frequency is not a good approach for large asset managers with billions to invest because of scalability issues. But most investors draw upon the same universe of momentum stocks. Alpha Architect shows the top 100 momentum stocks on their website each month to those who register there. All investors, not just multi-billion-dollar asset managers, may experience adverse price impact from trading the same momentum stocks that everyone else does.

Transaction costs are also an important issue. W&J point to a paper in the Journal of Financial Economics by Lesmond, Schill, and Zhou (2002) called "The Illusionary Nature of Momentum Profits." Lesmond et al. conclude that after transaction costs, momentum profits are largely illusionary. W&J also mention research by Korajczyk and Sadka (2004) showing that stock momentum has a limited capacity of only about $5 billion.

Offsetting these arguments, W&J present findings by Frazzini, Israel, and Moskowitz (2014) of AQR. Frazzini et al. argue that momentum trading costs are manageable using some kind of optimized trading of AQR’s own proprietary data from 1998 through 2011 if one is willing to accept added tracking error.

Fisher, Shah, and Titman (2015), using observed bid-ask spreads from 2000 through 2013, report that their estimates of trading costs are generally much larger than those reported in Frazzini et al.and somewhat smaller than those described in Lesmond et al. and Korajczyk and Sadka. Research by Jason Hsu PhD, co-founder of Research Affiliates, also supports the higher transaction cost conclusions of Fisher et al. and Lesmond et al. with both monthly and quarterly rebalancing.
Finally, Novy-Marx and Velikov (2015) find that stock momentum disappear even with optimal trading strategies once the aggregate amount of capital invested in momentum approaches $6 billion.
Chapter 6 is where W&J explain path dependency and why it matters. They cite research by Da, Gurun, and Waracha (2014) showing that smooth and steady past performance is preferable to jumpy performance.

To implement this idea, W&J advocate double sorting stocks on both their 12-2 month momentum and their percentage of positive daily returns over the past 252 trading days [1]. What they call “high-quality momentum" are top decile momentum stocks with the largest percentage of positive daily returns. Results below are from 1927 through 2014. Transaction costs are not included.

The improvement in high-quality over generic momentum performance looks good. But a possible warning sign is W&J’s statement at the beginning of Chapter 6: “For over a year, we examined every respectable piece on momentum stock selection strategies we could find…”

Extensive data mining increases the odds that favorable results may be due to chance. Say you have some studies each showing no significance with a 95% confidence level of being correct. If you examine 20 or more of these studies, there is a good chance that one of them will be look significant even though the chance of it being correct is still only 5%. The classic green jelly bean example should make this clear.

                                             Source: http://xkcd.com/882

In Chapter 7 W&J attempt to further enhance momentum by adding seasonality. In the turn-of-the-year or January effect, investors engage in year-end tax loss selling. They hold on to their strongest stocks and may buy more as replacements for the stocks they sell. This can create some abnormal profits in these stronger stocks.

Window dressing to make their quarter-end portfolios look more attractive may also cause investment professionals to sell their losers and buy more winners before the end of the quarter. To take advantage of these seasonal tendencies, W&J advocate rebalancing their momentum portfolios at the end of February, May, August and November. instead of each calendar quarter.

Here are the results from incorporating seasonality as “smart rebalancing.”

There is very little risk-adjusted improvement over agnostic (generic) momentum as seen from the increase of only .01 in the Sharpe and Sortino ratios.  But since portfolios are rebalanced quarterly anyway, there should be no harm in picking non-calendar ending quarters for doing so.

In Chapter 8 W&J suggest that readers address the trading cost issue by comparing the analysis presented in Lesmond et al. to Frazzini et al. They do not mention here the more recent studies by Fisher et al. and Hsu.

W&J then do an in-depth analysis of “quantitative momentum” with respect to reward, risk, and robustness. W&J then say, “… strategies like value and momentum presumably will continue to work because they sometimes fail spectacularly relative to passive benchmarks.” This may not be great news for those who at that time hold momentum or value stocks. But W&J offer these words of  encouragement, “The ability to stay disciplined to a process is arguably the most important aspect of being a successful investor” (emphasis added).

In Chapter 9 W&J look at a recommended 50/50 allocation to an equal weight, quarterly rebalanced  momentum and value portfolio from 1974 through 2014.

The combined portfolio return is higher than momentum or value on their own. The combined portfolio has less tracking error vis-a-vis the broad market. Combining value and momentum also shortens both the length and depth of periods of benchmark under performance.

But volatility and drawdowns are still high. So as a final tweak to their approach, W&J apply a trend following overlay to the combined value and momentum portfolio. If a 12-month moving average of the S&P 500 index is greater than zero, they hold the combined portfolio. If the moving average is less than zero, they hold Treasury bills. Using this trend filter, the worst drawdown of the combined approach goes from -60.2% to -26.2%. But investors give up 1.5% in compound annual return, and there is an increase in tracking error.

My research shows that trend-following is more effective when applied to broad stock indices. The reason for this has to do with volatility. The standard deviation of W&J’s quantitative momentum and combined portfolios are 25.6% and 21.4%. The standard deviation of the S&P 500 index is 15.5%. Higher volatility means you give up more profit before you can exit or re-enter stocks when using a trend following filter.This is why combined stock portfolio investors give up 1.5% in annual return, while index momentum investors earn higher returns from adding a trend following filter.

W&J finish up by again mentioning relative performance risk. One cannot stress often enough the warning that myopic investors give up potentially superior results when they become nervous or impatient and abandon their strategies.
In an Appendix, W&J examine some possible enhancements to quantitative momentum. These include earnings momentum, proximity to 52-week highs, stop losses, and absolute strength. Although W&J use the terms interchangeably, you should not confuse absolute strength with absolute momentum. Otherwise, their analysis here is first rate.

Overall, I remain skeptical about momentum applied to individual stocks. Momentum used with stock indices is a simpler approach that shows the same potential high returns as "quantitative momentum.” [2] Momentum with indices has substantially lower transaction costs and no problems with scalability. It responds better to trend-following. It does not suffer from a diminished premium.

I still recommend Quantitative Momentum for the following reasons:
1)    Its emphasis on the importance of sustainable investors who can keep the big picture in mind and not be swayed by short-term performance
2)    Its good review of momentum principles and behavioral biases
3)    Its rigorous research in the book’s Appendix

 [1] Because of mean reversion, there is a small benefit to skipping the last month when using momentum with individual stocks. This is not the case when using momentum with indices or asset classes.

[2] My research and research by Geczy and Samov (2015) both show that momentum applied to stock indices outperforms momentum used with stocks even before transaction costs.

September 16, 2016

Factor Investing: Buyers Beware

A highlight of the 2016 Morningstar ETF Conference was the keynote address by the former leader of U.S. Navy Seal Team Six, Rob O’Neill. Chief O’Neill shared some stories about his training and operations as an elite Navy Seal. The take away lessons from his talk were the importance of preparation, discipline, and keeping the mission goal in mind.  Overriding all this is the importance of tenacity. A Navy Seal survives eight months of insanely intense training by advancing one hour at a time without ever giving up.

Another important speaker at the event, Jason Hsu, showed that many professional investors do poorly because they lack this tenacity. They are instead influenced like the public by short term cyclical performance swings.. 

Investors often select investment managers or approaches based on 3 to 5 years of past performance. But 3 to 5 years is mean reverting with both markets and managers. Fired managers on average do 250 bps better than the new ones taking their place.  Most investors, both professional and public, tend to be market timers whether they know it or not. And they are poor ones at that. 

What we should do, according to Hsu, is stick with our long term goals and ignore shorter term cyclical performance swings.  In other words, investors would do well to follow Chief O’Neill’s advice – prepare well, and stick to your plan with discipline and determination.

To proceed with confidence, we need to have a good understanding of the investment factors we are using. There has been abundant academic research on factors, beginning in the early 1990s with size and value. Factors in general have shown favorable results on paper.  But now that factor-based investing has been around for a while, it might be useful to look at how factors have done on a real-time basis.

Out-of-Sample Factor Performance

McLean and Pontiff (2015) looked at 97 factors from academic literature that predicted cross-sectional stock returns. They found that factor returns were 58% lower following their publication. Calluzo, Moneta, and Topaloglu (2016) looked at 14 well-documented anomalies from 1982 through 2014. They included value, momentum, profitability, and investment. These authors found a 32% decay in average factor returns post-publication.

Glushkov (2015) examined a comprehensive sample of 164 domestic equities smart beta (SB) ETFs from 2003 through 2014. The factors examined were size, value, momentum, quality, beta, and volatility. Glushkov concluded, “I found no conclusive empirical evidence to support the hypothesis that SB ETFs outperformed their risk-adjusted benchmarks over the studied period.” 

Yet factor based investing has been growing in popularity. The emphasis of the Morningstar ETF Conference was factor investing, and Conference sponsors were busy promoting factor-based ETF products.

The Conference set the tone for this with an early talk by Ronen Israel of AQR that featured the two most popular factors, value and momentum. Israel pointed out momentum’s tax efficiency and how it can help offset value traps in a diversified value and momentum portfolio.

Momentum Issues

One of the issues associated with stock momentum is price impact due to scalability limits. Momentum performs substantially better with focused portfolios of 100 or fewer stocks and with frequent rebalancing. Unlike value, momentum is a high turnover strategy. If you turn over 30% of a 100 stock momentum portfolio each quarter, it does not take many billions of dollars to have a substantial impact on price. Israel did not address this issue, but his firm, AQR Capital, is not ignorant of this fact. AQR has held an average of more than 400 stocks in its U.S. large cap momentum fund portfolio.

Momentum stocks are also volatile with wide bid-ask spreads. This volatility contributes to their higher transaction costs. Israel pointed out a study by Lesmond et al (2004) in which transaction costs completely offset the profits of momentum investing. Israel then pointed to a proprietary 15-year data set showing momentum portfolios earning decent profits at the cost of more tracking error. But a recent study by Fisher, Shah,and Titman (2015) using observed momentum stock bid-ask spreads found transaction costs to be higher than Israel’s figures and closer to Lesmond’s.

Momentum Performance

Let us take a look then at the performance of the two oldest rules-based momentum funds. They are the PowerShares DWA Momentum ETF (PDP) that began in March 2007 and the AQR U.S. Large Cap Momentum Style Fund (AMOMX) that started in July 2009. Both funds have underperformed their Morningstar designated benchmarks from their beginnings until now.

Annual Returns from Inception

PowerShares DWA Momentum 6.24
Russell 3000 Growth 8.11
Difference  -1.87

AQR Large Cap Momentum  14.24
Russell 1000 Growth 15.65
Difference  -1.41
Value Investing

Let us move on to value, which is the most popular investment factor. Of the 8000 or so U.S. mutual funds, more than 1000 are value funds. Value is the only factor that appears in every multi-factor ETF.

Israel showed that value is best determined using a combination of multiple valuation methods. All metrics performed about the same over the long run, but performance varies considerably over time. Of five different value metrics, earnings-to-price (E/P) was best overall, but it was the top metric in only 2 out of 6 decades.

The value premium has been insignificant among U.S. large cap stocks [1]. But Israel pointed out that value can still be useful when combined with momentum. According to Israel, value should make up one-third of a combined value and momentum portfolio, even if value has zero expected return. This is because value can reduce the volatility and tracking error of a momentum portfolio. But diversification this way can create considerable performance drag. In our Morningstar Conference breakout session on momentum, Wes Gray, Meb Faber, and I described how trend following could create a reduction in risk exposure without this kind of performance drag.

Value Performance

As we did with momentum, let us see now how value funds have performed real time. Using the CRSP database, Loughran and Houge (2006) looked at the performance of U.S. equity funds from 1962 through 2001. They used the prior 36 months to sort funds by style (top versus bottom quartile) and size (top versus bottom half). From 1965 through 2001, the average large cap growth fund returned 11.3% annually, while the average large cap value fund returned 11.41%. The outperformance of 0.11% for value over growth was insignificant.

For small caps, where value is said to have a greater advantage over growth, the authors’ results showed the opposite to be true. Small cap value funds earned 14.10%, while small cap growth funds returned 14.52%. Small cap value underperformed small cap growth by 0.42% per year. The authors say that bid-ask spreads, transaction costs, and the price impact of trading likely work against the capture of value premium in small-cap stocks. These are the same issues that concern us with respect to stock momentum. The authors conclude, “We propose that the value premium is simply beyond reach…investors should harbor no illusion that pursuit of a value style will generate superior long-run performance.” [2]
Source: Loghran and Houge (2006), “Do Investors Capture the Value Premium”

I was curious about the performance since 2001. Vanguard has had value and growth index funds since November 1992. According to the Vanguard website, the annual return from inception of the value index fund (VIVAX) has been 9.22%, while the annual return of the growth index fund has been 9.07%. However, because of the difference in fund volatility, an investor in the growth fund would have earned more than an investor in the value fund. Again, real world results contradict academic ones.

In addition, there is horrendous tracking error associated with value investing. From January 1929 through June 1932, small cap value underperformed the market for 42 consecutive months. More recently, small cap value underperformed for 26 consecutive months from July 1989 through April 1981 and for 21 consecutive months from May 2014 through February 2016. I can't imagine many investors who would be willing to endure this.

Real World Versus Academic World

Everyone likes the idea of value investing. We are used to finding bargains and buying what is cheap. But value stocks may look cheap for a reason. Serious tracking error and lower than expected real time returns are additional risk factors that make them less appealing. Perhaps Fama and French were on to something when they omitted momentum and made value redundant in their latest factor pricing model. 

The Capital Asset Pricing Model (CAPM), Mean-Variance Optimization (MVO), and Portfolio Insurance were all elegant academic concepts that looked great on paper, but never held up in the real world. Maybe factor-based stock investing will suffer the same fate. As Benoit Mandelbrot once said, "Many a grand theory has died under the onslaught of real data."
[1] See Asness et al.(2015).
[2] The median expense ratio for growth funds was 11 basis points higher than for value funds. Since growth funds also realized slightly higher average returns, expense ratios cannot explain the absence of a value premium across mutual fund styles.

August 29, 2016

Risk Tolerance Assessment

(An earlier version of this article first appeared on the Alpha Architect blog.)

When I attended the Harvard Business School my favorite class was Managerial Economics.  It focused on decision making under uncertainty [1].

The first thing to understand here is the concept of expected value. You determine this by multiplying each outcome by the probability of its occurrence, then adding them all together. For example, the expected value of a coin flip where you win $10 with heads and lose $5 with tails is (.5 * $10) + (.5 *-$5) = $2.50. We should be indifferent between playing this game and receiving $2.50 without doing the coin flip. In this case, $2.50 is both the expected value and the “certainty equivalent,” or what we would accept for certain instead of playing the game.

Three elements affect how we play the coin flipping game:
  1. Risk aversion
  2. Risk capacity
  3. Risk tolerance

Risk Aversion

Let’s say we raise the stakes and with the same one-time coin flip we could win $10,000 with heads and lose $5000 with tails. Our expected value is $2500, but the amount we would accept for certain may now be different than $2500. Those who are risk seeking might play the game for an amount equal or greater to its expected value of $2500. Those who are risk averse would accept less than $2500 instead of playing the game. Someone conservative, who does not like the idea of losing $5000 on a coin flip, might pay something to not have to play.


Risk Capacity

The amount of risk aversion we have depends on the size of the outcome relative to our financial condition. Because of risk aversion, we buy insurance having a negative expected value (and a positive one for the insurance company) in order to avoid the risk of catastrophic loss. On the other hand, risk seekers may buy low-cost lottery tickets with extremely negative expected values for the small chance of an enormous payoff. This can be especially appealing to those having little to lose and much to gain.

Risk Tolerance

Risk tolerance defined by the ISO 22222 Personal Financial Planning Standards is “the extent to which a consumer is willing to risk experiencing a less favorable financial outcome in pursuit of a more favorable financial outcome.” It is an assessment of our psychological ability to deal with uncertain outcomes. It is not symmetric due to loss aversion. Investors will often trade $1.5 to $2 in gains to avoid $1 in losses [2].

Risk tolerance is generally a stable personality trait. But it is subject to situational influences, such as our mood, and may change due to our life experiences, such as aging.

Knowing our risk tolerance is important because financial decisions are motivated by emotional as well as logical factors. Investors, for example, often chase performance. They may invest based on attractive past results, then bail during periods of underperformance.

The 2016 annual Dalbar report showed the average U.S. equity fund investor earning 4.7% over the past 20 years, while the S&P 500 index gained 8.9%. Poor timing decisions caused nearly half of this underperformance. A dramatic case of this effect involved CGM Focus (CGMFX), the highest return U.S. stock fund from 2000 through 2010. It’s average annual return was 18.2%, but the fund’s typical shareholder lost 10% during that same period!  Investors added heavily to this volatile fund near the top and bailed out as the fund neared its bottom.

When markets go up we may hop on board without considering the volatility that lies ahead. Risk tolerance assessment can help us avoid this behavior by showing us ahead of time our psychological ability to deal with uncertainty and risk. This can help us choose more suitable investments.

Recognizing that we are sometimes more emotional than rational, FINRA issued Regulatory Notice 12-25 in July 2012. It added risk tolerance to the list of factors that should be used to determine investment suitability. The other factors are age, financial condition, investment holdings, investment experience, time horizon, liquidity needs, tax status, and investment objective.

Current Practice

Yet many investment firms still use only traditional indicators of investor suitability that focus on the ability to absorb losses and on investment horizon. Fidelity, for example, asks new clients for the following information: investment purpose, time horizon, investment objective, annual earnings, net worth, liquid assets, investment experience, and liquidity needs.
Other firms try to integrate risk tolerance into their investor profile questionnaires. Vanguard, for example, added five risk tolerance questions to the other six questions in their client Investor Questionnaire [3]. Kudos to them for including a real world question of how you would (and did) react in 2008 when stocks lost 31% of their value. Our rational choices are not always the same as our emotional ones during times of actual market adversity.

I believe it is better to keep risk tolerance questions separate from questions like our time horizon, financial goals, and investment objectives. Risk tolerance and other investor profile questions should be evaluated separately to gain more insight into the differences between our financial goals and our behavioral biases. A robust risk tolerance questionnaire will tackle the behavioral elements of risk not covered by standard investor profile questions.
Risk Tolerance Questionnaire

A risk tolerance assessment can show us if our financial objectives are too conservative or too aggressive. Ignoring risk tolerance can cause us to abandon our financial plans during times of market stress. According to FinMetrica, 60% of the people who take FiMetrica's risk tolerance questionnaire (RTQ) find there is no strategy that will allow them to reach all their investment goals while adhering to their risk tolerances. In such cases, investors might want to use their risk tolerance profiles to revise their financial goals.
What to Do

How do we go about using RTQs? In the 1980s, I developed my own. I asked investors to choose between various financial outcomes. From this information, I constructed their risk profiles. I was surprised to see how much variation there was in risk tolerance. It was then I realized this information could be useful for portfolio planning purposes.

The science of psychometrics, which is the blending of psychology with statistics, has evolved since that time. You no longer have to do all the work yourself. There are several services, like FinMetrica and Riskalyze, that offer RTQs to financial planners. There is also a freely available online RTQ by Ibbotson Associates and Financial Planning Services Australia.

In addition, John Grable and Ruth Lytton, two financial planning professors, have an RTQ you can access online. Several research papers document the validity of their questionnaire:  Grabel and Lytton (1999) and Gilliam, Chatterjee, and Grabel (2010).
RTQ Issues

RTQs were criticized during the 2008 financial crisis for not anticipating how market turmoil could cause changes in risk tolerance. Critics argued that risk tolerance depends on market return and volatility. But Roszkowski and Davey (2010) present data collected pre- and post-crisis showing that the decline in risk tolerance was relatively small. What mostly changed was investors’ perception of risk.

The authors conclude that risk tolerance is a stable personality trait. Risk perception, however, changes because it is a cognitive appraisal of external conditions based on one's mental state. This is good news since risk perception can be modified through more information and better education.

We cannot however look at risk tolerance just once and then forget about it. Risk tolerance does not take into account life changing events and shifting investment goals. We should periodically reevaluate risk tolerance, which is easy to do using the above tools.

Example of How to Use RTQs

I have three proprietary dual momentum models. I encourage investment professionals who license my models to use RTQs with their dual momentum clients. This can help them decide which model(s) best suit their investors' risk preferences while meeting their investment goals.

Other advisors should consider doing the same. If you manage your own account, you can follow the Greek maxim "Know Thyself" by using the RTQs by Ibbotson Associates or Grabel and Lytton. They can help you see if your investment portfolio is suited to your own risk tolerance and if, based on this, you should consider making some portfolio changes. Your financial and psychological health may depend on it.

[2] See Tversky and Kahneman (1979).
[3] Another publicly accessible questionnaire that combines risk tolerance with other factors is in the Financial Planning Practitioner’s Guide  by the Canadian Institute of  Financial Planners.