A few years ago when "fundamental indexing" was the topic de jure, I saw Rob Arnott, chairman and founder for fundamental indexing firm Research Affiliates, debate academic legend and Nobel Laureate Bill Sharpe.
During the debate, Sharpe had a great zinger: “I’ve never met a back-test that I didn’t like.” He went a step further when he said that he wanted to invest in a strategy with horrible back-testing results, thinking that they would likely do much better than the strategies with wonderful back-tests since the winning back-tests frequently don’t live up to their hype.
I thought I had found such a back-test when I looked at the Research Affiliates Fundamental (RAFI) U.S. Equity Long-Short (LS) index. On its website, Research Affiliates provides a Bloomberg ticker that I used to analyze the back-test data and the results that I found were not particularly good.
Beginning in 1980 and ending in 2010, the total return for the index was 3.82% and had a volatility of 13.95 (using annual data). The correlation was low at 0.05 to stocks and 0.16 to bonds, but with returns under three-month Treasury bills, the RAFI LS index didn’t seem particularly compelling.
Since this index is now being offered in an ETF through ProShares (NYSEARCA:RALS), I decided to look at the Morningstar commentary. I was surprised to read the analyst report by Sam Lee, which said that the annual returns since 1980 were "roughly 9%."
After double checking my numbers, I contacted Lee to see what I was missing. It turns out that he had originally written his report just like I did, based on the index data that Research Affiliates made available.
Shortly thereafter, Arnott contacted Lee to explain that the index didn’t include the yield that would have been earned on the cash collateral from the stock short sales. Arnott apparently told Lee that the yield from the collateral would have been around 5.6% over the time period, and if you include that cash collateral yield, the total return was 9.4%.
I found historical LIBOR data on Bloomberg going back to 1984. The average spread between Libor and Treasury bills was 40 basis points, so I took three-month Bill rates and added 40 bps to estimate LIBOR for 1980-1983.
Adding the RAFI LS index returns and the LIBOR data, I found that the returns were 9.62% with a standard deviation of 13.93%, for a Sharpe Ratio of 0.31, not quite as high as the Sharpe Ratio for the S&P 500 over the same time period, which was 0.34. Still, because the correlation between the two indexes was 0.10, the RAFI LS could provide an attractive complement to a stock portfolio.
It occurred to me that almost 60% of the return for the RAFI LS was due to the cash yield associated with selling stocks short. Interest rates have steadily declined since 1980, which started near 12% and steadily fell to the current rate of approximately 30 basis points.
On this basis, it appears appropriate to think of future expected returns closer to the "excess return" associated with the RAFI LS (3.82%) plus the current or expected cash rate.
Using long-term Ibbotson data, the risk-free-rate has historically been approximately 3.75% since 1926. If we use that as a starting point, add the 40 basis points for LIBOR and the 3.82% "‘excess return" of the RAFI LS index, we get a total expected return of approximately 8%.
It seems reasonable to expect that the standard deviation would stay around 14% and that the correlation would be low, but given the medium to high single digit return and the low double digit standard deviation, the Sharpe ratio would work out to be approximately 0.15.
Even though return expectations may be more muted and the Sharpe ratio a little less than the "gross" numbers would suggest, the RAFI LS may still be a useful addition to a portfolio.
First, using my expected return, standard deviation and correlation assumptions, the RAFI LS still expands the efficient frontier, albeit not as much as it may have in the past due to today’s lower interest rates.
Research Affiliates claims that the RAFI LS is “an absolute return strategy, meaning that its goal is to create a positive return regardless of market conditions.”
Even though I believe that the RAFI LS may be a viable strategy and a good complement to a diversified portfolio, I have a hard time accepting that the returns will be positive regardless of market conditions.
For starters, the index return plus LIBOR hasn’t even produced positive returns all of the time. There have been two three-year periods with negative annual returns: the three years ending in 1999 had a negative annual return of -4.30% and the three years ending in 2008 had a negative annual return of -3.91%.
During those periods, LIBOR earned 5.63% and 3.81%, respectively, which is a much larger cushion than the 0.30% that we have today. Given the interest rate current environment, if you are considering an investment in the ProShares product, it’s important to pay attention to the sources of past returns and consider how that may affect returns in the future.
Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.
Additional disclosure: The views expressed do not necessarily represent the views of Acropolis Investment Management, LLC. or its members.