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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Fundamental Indexing
exchange-traded fund

An article from MarketWatch dismisses the latest fundamentally-indexed exchange-traded funds (ETFs) announced by Charles Schwab Investment Management as “different” as opposed to “better” mousetraps.

The question for investors is whether they are the rodent, getting snapped up by the contraptions that financial inventors are creating.

Catchy metaphors aside, according to a note from Reuters

San Francisco-based Schwab, long a leader in selling mutual funds to investors, already has five mutual funds based on fundamental indexing. Those five funds, which launched in 2007, had $4.5 billion in total assets under management as of June 30.

From Schwab’s website

Fundamental indexes use fundamental measures of company scale and success—such as adjusted sales, retained operating cash flow, and dividends + buybacks—to construct the indexes. These fundamental factors address the inherent bias of traditional indexes, which are based on market capitalization and can give too much weight to overpriced securities and too little weight to underpriced securities.

Hence the tilt towards value investing (i.e. higher weights of underpriced securities) inherent in these funds. While some research shows that fundamental investing can add a statistically significant value, apparently this is limited to a few specific indices and regions.

As the article states

Just as studies have shown that value investing holds a slight edge over growth investing over the long haul, fundamental investing has shown an ability to outperform its traditional cap-weighted peers, although that history is not long once you throw out back-testing (results “proven” by looking backward and seeing how the strategy might have performed had it existed years ago).

Since Schwab’s fundamentally-indexed mutual funds have been in existence for over six years now, and that period spanned a significant market downturn, it is worthwhile to take a look at their historical risk-adjusted performance, as measured by the trailing five-year Sharpe Ratio (all data from Morningstar):

Schwab Fundamental Fund Ticker SR Best-Fit ETF Ticker SR
US Large Company Index SFLNX 0.60 iShares Russell 1000 Value IWD 0.47
US Small Company Index SFSNX 0.56 iShares Russell 2000 IWM 0.49
International Large Company Index SFNNX 0.19 iShares MSCI EAFE Value EFV 0.14
International Small Company Index SFILX 0.37 iShares MSCI EAFE Growth EFG 0.16
Emerging Markets Large Company Index SFENX 0.13 iShares MSCI Emerging Markets EEM 0.13

In all cases, the Sharpe Ratio of the fundamentally-indexed fund was greater than or equal to that of the ETF that follows the best-fit index for the fund. While past performance does not guarantee future results, the above data certainly support the introduction of ETFs based on the same (and one more, the U.S. Broad Market) fundamental indices. They may be better mousetraps after all.

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