In the last post I introduced the concept of “real momentum” which is a trend following signal based on real returns. In the post I used both expected inflation and risk-free returns to net out from the S&P500 to create a real excess return. This was done to make the hurdle for buy positions higher than the standard method. Several comments from readers indicated that this is”double-counting” and obviously from an economic standpoint this is true: real returns should only subtract out the return of inflation (or expected inflation). Theory would dictate taking this approach versus a real excess return. Since this is a simplification, that is desirable since it better avoids claims of “data-snooping.” Furthermore, since this was a preliminary study, in the previous post I did a quick test using only 10 years of data with the ETFs available. Clearly this is not ideal for assessing whether the concept has merit or is robust. To obtain more data, I used mutual fund proxies for TIP and IEF I was able to extend results back to 1995 ( for TIP I used Loomis Sayles Inflation Protected Secutities Mutual Fund (LSGSX) and for IEF I used T Rowe Price US Treasury Intermediate Fund). Following the advice of readers I subtracted out the expected inflation rate only- which is the differential return between TIP and IEF (smoothed using an optional lookback- anywhere between 3-10 days yields similar results, I chose 5 for these tests)- from the daily returns of the S&P500 (SPY) and then take the average of those returns. If the return is positive then go long, if negative then go to cash. Without assuming a return on cash here are the results compared to a traditional absolute/time-series momentum strategy that uses a risk-free rate or proxy such as short-term treasurys (SHY). Note that rebalancing was done on a monthly basis.

The results seem to clearly favor Real Momentum- which is impressive considering we simplified the calculation and also extended the lookback for 10-years that are “out of sample.” On average, the Real Momentum signal produces nearly a 1% advantage in CAGR annualized and a near 15% improvement in the sharpe ratio. It seems on the surface that real equity risk premiums may be more important to large investors that can move markets. But as my colleague Corey Rittenhouse points out, if you aren’t going to invest in something that has a negative real rate of return then you need to have an alternative. I agree with this point, and one logical option is to hold TIP- or Inflation-Protected Treasurys when Real Momentum is negative. Using a 120-day Real Momentum with the strategy parameters above, a baseline strategy goes long SPY/S&P500 when Real Momentum is >0 and holds TIP when momentum is <0. Here is what this looks like:

For comparison, here is absolute momentum using SPY and SHY with the same 120-day parameter:

As you can see the Real Momentum strategy outperforms the Absolute Momentum strategy, with higher accuracy on winning trades and higher gains per trade along with higher return and a higher sharpe ratio with a similar maximum drawdown. Some readers may point out that this comparison may not be fair because TIP returns more than SHY as the cash asset. As the first table shows, the timing signal itself is superior so that is unlikely to be the driving factor. But just to prove that, here is the Absolute Momentum strategy using SHY as the asset to trigger the signal but holding TIP as the cash asset:

This is substantially worse than the Real Momentum strategy and worse than the Absolute Momentum strategy using SHY as the cash asset. While not shown, using TIP as the signal asset and the cash asset does the worst of all. So apparently there is something there with respect to looking at Real Momentum- or effectively the expected real return to the broad equity market/S&P500. This is not the final word on the strategy, and it would be helpful to run an even longer-term test (one can never have too much data as they say….). But after looking at the performance on other risk assets using this signal, I can’t reject the hypothesis that there isn’t something there at first pass. It is something that makes sense, and seems to be supported by data even after simplification and an out-of-sample test. It would be interesting to run a deeper analysis to see what is going on and whether this is merely a spurious result that is driven by some other factor. A basic Real Momentum strategy that holds the S&P500 when expected real returns are positive and holds Treasury Inflation Protected Securities when they are negative earns very good returns and risk-adjusted returns and beats buy and hold over a 20-year period by nearly 5% annualized. The strategy also happens to be relatively tax-efficient compared to more complex strategies which is a bonus.

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Did you do a little data snooping before you naughty boy?

nah–no dice, i didn’t actually have time to have Corey program things for proper testing the first time around so the initial post was a virgin mockup in excel with ETFs.

Thanks for your work.

If someone is going to leverage a strategy through futures, the Sharpe ratio computed as returns minus the risk-free rate is appropriate. For Individual investors not using leverage who care about the volatility of real returns, a Sharpe ratio computed using returns minus inflation could be more relevant. Have you computed a “real Sharpe ratio” for the strategies.

hi beliavsky, i can see your point regarding leverage. as for real sharpe ratios i think this would be a useful metric since 60/40 portfolios probably had positive nominal sharpe ratios in the 1970s but negative real sharpe ratios.

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david

Hi, Thanks for sharing your insightful and creative research. In the case of comparing the “signalling strength” of TIP and SHY, I think there are two things that need to be separated: future expected inflation and the sensitivity to changes in interest rate (duration). Any change in interest rate will be more exaggerated in the ETF whose underlying bonds have longer duration (in this case, TIP). Since bonds have been rallied throughout your testing period, it is not surprising that TIP is the winner in this case. As we’ve seen recently, this long bull market in bonds may be coming to a head (famous last words).

To see if inflation expectations baked into TIPs prices truly have signalling power, comparing two ETFs that have the same/similar duration (preferably issued by the same company), with one being inflation protected, and one not would be the way to go in my opinion. Keep up the great work!

hi Osamu, thanks for your comments. i agree and highlighted in the previous post that they must be matched by duration. fortunately the duration of IEF and TIP are quite close. a comparison of their interest rate betas yields similar results. ideally one can use the Fed’s interpolation of the real yield although that isn’t available in real-time so one would combined the two pieces of information.

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david

Hi David. Thanks for the post. When you explained that you used a 5-day period for the differential return between IEF and TIP, did you divide it by 5 before subtracting from the daily SPY return? Thanks.