Sharpe Ratio of Smart Beta
exchange-traded fund

A post in Barron’s and an article in GlobeAdvisor cover a report by strategists at Pavilion Global Markets on historical performance of “smart beta” strategies.

The report analyzed a number of monthly-rebalanced portfolios consisting of equities in the S&P 500® index since 1991. The conclusion stated in the post was that

All the methods beat the no-frills S&P 500. But the group found that only one strategy — screening for stocks exhibiting low volatility over three months — beat the index with reduced risk.

In particular, the article says that

One strategy draws from the same index, but weights stocks equally rather than by market capitalization. Since 1991, this approach turned a $100 investment into $892, or about 70 per cent more than the benchmark index. The divergence between the two approaches picked up noticeably after 2001.

An index that weighted stocks based on sales outperformed the benchmark by 53 per cent, an index that weighted stocks based on earnings outperformed by 77 per cent and an index that weighted stocks based on return-on-equity outperformed by 114 per cent – an astounding difference when you consider that it still draws from the same 500 stocks as the benchmark index.

This is further illustrated in the following chart:

Annualized Return and Risk of 'Smart Beta' Strategies

Since “smart beta” strategies exhibit both higher returns and elevated volatility compared to the index, naturally a question arises: What is the incremental return per unit of risk of these strategies compared to that of the index? This is where the ex-post Sharpe ratio (SR) comes in.

To estimate the SR for each strategy and the index, we can

  • Read the annualized return and volatility figures from the chart. While the annualized (geometric average) return is different from the arithmetic average required in the SR calculation, it should suffice as a rough equivalent.
  • Obtain an average risk-free rate (RF) in the analysis period. As a proxy for the risk-free rate, many SR calculations use a three-month Treasury bill rate; because each strategy was rebalanced monthly, we could also use a four-week bill rate.
  • Assume that the volatility of Treasury bill returns is negligibly small compared to that of the strategy. Further assume that the correlation of these returns to strategy returns is close to zero. This means that the denominator in the SR effectively becomes the risk of the strategy.

The rate on three-month Treasury bills since 1991 can be obtained from the FRED® service of the Federal Reserve Bank of St. Louis. (Data on four-week Treasury bill rates are only available from July 2001.) It turns out that the average annualized rate in that period was about 3%.

The following table shows the estimated SRs:

Strategy Return Return – RF Risk Sharpe Ratio
ROE Weighted 0.112 0.082 0.157 0.52
Low-Vol Weighted 0.098 0.068 0.144 0.47
Earnings Weighted 0.103 0.073 0.163 0.45
Equal Weighted 0.101 0.071 0.165 0.43
P/E Weighted 0.101 0.071 0.166 0.43
Profit Margins Weighted 0.100 0.070 0.164 0.43
Sales Weighted 0.096 0.066 0.155 0.43
High-Vol Weighted 0.099 0.069 0.197 0.35
Market-Cap Weighted 0.075 0.035 0.146 0.31

All of the fundamental indexing strategies exhibited a higher SR than that of the traditional market-cap index. In addition, the return-on-equity strategy beat the low-volatility strategy on a risk-adjusted basis. No wonder that, according to the article, fundamental indexing is gaining momentum:

Whatever you prefer to call them, there are now 326 U.S. ETFs that fit the description in one way or another, according to IndexUniverse, and this number doesn’t include leveraged and inverse strategies. These funds account for 40 per cent of all U.S.-listed ETFs and about 14 per cent of ETF assets. This year alone, nearly $46-billion (U.S.) has flowed in.

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Alternatives vs. Bonds
alternatives, correlation

In light of a recent downturn in bonds caused by a perception of the Fed’s upcoming actions, a Barron’s blog post and a Morningstar article explore alternative investments with “bond-like” returns. However, it turns out that these alternatives behave mostly like stocks with poor return-to-risk characteristics, and thus do not provide diversification to a broader portfolio.

To illustrate, here are correlations to stocks and Sharpe Ratios derived from Morningstar’s statistics for mutual funds and ETFs mentioned in the post and article:

Fund Ticker Category Beta StDev Correlation Sharpe Ratio
S&P 500® SPX Stock Index 1.00 13.56 1.00 1.32
IQ Merger Arbitrage ETF MNA Market Neutral 0.26 5.08 0.69 0.37
Merger MERFX Market Neutral 0.12 2.63 0.62 1.07
Robeco Boston Partners L/S Rsrch BPRRX Long/Short N/A N/A N/A N/A
IQ Alpha Hedge Strategy IQHOX Multialternative 0.31 6.54 0.64 0.36

These three-year statistics indicate a high positive correlation to stocks coupled with sub-par risk-adjusted returns. This observation is corroborated by a new study from the Leuthold Group cited in The Wall Street Journal article that states:

“From 1994 through May, it found that hedge-fund correlations have slowly been inching up to 0.75, almost 36% higher than earlier levels. Since a measure of 1.00 represents lock-step movements, hedge fund returns are generally following the tendencies of stocks about three-quarters of the time… Funds with correlations to stocks of 0.6 or less are prized by investors since they can significantly reduce portfolio volatility and limit risks over full-market cycles.”

In the past month or so, these alternative funds held their value well relative to bond investments. This is supported by their negative or low positive three-year correlations to iShares Core Total U.S. Bond Market ETF (AGG), as estimated by Alpholio™:

Fund Ticker Correlation
IQ Merger Arbitrage ETF MNA -0.30
Merger MERFX -0.24
IQ Alpha Hedge Strategy IQHOX 0.27

For reference, the correlation of SPDR® S&P 500® ETF (SPY) to AGG over the same period is -0.33. Therefore, these alternatives do not provide a significant amount of diversification to a balanced equity-and-bond portfolio, but could be marginally helpful if the portfolio contains only bonds. However, even in the latter case they could be a drag on the risk-adjusted performance of the portfolio: at 1.31, the Sharpe Ratio of SPY is higher than that of any of the above funds.

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Boring Is Better
exchange-traded fund

A recent post from Barron’s attempts to compare the performance of PowerShares S&P 500® Low Volatility Portfolio (ticker SPLV) to that of PowerShares S&P 500® High Beta Portfolio (SPHB). In doing so, the post uses charts of price returns of these exchange-traded funds (ETFs).

First, given that both ETFs had dividend distributions and at disparate levels (12-month yield of 2.76% for SPLV and 0.75% for SPHB, according to Morningstar), a comparison of total instead of price returns would be more appropriate.

Second, the comparison does not take into account the volatility of either ETF. The simplest approach to do that would be to use a Sharpe Ratio (SR) for both funds. Unfortunately, since these funds have been in existence for only a little more than two years, the SR and standard deviation (SD) figures are not yet available (typically, they are only calculated for funds older than three years). So, here are the results derived from the available monthly return data since May 2011:

SR vs. TB 0.44 0.07 0.27
SR vs. SPY 0.02 -0.13 0.00
SD 8.73% 25.94% 13.28%

Traditionally, SR is calculated using a risk-free rate; in the above table, TB stands for the 4-week Treasury Bill, the interest rate of which is appropriate because monthly returns of ETFs are used. However, an ex-post SR can also be calculated using an arbitrary benchmark; in this case, returns of the SPDR® S&P 500® ETF (SPY) were used.

The above results clearly demonstrate that over the most recent two-year period, SPLV exhibited a return/risk performance superior to that of either SPHB or SPY. However, only time will tell if this outperformance persists in the future.

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Sharpe Ratios of Low-Volatility ETFs
analysis, exchange-traded fund

A recent article on Barron’s compared the returns of two low-volatility ETFs, SPLV and USMV, to that of the S&P 500® index. However, returns (even if total, not just price returns) do not tell the whole story. After all, the main feature of these two ETFs is low volatility.

One of alternative ways of assessing relative performance is the Sharpe Ratio. Since the two ETFs in question have less than three years of history, popular online services do not yet provide this measure. So, we did the calculations based on the common historical period from November 1, 2011 to March 1, 2013 for both funds, and used SPY as an implementation of the S&P 500® index. The results are:

Sharpe Ratio 2.13 2.82 2.93

Although SPY beat both ETFs in terms of the total return, each of them had a higher Sharpe Ratio. While the analysis period was relatively short (16 months), this bodes well for the future.

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