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:

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 (R
_{F}) 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 – R_{F} |
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.