June 18, 2015

Momentum Due Diligence

Sometimes I get asked how well momentum has done the past year or the past several years. If I am in a snarky mood that day, I’ll respond, “What will that tell you?” The truth of the matter is that, in most cases, short-term performance is indistinguishable from noise and cannot tell you anything meaningful.

Here are the questions that one should ask instead:

1)  Why does momentum investing make sense? What is the economic rationale behind it?
2)  Why should momentum investing continue to outperform in the future?
3)  What are the possible drawbacks to momentum investing? 
4)  How is momentum investing robust? How much out-of-sample validation is there?  

Let us examine the answers to these questions one at a time.

Does It Make Sense?

Until the 1990s, most academics did not accept momentum due to the efficient market hypothesis (EMH). EMH said that nothing could consistently beat buy-and-hold. In the 1990s, Lo and MacKinlay and others showed that stocks have positive autocorrelation (serial correlation).  This meant that stock returns are trending, which contradicts the EMH and opened the door for momentum researchers.

In 1993, Jegadeesh and Titman issued their seminal study demonstrating the effectiveness of relative strength price momentum with U.S. stocks. Almost immediately, researchers began searching for reasons that could explain why momentum worked so well. The most cogent explanations have been based on behavioral factors, such as anchoring, herding, and the disposition effect. These can cause stocks to underreact on a short-term basis and overreact longer term.  Chapter 4 of my book explores this in more detail. No one knows precisely which factors cause momentum to work so well, but there are plenty of viable explanations for it, and there is no longer any doubt that momentum does offer superior risk-adjusted returns.

Will It Continue?

I also point out in my book that behavioral factors, such as herding, are ingrained in our DNA. They are not easily changed, and they therefore create formidable limits to the arbitraging away of extraordinary momentum profits.

Furthermore, there are plenty of non-momentum investors out there, such as value seekers, fundamentalists, buy and holders, etc.  Both relative and absolute momentum are based on autocorrelation, which is trend following. Relative momentum looks at an asset's trend compared to other assets, while absolute momentum looks at an asset's trend compared to its own past. There has been so much prejudice against all forms of trend following that momentum may never attract the attention that it really deserves.

Possible Drawbacks

There are two commonly perceived drawbacks to momentum investing, and they both pertain to relative rather than absolute momentum. First are the so-called "momentum crashes" that occur on the short side of long/short momentum portfolios when stocks rebound sharply at bear market bottoms. In practice, however, very few investors actually use long/short momentum portfolios. Shorting can be problematic, and stocks have a natural upside bias over time.

The second potential problem is the increased left-tail risk (drawdown) associated with relative strength momentum. This can be easily overcome by using both absolute (time-series) and relative momentum together as dual momentum. Absolute momentum not only improves risk-adjusted return, but it can dramatically reduce left-tail risk.[1]  

Robustness

Robustness is a key factor in ascertaining the continued efficacy of momentum or any other investment approach. There are several ways to assess robustness. Here are some common ones:

1)  How simple and straightforward is the model?  Simpler means there is less chance of over fitting and mining the data, which may give spurious results.

Momentum is very simple. It has only one main parameter, the look back period.

2)  How well does the model hold up when its parameter values change?

Momentum works well over a broad range of look back periods ranging from 3 to 12 months.

3)  How well does the model hold up when it is applied to other markets?

Momentum is effective with and across many different asset classes, including U.S. stocks, non-U.S. stocks, industries, global sectors, country indices, bonds, commodities, currencies, and real estate.

4)  How stable are the model parameters over time?  How consistent are the results?

Cowles and Jones were the first to discover the effectiveness of momentum back in 1937. They used a 12-month look back period applied to U.S. stocks. This 12-month look back has held up remarkably well ever since. The following table from RBC Capital Markets shows that 12-month based momentum has consistently earned higher returns than buy-and-hold for every decade since 1930:


5)  How has the model performed on out-of-sample data? How far back does the new data go?

These are the most important factors, and we will devote the rest of this report to that topic.

Out-of-Sample Validation

The Cowles and Jones study showed momentum earning extraordinary profits with U.S. stocks from 1920 through 1935. The Jegadeesh and Titman study corroborated the research by Cowles and Jones and included a longer test period from 1962 through 1989.

Since Jegadeesh and Titman's paper in 1993, there have been dozens of additional studies validating momentum on new data and additional asset classes throughout the 1990s and 2000s. Several years ago, Ken French added momentum to his online data library allowing researchers to further validate U.S. stock momentum continuously back to the year 1927.

One study using the additional data was by Israel and Moskowitz (2012). The authors found that long-only momentum produced an annual information ratio almost three times larger than value or size. The momentum premium was positive and statistically significant in every 20-year period through 2011.[2]  Going back further in time, Chabot et al. (2009) showed that abnormal stock momentum profits held up well going back to 1866 in Victorian England. 

In 2013, the longest back test yet of relative strength momentum was by Geczy and Samonov in their paper “212 Years of Price Momentum - The World’s Longest Back test: 1801-2012”. The authors showed that U.S. stock momentum profits remained positive and statistically significant throughout the 212 years of their data. The equally weighted top third of stocks sorted on momentum outperformed the bottom third by 0.4% per month (t-stat 5.7).


In their most recent paper, “215 Years of Global Multi-Asset Momentum: 1800 – 2014 Equities, Sectors, Currencies, Bonds, Commodities, and Stocks”, Geczy and Samonov (2015) extended their earlier work to include a 215-year history of multi-asset momentum with six different asset classes. They found the momentum premium to be consistently significant in every asset class, across asset classes, and in combination with each other. They also found comparable results applying absolute (time-series) momentum to the same data.[3]  

What It Means

During the past 25 years, there is nothing in finance that has been so extensively researched and back tested as price momentum. If academics were going to discard the EMH, they wanted a mountain of evidence before doing so.

As practitioners, we are fortunate to have this much out-of-sample validation showing the consistency and effectiveness of momentum, not to mention all the other indications of robustness. The best due diligence one can do with respect to momentum investing is to read the above referenced research papers and some of the others freely available on the Social Science Research Network (SSRN).[4] You could also read the studies referenced in my book and examine all the pages of my website.

Rigorous and extensive research has clearly shown that momentum offers superior risk-adjusted returns. It is the strongest known anomaly, and is stronger than value, buy-and-hold, and everything else that has been extensively studied. If your core investment portfolio does not utilize momentum, then you are missing the boat.

[1] See my book on Dual Momentum Investing or my research paper on absolute momentum.
[2] For more details, see my post “Momentum…the Only Practical Anomaly?
[3] There are other studies going back 200 or more years validating absolute momentum.
[4] The word “momentum” appears in the titles of 667 SSRN papers.  

June 13, 2015

Momentum and Stop Losses

Stop losses are a form of trend following in which you switch from risky assets, such as stocks, to a risk-free or fixed income asset after there are pre-determined cumulative losses. The random walk hypothesis (RWH) was widely accepted in the 1960s and 1970s. It was synonymous with market efficiency. It effectively eliminated any academic interest in stop loss rules. Under RWH, with stock returns being independent, stop losses would decrease a strategy’s expected return.

There remains a cultural affinity to RWH despite strong contrary evidence now. This may explain why there is still considerable indifference to stop loss policies and trend following in general among institutional investors who were schooled in old academic ideas.

In their paper, “When Do Stop-Loss Rules Stop Losses?”, Kaminski and Lo (2013) show both mathematically and empirically that if stock returns have positive serial correlation (there is overwhelming evidence they do), then stops can add value. Over monthly intervals using daily stock futures data from 1993 through 2011, the authors found that volatility-based stop loss rules could increase monthly returns 1.5%, while substantially decreasing volatility. They found that slower moving stops worked best.

In “Taming Momentum Crashes: A Simple Stop-Loss Strategy”, Han, Zhou, and Zhu (2014) showed the effectiveness of a stop loss overlay applied to a momentum-based strategy. The authors examined the top decile of U.S. stocks from 1926 through 2011 based on relative strength momentum over the preceding 6 months (the authors showed similar results using 12-month momentum). They sold any stock if it's daily opening or closing price dropped 10% below the beginning price of the month. They followed the same procedure for short positions. Portfolios were rebalanced monthly.

This stop loss strategy raised the average monthly return from 1.01% to 1.73% (buy and hold was 0.62%) and reduced the monthly standard deviation from 6.07% to 4.67%.[1]  Momentum crash risk (from short positions) was completely eliminated. Results from using a 5% stop were even better.


The worst monthly return for buy and hold was -28.98%, while the worst monthly return for an equally weighted momentum strategy was -49.79%, showing the increased risk from applying relative momentum to individual stocks. A 10% stop loss overlay improved the worst monthly return to only -11.34%. For value weighted rather than equal weighted portfolios, the maximum monthly loss for momentum and 10% stop loss portfolios were -65.34% and -23.69%, respectively. Average returns and Sharpe ratios doubled by using stops.

This stop loss strategy also had a positive skewness of 1.86, versus a negative skewness of -1.18 for the original momentum strategy, indicating a dramatic reduction in left tail risk when using stops.

Both these papers show theoretically and empirically that risk control overlays, such as stop loss rules, can have dramatically positive effects on momentum-based strategies. This applies also to other trend following methods of risk control, such as moving average filters and absolute momentum, that can work as well or better than stops (the subject of a future post).

Stop losses and other trend following methods are a way to head off some of the usual pitfalls of human judgement, such as the disposition effect, loss aversion, ambiguity aversion, and flight-to-safety. There is no reason why they should not be used by all momentum investors.

[1] Stop losses increased trading activity by 40%, but increases in return of about 70% helped overcome these high transaction costs.

June 2, 2015

Dual Momentum for non-US Investors

       Gogi Grewal is an engineer and astute analyst who has been following my work for a number of years. He has an excellent grasp of dual momentum. Since Gogi lives in Canada, he decided to research the best way for non-US investors to utilize dual momentum. Gogi has generously offered to share his findings with us here. Take it away, Gogi....  

       INTRODUCTION

Momentum is a well-studied anomaly where markets with strong relative strength continue outperforming, while weak markets continue to underperform. Gary Antonacci has furthered this area of research considerably by introducing us to Dual Momentum. By combining trend-following absolute momentum and traditional relative momentum, investors can increase their expected return while reducing volatility and severe bear market drawdown.

In his book, Dual Momentum Investing: An Innovative Strategy for Higher Returns with Lower Risk, Gary has given us a simple yet robust strategy called Global Equities Momentum (GEM). I have been very interested in implementing GEM but as a Canadian, there are some additional questions that arise. The most obvious question is: How should GEM be implemented by foreign investors?

More specifically, I want to explore how the following decisions affect GEM performance:
  
1) GEM analysis done in US dollars versus the investor’s local currency   
2) Hedged versus unhedged ETFs for execution
3) Alternate stock indices to the S&P 500 and the MSCI ACWI ex-US
4) Trades performed on local stock exchanges versus the US exchange

This study is meant to further the research that Gary has presented and help non-US investors to implement GEM correctly.

       METHODOLOGY

Before we explore GEM in foreign currencies, I will first start off by independently replicating Gary’s results in US dollars. I use the same GEM indices, rules, and back test period (1974-2013) that Gary uses in his book.

After alignment with Gary’s results is established, GEM will be tested in the following four currencies: CADUSD, AUDUSD, GBPUSD and JPYUSD. Figure 1 below is a graph of normalized performance for these currency pairs.


Figure 1: Normalized Exchange Rate Data, 1971-2015 (Source: US Federal Reserve)

The first 3 rates have fallen between 20-40% since 1971, while JPYUSD has risen more than 3-fold over the same period. When an investor’s home currency falls significantly, the investor benefits by being in foreign currencies. The opposite is true when the home currency rises. Thus, by looking at the chosen currency pairs, we will cover both rising and falling currency environments that a foreign investor can encounter.

Cases Analyzed

For each of the four non-US currencies (CAD, AUD, GBP and JPY), we look at four test cases which are described in the following table:

 Table 1: Description of the Four Test Cases

Data Sources

Data sources were from Standard and Poor’s, MSCI, Bloomberg, and the US Federal Reserve. All data represents total returns with dividends and coupons included.

Our back test period is 1971-2014. The start date was restricted by forex data. The Barclay’s US Aggregate Bond Index only has data going back to 1976. I approximated this index between the years 1971-1975 using 5-year US Treasury Bonds.

       RESULTS: Part I

Before doing any sort of currency analysis, my first step was to replicate the results Gary presented in his book and on this blog.  Below are my results.


         GEM
    S&P 500
      ACWI   ex US
    US AGG
Compound Annual Return
16.8%
11.0%
10.2%
7.8%
Average Annual Return
17.7%
12.6%
12.5%
8.0%
% Positive Years
95%
80%
75%
92%
Worst Year
-16.8%
-37.0%
-45.2%
-2.9%
Std Dev of Annual Return
13.1%
15.6%
17.4%
5.5%
Sharpe Ratio
0.97
0.48
0.43
0.55
Table 2: GEM in US$ compared to S&P500, ACWI ex-US, and Aggregate Bonds (1974-2013)
                           
These results are the same as those reported by Gary in his recent blog post in which his average annual return is 17.7% and monthly standard deviation is 12.4%. From these results and Gary’s findings, we see that Dual Momentum provides a significant increase in annual returns while reducing volatility.

        RESULTS: Part II

In this section, we look at GEM from the perspective of a foreign investor (Canadian, Australian, British and Japanese). Results are presented for the 4 cases we described in section 2.

CASE 1: Base Case

      Foreign investors trade on the US stock exchange when GEM is in equities and on their local stock exchange when GEM is in bonds. When in bonds, investors hold a currency-hedged version of the US Aggregate Bond Index. 

      Foreign investors do the GEM analysis in USDs, while the transactions are done in their local currency. We use the S&P 500, MSCI ACWI ex-US, and Barclay’s US Aggregate Bond Index.

Below are the results:


GEM (USD)
GEM (CAD)
GEM (AUD)
GEM (GBP)
GEM (JPY)
GEM (Local)
Compound Annual Return
17.4%
18.1%
21.9%
18.3%
15.2%
15.7%
Average Annual Return
18.3%
19.0%
24.3%
19.5%
16.4%
16.5%
% Positive Years
93%
91%
88%
86%
81%
88%
Worst Year
-8.2%
-5.7%
-15.7%
-6.8%
-12.9%
-16.0%
Std Dev of Annual Return
13.3%
12.2%
17.0%
14.3%
15.2%
12.4%
Sharpe Ratio
1.00
1.14
1.14
1.01
0.75
0.93
Table 3: Performance of GEM in Various Currencies, Base Case

NOTE: “GEM (Local)” is when foreign investors trade permanently on their local stock exchange using currency-hedged ETFs for both equity and bond trades. The results for this fully currency-hedged version of GEM will be the same for all foreign investors, regardless of their country.

The model made a total of 49 trades over the 43-year back test (1.1 trades/year). The model was in US stocks, non-US stocks, and bonds for 40.5%, 39.5% and 20.0% of the time, respectively.

Here are the 3 main observations:

1.      All GEM versions (USD, CAD, AUD, GBP, JPY, Local) considerably outperformed the stock & bond indices in terms of annual return and Sharpe ratio. Even GEM in yen outperformed with a 16% average annual return despite the JPY:USD rate tripling over the back test period. This shows that every world investor is much better off using GEM rather than a traditional fixed-allocation portfolio.

2.      GEM in CAD, AUD and GBP all outperformed GEM (USD) in terms of annual return and Sharpe ratio. This was expected since these 3 currencies fell against the USD over the back test period.  GEM (JPY) underperformed GEM (USD). This was expected since the JPY:USD rate more than tripled over the back test period. Would currency-hedging stocks help?

3.      GEM (Local) barely outperformed GEM (JPY) but significantly underperformed GEM in all other currencies. This shows that hedging currency on equities should not be done. Doing so would mean you will significantly underperform when your home currency falls and barely outperform when your home currency rises.

Let’s elaborate further on observation #3. Why does currency hedging underperform so much? Below is a 20-year chart comparing the performance of the US Dollar Index to the performance of the ratio between US and non-US stocks. Notice the strong correlation.

 Figure 2: Performance of US Dollar Index vs S&P500:MSCI World ex-US Ratio, 1995-2015

NOTE: Both blue and red lines are displayed in percent gain (since 1995) and smoothed with a simple 10-week moving average. Both the S&P500 and the MSCI World Index ex-US indices are priced in USD.

This chart shows that the US Dollar Index plays a big part in the relative performance between US and non-US stocks. By using currency hedged ETFs, investors (both US and non-US) are losing out on this relative performance. In the case of a US investor that hedges non-US stocks, she does not gain much benefit from having non-US stocks in the model. In fact, when the model is run with only the S&P 500 and bonds, both the average and compounded annual returns drop to 14% - which is in line with the results of the GEM currency-hedged model. For further reading, GMO’s Catherine LeGraw recently wrote an excellent article: The Case for Not Currency Hedging Foreign Equity Investments

CASE 2: Both Analysis AND Transactions in Local Currency

The next step is to see what happens when investors do the GEM analysis in their local currency in addition to transactions, with all else being equal to the base case. Below are the results.


GEM (USD)
GEM (CAD)
GEM (AUD)
GEM (GBP)
GEM (JPY)
GEM (Local)
Compound Annual Return
17.4%
17.6%
18.1%
15.6%
13.1%
15.1%
Average Annual Return
18.3%
18.6%
19.5%
16.8%
14.5%
15.9%
% Positive Years
93%
93%
91%
81%
77%
91%
Worst Year
-8.2%
-11.5%
-8.5%
-11.4%
-15.4%
-7.7%
Std Dev of Annual Return
13.3%
12.3%
13.5%
13.9%
14.6%
12.1%
Sharpe Ratio
1.00
1.10
1.08
0.85
0.65
0.90
Table 4: Performance of GEM in Various Currencies, Case 2

We see that by doing the GEM analysis with prices in the investor’s local-currency, performance drops compared to the base case. The annual return drops by average of 240 basis points for the CAD, AUD, GBP and JPY versions. However, the standard deviation drops as well by an average of 110 basis points. Overall, the Sharpe Ratio drops by an average of 10.6%.

Thus, foreign investors are better off doing the GEM analysis with prices in USD.

Again, currency hedging the stock indices provides little benefit. We will not be studying it any further.

CASE 3: Using Alternative Stock Indices

In this case, we look at the results for when foreign investors have their portfolio permanently on their own local stock exchange. When GEM is in stocks, investors would use unhedged ETFs. When GEM is in bonds, investors would use either their local country’s aggregate bond index or a currency-hedged version of the US Aggregate Bond Index.

Because foreign investors will likely not have access to an ETF tracking the ACWI ex-US index on their local stock exchange, we will instead use the MSCI US and MSCI EAFE equity indices. This change in indices is really the only consequential difference between this case and the base case.


GEM (USD)
GEM (CAD)
GEM (AUD)
GEM (GBP)
GEM (JPY)
Compound Annual Return
15.3%
16.1%
19.8%
16.5%
13.3%
Average Annual Return
16.3%
17.2%
22.3%
17.8%
14.4%
% Positive Years
91%
88%
81%
81%
77%
Worst Year
-17.9%
-12.7%
-16.0%
-10.6%
-16.6%
Std Dev of Annual Return
13.3%
12.4%
17.8%
14.4%
14.9%
Sharpe Ratio
0.85
0.98
0.98
0.89
0.63
Table 5: Performance of GEM in Various Currencies, Case 3

The model made a total of 63 trades over the 43-year back test (1.5 trades/year). The model was in US stocks, non-US stocks, and bonds for 40.3%, 39.5% and 20.2% of the time, respectively.

We see that by replacing the S&P500 and ACWI ex-US indices with MSCI US and EAFE, performance drops compared to the base case. The annual return drops by average of 190 basis points for the CAD, AUD, GBP and JPY versions. The standard deviation rises, although only by 20 basis points. Overall, the Sharpe ratio drops by an average of 16%.

Perhaps this drop in performance is because the ACWI ex-US index contains Canada and emerging markets in addition to all the countries in the EAFE index.  It is recommended that foreign investors have their portfolio on the US exchange when GEM is in stocks (as in the base case). If foreign investors are restricted to invest on their local exchange, then they should try and find as close of an equivalent to the MSCI ACWI ex-US index as possible. While a direct equivalent is unlikely, there may be an ETF for the World ex-North America index. If not, only then should investors use MSCI EAFE.

CASE 4: Non-Currency Hedging the Aggregate Bond Index 

In this case, we look at the results when foreign investors have their portfolio permanently on the US stock exchange. We assume foreign investors will not have an ETF on the US exchange that tracks their home country/continent’s aggregate bond index[1].  Therefore, when GEM is in bonds, foreign investors will be in the Barclay’s US Aggregate Bond Index and therefore exposed to the US dollar. Everything else is the same as the base case.


GEM (USD)
GEM (CAD)
GEM (AUD)
GEM (GBP)
GEM (JPY)
Compound Annual Return
17.4%
17.8%
22.2%
18.8%
14.8%
Average Annual Return
18.3%
18.8%
24.8%
20.2%
16.3%
% Positive Years
93%
91%
86%
81%
79%
Worst Year
-8.2%
-6.2%
-14.6%
-10.1%
-23.7%
Std Dev of Annual Return
13.3%
12.6%
17.9%
14.8%
15.8%
Sharpe Ratio
1.00
1.09
1.10
1.03
0.71
Table 6: Performance of GEM in Various Currencies, Case 4
                         NOTE: The trades made in this case are identical to the base case.

We see that by not currency-hedging bonds, performance has a negligible change. Compared to the base case, the annual return increases by an average 20 basis points for the CAD, AUD, GBP and JPY versions. The standard deviation rises, although only by 60 basis points. Overall, the Sharpe ratio drops by an average of a mere 2.6%.

It is expected that results would drop, since when you are in bonds, GEM has no mechanism to control your currency risk like it does when you are in stocks. It is also expected that the performance drop would be minor, since GEM was only in bonds 20% of the time over the past 43 years. The interesting conclusion is that GEM (JPY) was hardly affected despite the JPY:USD rate tripling over the back test period.

Because whether you currency-hedge bonds or not makes little difference to performance, foreign investors are advised to permanently leave their portfolio on the US exchange, the same as US investors. This saves the hassle and cost of switching between US and local exchanges every time GEM switches between stocks and bonds.

         CONCLUSION

We performed a 43-year back-test of GEM from the perspective of various foreign investors (Canadian, Australian, British, and Japanese). During the back test period, Japanese investors saw their local currency appreciate considerably (over 300%) against the USD, while the other 3 investors saw their local currency fall (between 20-40%) against the USD.

In both rising and falling currency environments, we have shown that all world investors can still use Dual Momentum to considerably outperform traditional fixed-allocation portfolios.

We see that the ideal way for foreign investors to implement GEM is to permanently have their portfolio on the US exchange. Foreign investors would be exposed to currency risk when the model is in bonds, but this hardly affected GEM performance over the past 43 years. This would give the results in case 4.

The second best way to implement GEM would be for foreign investors to trade on the US stock exchange when GEM is in equities and on their local exchange when GEM is in bonds. In the latter case, investors should either use their local country’s aggregate bond index or a currency-hedged version of the US Aggregate Bond Index, if available. This reduces currency risk when the foreign investors are in bonds, but there would be the on-going cost and hassle of switching between local and US exchanges. This would give the results in case 1 (base case).

We realize it is not possible for all foreign investors to trade on the US exchange. The third best way to implement GEM is for investors to have their portfolio permanently on their own local exchange. However, since an ETF tracking the ACWI ex-US index will likely be unavailable, investors would have to use an ETF tracking the MSCI EAFE index. EAFE is not as good as ACWI ex-US, but at least the investor does not have to worry about currency conversions and currency risk. This would give the investor the results in case 3.

It should be noted that investors wanting to have their portfolio permanently on their own local stock exchange should not use currency-hedged equity ETFs. Doing so would greatly diminish the relative performance between US and non-US equities. Foreign investors significantly outperform a fully-hedged GEM model when their local currency falls relative to USD. And when their local currency appreciates significantly, the fully-hedged GEM model does not perform that much better.

No matter which of the above 3 execution methods are used, foreign investors are best advised to do the GEM analysis in USD. This was shown in case 2. Best wishes to all of you with GEM.



[1] Looking at this comprehensive ETF Industry Guide published annually by State Street Global Advisors, we see that there are ETFs tracking some foreign countries’ bond indices, but not all. For example, Canada’s Aggregate Bond Index is not available on the US exchange.