Evaluating Lazy Portfolios
August 11, 2016
Analysis of First Eagle Global Fund
MarketWatch tracks eight lazy portfolios. Each of these simple portfolios consists of three to eleven, low-cost, no-load index mutual funds from Vanguard®. The fund membership and weights in each portfolio remain constant over time. (In theory, this implies that each portfolio would have to be perfectly rebalanced daily. This is not only impractical but also impossible because the fund’s daily NAVs, and hence their new weights, are not known until after the market close.)
Unfortunately, MarketWatch compares lazy portfolios solely on the basis of annualized returns in one-, three-, five- and ten-year periods. Volatility of returns as well as other performance measures are not taken into account. Luckily, Alpholio™ can help – not only does our Basic Portfolio service provide ample statistics, but it also allows for a selectable periodic rebalancing of portfolio positions to their original weights. For the purpose of this analysis, let’s assume a 15-year evaluation period from July 2001 through June 2016, as well as quarterly rebalancing of each portfolio.
Let’s start with the most complex Aronson Family Taxable Portfolio that consists of 11 funds. The following chart shows the cumulative return and related statistics for this lazy portfolio:
The fixed-income portion of the portfolio comprises inflation-protected securities (15%), long-term Treasury bonds (10%) and high-yield corporate bonds (5%). The portfolio’s holdings also include domestic (40%) and foreign (30%) equities.
The alpha and beta of the portfolio were measured against the broad-based U.S. stock market ETF, and not just a large-cap index, such as the S&P 500®. Because high-yield bonds generally have a substantial correlation to equities, it could be expected that the portfolio’s beta would be approximately between 1 – (0.15 + 0.10 + 0.05) = 0.7 and 1 – (0.15 + 0.10) = 0.75, which it was at 0.73.
The key measures of risk-adjusted performance are the Sharpe and Sortino ratios. Unlike the former, the latter penalizes portfolios with a large downside deviation.
Finally, the maximum drawdown measure is the maximum percentage loss of the portfolio value from a peak to a subsequent trough. Given the chosen evaluation period, this typically means a decline in each lazy portfolio’s value from October 2007 to March 2009.
The following chart shows rolling volatility (measured as a standard deviation of two years of monthly returns) and accompanying statistics for the portfolio:
As could be expected, volatility of the portfolio significantly increased during the financial crisis. In general, a good lazy portfolio should maximize returns, minimize volatility, and reduce the magnitude of volatility changes over time.
Similar charts and statistics can easily be generated for all lazy portfolios. They are not published in this post to limit its size. Instead, here is a summary table of statistics:
Buy & Hold
The Yale U’s Unconventional portfolio had the highest risk-adjusted returns, as measured by the above Sharpe and Sortino ratios. This was likely due to the relatively large positions in REITs and long-term government bonds, both of which benefited from falling interest rates. Please also note that at times, correlation between returns of the REIT and total stock market mutual funds was quite high (which reduced portfolio diversification), as illustrated by the following chart:
The Coffeehouse portfolio had similar characteristics. Compared to others, this portfolio also exhibited the smallest maximum drawdown.
The Fundadvice Ultimate Buy & Hold portfolio had the third best return-to-risk profile, as well as the second lowest maximum drawdown. While bond funds in this portfolio had short and intermediate maturities, its total fixed-income component was significant, as was the case with the previous two portfolios.
For completeness, here are the statistics for lazy portfolios over a ten-year period through June 2016:
Buy & Hold
Over this shorter evaluation period, the Coffeehouse portfolio had the best risk-adjusted returns, followed by the Yale U’s Unconventional portfolio, and Dr. Bernstein’s Smart Money portfolio that had a slightly higher Sortino ratio and a smaller maximum drawdown than the Aronson Family Taxable portfolio. This goes to show that the ranking of portfolios heavily depends on the analysis time frame.
We hope that this analysis will give investors additional insights into historical performance of lazy portfolios. Of course, there is no guarantee that this performance will be repeated in the future.
May 1, 2016
Substituting Liquid Alternative Funds
This weekend’s piece in Barron’s features the First Eagle Global Fund (SGENX; Class A shares). This $48 billion fund has a 5% maximum sales charge, 1.11% total expense ratio and 11% turnover. According to the article, the fund
…beats at least 93% of its world-allocation peers for every major trailing time period, according to Morningstar. The fund holds its own in bad times—the MSCI World Index is down 4.6% over the past 12 months, while the fund is up 0.6%. Though it’s trailing the index over the past five years—up 5.9% annually, versus the index’s 6.4%—it’s still beating 94% of its peers.
Not surprisingly, when a fund is unable to beat its index benchmark over a longer, more relevant period of time, the focus of the comparison has to shift to either a shorter period or to its peers. The reason for the latter is obvious: An average actively-managed fund underperforms its index benchmark by at least its expense ratio. Consequently, when a fund is compared to its peers in a given “category,” the threshold required for outperformance decreases.
The prospectus benchmark for First Eagle Global is the MSCI World Index. Unfortunately, the longest-lived ETF tracking this index, the iShares MSCI World ETF (URTH), has only been available since January 10, 2012. From February 2012 through March 2016, the fund returned less than the ETF in all rolling 36-month periods, with a median cumulative underperformance of 14.4%. Similarly, the fund returned a median cumulative 9.9% less than the ETF in approximately 93% of all rolling 24-month periods, and 3.3% in 92% of all 12-month periods. This is corroborated by annualized returns of the fund over the three- and five-year periods:
Over the years, the management team of the fund underwent quite a few changes. Therefore, long-term results are largely irrelevant to current investors. The present pair of managers has been with the fund since the end of February 2011, which will become the starting point of further analysis.
To adjust for the fund’s risk, let’s apply the simplest variant of Alpholio™’s patented methodology. This approach constructs a reference ETF portfolio with both fixed membership and weights that most closely tracks periodic returns of the analyzed fund. Here is the resulting cumulative RealAlpha™ for the First Eagle Global:
Over the evaluation period, the fund produced about 0.4% of annualized discounted cumulative RealAlpha™ (to learn about this and other performance measures, please visit our FAQ). As of January 2016, the fund lost all of its cumulative RealAlpha™ and recovered some of it in the following two months. The fund’s standard deviation, a measure of volatility of returns, was about 0.4% higher than that of its reference ETF portfolio.
The following chart shows constant ETF membership and weights in the reference portfolio for the fund over the same analysis period:
The fund had major equivalent positions in the Guggenheim CurrencyShares® Swiss Franc Trust (FXF), PowerShares DB G10 Currency Harvest Fund (DBV), SPDR® Morgan Stanley Technology ETF (MTK), Vanguard High Dividend Yield ETF (VYM), WisdomTree Europe Hedged Equity Fund (HEDJ), iShares iBoxx $ High Yield Corporate Bond ETF (HYG), iShares U.S. Telecommunications ETF (IYZ), iShares U.S. Aerospace & Defense ETF (ITA), iShares MSCI Japan ETF (EWJ), and Guggenheim CurrencyShares® Euro Trust (FXE). (Positions in DXJ and PVI are shown as zero due to rounding.)
While the First Eagle Global Fund sports an impressive long-term performance, over the past five years under current management it failed to beat its benchmark. When compared to a fixed reference ETF portfolio of similar volatility, the fund added a modest amount of value. Both results would have been much worse with the fund’s front load taken into account. Despite the low turnover stemming from a long average holding period of securities, the fund had significant historical distributions, incl. short-term capital gains. This made it less suitable for taxable accounts.
To learn more about the First Eagle Global and other mutual funds, please register on our website.
March 1, 2016
Increasing Correlations of Asset Classes
A recent cover story in Barron’s features liquid alternative funds from AQR. According to the article
The liquid-alt pitch is that individuals can access the same types of investments as university endowments and other big institutions, to diversify equity-heavy portfolios, typically with a 10% to 20% allocation to liquid alts… The advantage of the [AQR Managed Futures] strategy […] is that it is uncorrelated with other asset classes, and “has the most consistently strong performance in equity bear markets.” That is when diversification matters most, as was the case in the third quarter of last year and the early part of this year.
Ideally, returns of a liquid-alt fund should not only be uncorrelated with those of both stocks and bonds but also significantly positive over a long evaluation period. Let’s take a look at the performance of three AQR funds with a sufficiently long history.
The following chart shows rolling return correlation of the AQR Managed Futures Strategy Fund (AQMIX) with the Vanguard Total Stock Market ETF (VTI) and the Vanguard Total Bond Market ETF (BND):
Please note that AQMIX had the first full month of returns in February 2010. Consequently, the first rolling 36-month return became available at the end of January 2013. As could be expected, the fund had lower correlation to stocks than to fixed income, although both coefficients were quite low (generally, correlation below 0.6 provides diversification benefits).
Here is a similar chart with related statistics for the AQR Multi-Strategy Alternative Fund (ASAIX):
Compared to AQMIX, this strategy had a higher correlation to bonds.
Here is a similar chart with statistics for the AQR Diversified Arbitrage Fund (ADAIX):
In contrast to AQMIX and ASAIX, this strategy had a higher correlation to equities than bonds; however, both coefficients were still pretty low.
The problem with any of these strategies is the lack of accessibility for most individual investors:
AQR’s approach can be hard to understand. Because of this—and to deter hot money—the firm sells its liquid-alt funds almost entirely through financial advisors. Retail buyers can access the funds directly through fund supermarkets like Fidelity, but direct investments involve a minimum of $1 million. Investments through advisors and 401(k) plans have no minimum.
Is there a way to substitute these liquid-alt funds with readily available ETFs? Let’s explore this possibility using Alpholio™’s patent-based analysis service for mutual funds. One variant of this methodology constructs a reference portfolio of ETFs with fixed both membership and weights. Here is the resulting cumulative RealAlpha™ chart for the AQR Managed Futures Strategy Fund (to learn more about this and other performance measures, please visit our FAQ):
As the statistics section below the chart shows, since its inception the fund had a smaller return and a much higher volatility (measured by standard deviation) than those of the reference portfolio. The following chart illustrates the constant composition of the reference ETF portfolio in this analysis:
The major positions in the reference portfolio were the PowerShares DB US Dollar Index Bullish Fund (UUP; fixed weight of 38.1%), iShares 20+ Year Treasury Bond ETF (TLT; 22.9%), iShares MSCI Netherlands ETF (EWN; 9.3%), Guggenheim CurrencyShares® Swiss Franc Trust (FXF; 6.0%), Consumer Staples Select Sector SPDR® Fund (XLP; 5.5%), and Utilities Select Sector SPDR® Fund (XLU; 4.7%). The Other component in the chart collectively represents addition five ETFs with smaller fixed weights.
The return correlation of the reference ETF portfolio over the entire evaluation period was 0.16 with VTI and 0.58 with BND. Given that these figures for AQMIX were approximately -0.07 and 0.21, respectively, the reference portfolio was not as good a diversifier for stocks and bonds as the fund was. However, the reference portfolio only had long positions in non-leveraged ETFs. It also returned about 8% more than the fund on a cumulative basis and with a 59% lower volatility. Similar analyses can be conducted for ASAIX and ADAIX. In the end, it is up to the investor to weigh the pros and cons of using reference ETF portfolios as substitutes for these funds in the context of the overall portfolio.
We hope that our Investment Toolkit™ will provide useful services for investors who want to construct well-diversified portfolios. If you would like to use it, please register on our website.
February 24, 2016
Equal-Weighting S&P 500
A recent column from Bloomberg Gadfly discusses increasing correlations of asset classes. The correlation coefficient of periodic returns is a measure of the extent to which these returns move in the same direction. Contrary to a common misconception, a high correlation does not imply that the two assets or classes are identical. Ideally, to diversify a portfolio, long-term correlations among portfolio components should low.
This correlation shift has a major impact on portfolio construction following the Modern Portfolio Theory. The article uses ten-trailing-year correlations of various indices:
While a point-in-time analysis of ten-year correlations between indices is instructive, it is of little practical value to investors. Luckily, Alpholio™ has just introduced a new Multi-Correlation service, which provides an interactive analysis of rolling correlations.
In a typical analysis, monthly returns are used because they are less “noisy” than weekly or daily returns. A span of 36 months (three years) of returns is usually sufficient to approximate the long-term correlation and, at the same time, to nimbly react to rapid correlation changes. A rolling-period approach provides insights on how the correlation coefficient evolved over time. It can also facilitate calculation of useful statistics. Finally, instead of artificial indices that cannot be bought or sold, Alpholio™ uses ETFs.
To demonstrate the Multi-Correlation service in action, here is a chart of rolling correlations between each of several analyzed ETFs and one reference ETF:
In the above chart, the analyzed ETFs are the iShares Core S&P 500 ETF (IVV), iShares MSCI EAFE ETF (EFA), iShares MSCI Emerging Markets ETF (EEM), and iShares Cohen & Steers REIT ETF (ICF). The reference ETF is the iShares S&P GSCI Commodity-Indexed Trust (GSG).
Please note that the youngest of these ETFs (GSG) determines the common time frame of this analysis: the first full month of GSG returns was August 2006, so the first 36-month rolling return became available at the end of July 2009. The Multi-Correlation service determines the longest possible analysis interval automatically.
The following table contains statics of rolling correlations between each analyzed ETF and the reference ETF:
By default, the statistics are ordered in the ascending order of median value, but can be reordered in any ascending/descending order by clicking on the header of the respective column. In conjunction with the chart, these statistics show that each of the equity ETFs had a substantial (above 0.6) correlation to commodities, while the REIT ETF had the lowest correlation. The correlation of all four analyzed ETFs to the reference ETF declined from the second half of 2014 onward, with the REIT ETF showing the strongest decoupling. The Forecast statistic is the expected value of the rolling correlation one month forward, or in February 2016 in this example.
We hope that the Multi-Correlation service will become a useful tool for investors who want to construct well-diversified portfolios. If you would like to use this and other Alpholio™ services, please register on our website.
July 12, 2015
Growth vs. Value
The popular market-proxy S&P 500® index is market-cap weighted. This is one of the factors that helps reduce the turnover of ETFs tracking this index. For example, the iShares Core S&P 500 ETF (IVV) has a turnover rate of only 4%. The following chart, produced by the Alpholio™ App for Android, shows the characteristics of a portfolio composed solely of this ETF:
(Note that Alpholio™ uses a broader ETF as a representation of “the market”; hence, the beta of IVV is different from the conventional one and alpha from zero.)
However, market-cap weighting implies that the largest companies’ stocks have the highest impact on the index. While returns of mega-caps in the index tend to be less volatile, they are usually lower than those of their smaller-cap peers. To overcome this limitation, other ETFs weight equities in the index differently. For example, the Guggenheim S&P 500™ Equal Weight ETF (RSP) assigns each of the 500 stocks a 0.2% weight. This tilts RSP toward smaller-cap equities in the index and results in a 18% turnover. Over the same analysis period, RSP produced markedly higher returns than IVV but at the expense of an elevated volatility and a slightly lower Sharpe ratio:
In addition to overweighting of mega-caps, some economic sectors in the index dominate others, as shown in the latest edition of S&P Capital IQ The Outlook:
To counteract this, the ALPS Equal Sector Weight ETF (EQL) applies the same weight to nine sectors (with telecommunication services considered part of information technology). Here are the characteristics of a portfolio consisting solely of this ETF over the identical analysis period:
While the annualized return of EQL was lower than than of IVV or RSP, it was more than adequately offset by a decrease in volatility, which resulted in an improved Sharpe ratio and maximum drawdown.
What if the investor wanted to equal-weight all ten sectors instead of just nine, i.e. keep telecoms separate from IT? To do so, the investor could construct a portfolio of Vanguard sector ETFs, excluding the Vanguard REIT ETF (VNQ). That is because real estate stocks are currently part of the financials sector and not expected to become a separate asset class until mid-2016. Here is how such a portfolio, rebalanced quarterly (just like EQL), performed over the same analysis period:
The Vanguard sector portfolio had the second highest alpha and Sharpe ratio as well as the second lowest standard deviation (a measure of volatility of returns).
The above analysis period was dictated by the inception date of the EQL, the youngest of all the ETFs used. Arguably, this approximately six-year period may be considered too short and not representative of performance over a full economic cycle. However, it was interesting to see that while equal-weighting the index on a security level produced highest absolute returns, equal-weighting on a sector-level delivered the highest risk-adjusted returns.
To conduct your own analyses of various ETF portfolios, download the Alpholio™ app from
May 4, 2015
Analysis of Leuthold Core Investment Fund
In one of the previous posts, Alpholio™ made the case for increasing the mid-cap stock holdings in the portfolio. As promised, in this follow-on post, we will examine the performance of growth vs. value equities.
A recent article on this topic in The Wall Street Journal states that
Over the past year, the average U.S. large-cap growth fund has risen 18.2%, while the average U.S. large-cap value fund is up 10.4%… from 2003 through 2013, the average gap between the two styles of stock-picking for large-cap stocks was 0.75 percentage point… it’s a similar story among small-company stocks, where growth-stock funds […] are up 16% over the past year. Funds investing in small-cap value stocks […] are up 7.7%.
The trend of growth equities outperforming value equities is hardly a past-year phenomenon. Contrary to what might be expected, this trend is also not confined to the last seven years since the market’s trough during the financial crisis. The trend is best examined using specific ETFs as opposed to hypothetical and unspecified “average U.S. [mutual] funds.”
To start with, let’s use the Total Return service of the Alpholio™ App for Android to review the long-term performance of a couple of long-lived large-cap ETFs, the iShares S&P 500 Growth ETF (IVW) and iShares S&P 500 Value ETF (IVE), from their inception through March 2015, using monthly total returns:
In that period, the large-cap value ETF handily outperformed its growth counterpart, albeit with a slightly higher standard deviation (a measure of volatility of returns). However, this only paints a part of the picture: in 2000, growth stocks significantly underperformed, following the deflation of the dot-com bubble. If the start of the analysis period is advanced to the beginning of 2001, growth slightly outperformed value:
Through the market peak in October 2007, growth stocks did not advance as much as value ones did, but they suffered a much smaller drawdown (45.4% for growth vs. 56.7% for value, as calculated by the Portfolio service).
The growth outperformance becomes even more pronounced when the beginning of the analysis is moved to April 2005 for a 10-year evaluation period:
Large-cap growth stocks returned about 2% more than their value counterparts, and did so with much smaller volatility. As shown by the Rolling Returns service, in the same period growth outperformed value in about 90% of all rolling 36-month intervals, 67% of 24-month intervals, and 63% of 12-month intervals:
The median difference of rolling 12-month returns over the last 10 years was over 2.6% in favor of growth.
For mid-cap stocks, let’s use the iShares S&P Mid-Cap 400 Growth ETF (IJK) and iShares S&P Mid-Cap 400 Value ETF (IJJ). As with large-caps, the 10-year performance of growth mid-caps was better than that of their value peers:
Finally, a similar chart for the iShares S&P Small-Cap 600 Growth ETF (IJT) and iShares S&P Small-Cap 600 Value ETF (IJS) also demonstrates the growth superiority over value:
It is worth noting that the outperformance of growth stocks over value ones in this analysis period appears to directly contradict the value effect in the classic three-factor model. However, the latest research from Fama-French indicates that this factor is less important in the presence of the beta, size, profitability and investment factors.
To see all the Alpholio™ App for Android services in action, download the app from
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March 7, 2015
A Case for Mid-Cap Stocks
Today’s profile in Barron’s features the Leuthold Core Investment Fund (LCORX, retail shares; LCRIX, institutional shares). This $850 million no-load, stock and bond fund has a net expense ratio of 1.15% (retail shares) and a 81% turnover. According to the article, the fund’s
7.1% annualized return over the past five years trails the Standard & Poor’s 500 by about nine percentage points. Yet, the fund ranks in the top 2% of the Morningstar moderate-risk category over the past decade, and some of its strongest years have been in downturns.
It should be noted that current managers of the stock portion of the fund have been at the helm only since early 2011, while the manager of the bond part started in August 2013. In addition, in 2013 the Leuthold Asset Allocation fund was merged into Core Investment. Nevertheless, this post will assess a long-term performance of the fund.
The fund’s primary prospectus benchmark is the S&P 500® index. One of accessible implementations of this index is the SPDR® S&P 500® ETF (SPY). According to Alpholio™’s calculations, since 2005 the fund returned more than the ETF in only 37% of all rolling 12-month periods. The frequency of outperformance increased to 47% for rolling 24-month periods and 44% for rolling 36-month periods.
The fund’s secondary prospectus benchmark is the Lipper Flexible Portfolio. According to Lipper,
Funds are assigned to the flexible portfolio (FX) objective if they do not state a percentage that is expected to be invested in each particular asset class.
This is a result of the fund’s declared asset mix fluctuation: 30% – 70% equity exposure and 30% – 70% fixed income exposure. Given these wide ranges, it is hardly practical to use such a reference portfolio as a benchmark.
In one variant of Alpholio™’s patented methodology, the reference ETF portfolio has fixed membership but variable weights. This variant lends itself well to the analysis of the Leuthold Core Investment fund because it can easily track changes in the fund’s composition over time. Here is a chart of the cumulative RealAlpha™ for the fund based on this methodology:
Since late 2004, the fund generated about -0.95% of regular and 0.4% of lag annualized discounted cumulative RealAlpha™ (to learn more about RealAlpha™, please visit our FAQ). The regular RealAlpha™ curve is the ultimate benchmark for the fund, while the lag one represents the RealAlpha™ generated vs. a reference ETF portfolio with a one-month lag to the fund. The substantial disparity between the two curves after 2010 indicates rapid changes in the fund’s holdings as a result of a momentum investing style.
At about 12.1%, the fund’s standard deviation was about 1.1% higher than that of the reference ETF portfolio. The fund’s RealBeta™ was 0.67.
The following chart shows changes of ETF weights in the reference portfolio over the same analysis period:
The fund had top equivalent positions in the iShares 1-3 Year Treasury Bond ETF (SHY; average weight of 30.5%), iShares Morningstar Mid-Cap Growth ETF (JKH; 12.3%), Vanguard Materials ETF (VAW; 10.4%), PowerShares Dynamic Market Portfolio (PWC; 10.3%), Vanguard Consumer Staples ETF (VDC; 7.8%), and iShares MSCI Canada ETF (EWC; 6.2%). The Other component in the above chart collectively represents six additional ETFs with smaller average weights.
Over the past ten years, the Leuthold Core Investment Fund delivered unimpressive results on a truly risk-adjusted basis. In 2014, the fund had series of distributions that totaled almost 7% of its net asset value (NAV); this indicates that the fund may not be the best fit for taxable accounts. It remains to be seen if the relatively new management team will improve the fund’s results in the future.
To learn more about the Leuthold Core Investment and other mutual funds, please register on our website.
February 15, 2015
All Weather Portfolio
In a traditional portfolio, mid-cap and small-cap equities receive much smaller weights than large-caps. For example, the most recent moderate asset allocation model portfolio recommended by the S&P Capital IQ Investment Policy Committee (see in the November 24, 2014 edition of the S&P The Outlook), consists of the following allocations:
- 50% to U.S. equities
- 15% to foreign equities
- 25% to bonds
- 10% to cash
To achieve the model allocation, the committee recommends specific ETFs for the 50% U.S. equity part of the portfolio:
Therefore, the mid-cap and small-cap stocks collectively account for only 20% of domestic equities in the portfolio. Is such a low allocation justified by historical performance of these asset classes? Let’s take a look using the Portfolio Service of the Alpholio™ App for Android.
The longest analysis time frame is determined by the existence of IJR, whose first full monthly return was in June 2000 (SPY’s first monthly return was in February 1993, and MDY’s in June 1995). Here are the statistics of a portfolio solely composed of SPY in a period from that month through 2014:
Similarly, for MDY:
And for IJR:
The mid-cap (MDY) and small-cap (IJR) ETFs had annualized returns more than twice that of the large-cap ETF (SPY). The Sharpe ratios of MDY and IJR were also approximately twice that of SPY. While IJR outperformed MDY in terms of the annualized return, alpha and Sharpe ratio (just slightly), it also had the highest standard deviation (volatility), maximum drawdown and beta of all three ETFs. Therefore, the mid-cap ETF appears to be a decent compromise between risk and reward.
For the 10-year period through 2014, the statistics are as follows:
* In this analysis period, alpha and beta are measured against a broader market index, represented by the Vanguard Total Stock Market ETF (VTI).
In the evaluation period, MDY clearly outperformed its peers by generating the highest annualized return, alpha and Sharpe ratio, while having the lowest maximum drawdown.
Another service offered by the Alpholio™ App for Android is the Rolling Returns analysis. In the 10-year period through 2014, SPY returned more than VTI in about 9.4% of all rolling 36-month periods (a rolling period of 36 months aims to approximate the average holding time of the ETF in an investment portfolio):
However, in the same period, MDY outperformed VTI in about 75.3% and IJR in 70.6% of all rolling 36-month periods. Based on this simple measure (it does not take risk into account), MDY again demonstrated a superior performance.
While past performance is not a guarantee of future results, this analysis indicates that mid-cap equities may deserve a higher allocation even in a moderate-risk portfolio. A follow-on post will examine the characteristics of growth vs. value equities, also using services of the Alpholio™ App for Android. The app is available at:
November 18, 2014
Merger Arbitrage Funds as Portfolio Diversifiers
Today’s post on Yahoo Finance discusses an “all weather” portfolio recommended by one of the most famous hedge fund managers. The portfolio strives to achieve an equal distribution of risk across macro periods of inflation, deflation, high and low economic growth.
The portfolio consists of:
- 30% stocks
- 15% intermediate-term government bonds
- 40% long-term bonds
- 7.5% gold
- 7.5% commodities
The portfolio has a large fixed-income component relative to equities to get close to a risk parity (yet, it does not use bond derivatives). The portfolio should be rebalanced at least annually.
Let’s use the Portfolio Service of the Alpholio™ App for Android to analyze this all weather portfolio. To do so, let’s construct a portfolio of ETFs that represent the above asset classes:
These ETFs were selected to have the earliest possible inception dates and lowest sponsor fees (expense ratios). The time span of the analysis is limited by the inception date of DBC. An alternative commodity ETF, the iShares S&P GSCI Commodity-Indexed Trust (GSG), became available about five months after DBC, therefore the latter was chosen. Since about 8% of DBC tracks gold, the weight of IAU is lower than that of DBC by one percentage point (due to the limitation of setting widgets, the app only accepts whole percentage weights).
Here is the setup for the analysis (the Dates, Return Frequency and Rebalance Frequency sections can be expanded by tapping their respective headers):
Here are the analysis results for the above portfolio with monthly returns and quarterly rebalancing:
With semi-annual (i.e. every six months) rebalancing, the all weather portfolio performed slightly better in terms of the higher annualized return and Sharpe ratio as well as smaller maximum drawdown:
Annual rebalancing yielded no further improvement in the annualized return or Sharpe ratio, but reduced the maximum drawdown to 12.1% and lowered the beta to 0.20.
For reference, here are the results for a traditional balanced portfolio, comprised of 60% SPY and 40% of iShares Core U.S. Aggregate Bond ETF (AGG), with monthly returns and semi-annual rebalancing in the same analysis period:
Compared to the traditional balanced portfolio, the all weather portfolio had all the desirable characteristics: a higher annualized return and Sharpe ratio, coupled with a significantly lower beta and maximum drawdown. However, the above analysis covered a prolonged period of decreasing and historically low interest rates that drove the returns of intermediate- and long-term bonds, the dominant positions in the portfolio. In an environment of rising interest rates (generally expected to begin next year) and falling commodity prices (already taking place), a risk-parity oriented portfolio, even with no bond leverage, may suffer.
November 10, 2014
A recent article in The Wall Street Journal’s Investing in Funds & ETFs report discusses merger arbitrage mutual funds. According to the article, such funds
…may offer an attractive way to diversify away from the risks of stocks or bonds …[but] can’t replace bonds, because their returns aren’t certain and come mostly through any price appreciation, not yield. But held in tandem with bonds, they can offer a way to hedge against interest-rate risk and might cushion part of a portfolio against stock-market volatility
Let’s take a closer look at these statements with the help of a recently introduced Alpholio™ App for Android, and specifically its Portfolio, Correlation, Total Return and Efficient Frontier services. For the purposes of this analysis, the base portfolio consists of 60% SPDR® S&P 500® ETF (SPY) and 40% of the iShares Core U.S. Aggregate Bond ETF (AGG), i.e. a traditional balanced mix of stocks and bonds. Here is the baseline chart with statistics generated from total monthly returns of both ETFs and quarterly rebalancing of the portfolio:
The reason why the beta of this portfolio is not exactly 0.6 (i.e. equal to the 60% weight of the SPY) is threefold. Alpholio™ uses a broader definition of “the market” than just the S&P 500® index. Also, the correlation between the market and AGG is not zero. Finally, the portfolio is rebalanced quarterly, not monthly, which can lead to a temporary divergence of SPY/AGG weights from the original 60/40% level.
For reference, in the same time frame a portfolio consisting of just the SPY would have an annualized return of 8.52% with a standard deviation of 14.25%, Sharpe ratio of 0.55 and maximum drawdown of 50.8%. Adding AGG to such an equity-only portfolio decreases its return but reduces its volatility even more, thus improving the Sharpe ratio. The maximum drawdown is also significantly diminished.
The article quotes two merger arbitrage funds with substantial assets: The Merger Fund® (MERFX) and The Arbitrage Fund (ARBFX). To effectively diversify the balanced portfolio, should either fund replace a portion of stocks, a portion of bonds, or a combination of both? What should be the extent of such a replacement?
To answer the first question, let’s take a look at the correlation between SPY, AGG and either fund using the Correlation service of the Alpholio™ app. Here is a chart of the rolling 12-month correlation coefficient for monthly returns of SPY and MERFX:
The starting date of the chart stems from the earliest availability of AGG whose first full monthly return was in October 2003. The average correlation of 0.56 indicates that MERFX was a marginal diversifier for SPY (generally, a correlation of 0.6 or less is desirable). Here is a similar chart for AGG and MERFX:
The average correlation of just below zero indicates that MERFX was a much better diversifier for AGG than SPY. Similarly, the average correlation between SPY and ARBFX was about 0.42 and virtually zero between AGG and ARBFX. Therefore, to effectively diversify the base portfolio, it should generally be better to allocate more of SPY rather than AGG to MERFX or ARBFX. However, this would also suppress portfolio returns — as the following total return chart shows, MERFX and ARBFX had steadier but smaller cumulative returns than SPY:
To answer the second question: a portfolio with the highest Sharpe ratio (i.e. the tangency portfolio) would be mostly composed of AGG and MERFX. Here is an efficient frontier chart in which the current portfolio, depicted by a standalone marker inside the frontier, had 80% in AGG and 20% in MERFX but no SPY and was very close to the tangency portfolio:
Adding MERFX at the expense of SPY decreased the portfolio volatility and increased its Sharpe ratio, but resulted in lower returns. To illustrate this further, here is a chart and statistics for a portfolio that consisted of 45% SPY, 40% AGG and 15% MERFX, rebalanced quarterly:
Ultimately, it is up to the investor to trade off portfolio returns for risk — some may choose to optimize for the highest return per unit of risk, while others may strive for higher returns at the expense of a sub-optimal Sharpe ratio. The Alpholio™ app for Android provides a set of tools that facilitate the exploration of historical data and construction of desired portfolios, with the usual caveat that the past performance is not a guarantee of future results.