Hydromod wrote: ↑Tue Jul 02, 2019 11:05 pm

Funny my name should come up now. I was about to update but I haven't figured out how to post images.

I have couple of items for people to consider. I've checked out some strategy options using backtesting on fixed-duration periods (e.g., 5 years, 10 years, etc.) with the UPROSIM and TMFSIM dataset, augmented with the daily returns for UPRO and TMF for the last few months. I've been running the strategy options for every possible start day to minimize sampling bias. For example, for a 5-year test, I run for 250 trading days times 5 years, starting on day 1, day 2, ..., as far as I can fit in.

I've been checking rebalance frequency, with cases of 1 (daily), 2, 5 (weekly), 10 (biweekly), 20 ("monthly"), 40 ("bimonthly"), 60 ("quarterly"), 120 ("semiannual"), and 250 ("annual").

As a comparison strategy, I calculate nominal CAGR for each test.

There is a clear trend, with daily rebalancing on average the best frequency, dropping to about biweekly, and relatively little difference from biweekly to quarterly. The daily rebalance tends to yield an extra 1 to 2 percentage points for CAGR relative to biweekly (e.g., 18 rather than 16 or 17).

This strategy reveals that there are some quarterly cycles up to around 1996 that pop up with longer rebalance frequencies. In general, offset start dates within a month or two may differ in rolling CAGR by 5 or more percentage points. So there is a good opportunity for cherry picking results if one were so inclined.

I've looked into the inverse-volatility weighting a bit more, in particular the strategy for calculating volatility. It does seem to improve the expected CAGR by a percentage or so. I looked at 10, 20, 40, 60, 120, and 250 days for the period used to calculate standard deviations. I looked at both raw standard deviation and downward standard deviation (setting upward changes to zero) in calculating the inverse-volatility weighting. The volatility calculated with downward standard deviation tends to yield an extra half to one percentage point, at least for short volatility windows and frequent updates.

I've pretty much concluded that I will go with calculating inverse-volatility weights using the downward standard deviation with a window of ten days going forward (the last 10 trading days before rebalancing). It won’t affect much with monthly to quarterly updates. There’s something to be said for using a 40-day window with monthly to quarterly updates.

I will likely try to update weights roughly weekly going forward, but I won’t sweat it if I drop off to monthly.

The other issue that has bothered me with the method is the risk of big drops. I know that market timing is a big issue with many Bogleheads, but given the excellent performance of the method Hedgefundie has provided, I’m quite comfortable sitting out and even missing the initial bounce-back. Trend followers have long recognized that a rise in the monthly unemployment rate is a useful macroeconomic indicator that has tended to lead each recession by zero to six months since 1919. The FRED site (

https://fred.stlouisfed.org/series/UNRATE) provides this data. One indicator that has been suggested is comparing the latest monthly unemployment rate with a moving average over N months. If the latest rate is higher, that is an indicator sensitive to recession. If the latest rate is lower, that is an indicator of economic health.

This information is particularly useful in two ways. It can indicate when to get out of the market (e.g., go completely to TMF), and it can indicate when the market is unlikely to badly misbehave in the short term. Folks tend to use averaging durations of 7 to 12 months as a crossover criterion between states. Short averaging durations give spurious signals, which can lead to whiplash. Long averaging durations may lag the actual start of a recession. I’ve done some playing with the index, and it seems like each of the recession events since 1986 would have been captured with an averaging period of 12 to 16 months.

I think that it is reasonable to use the index to systematically bias the overall strategy. If there is a clear signal of a recession, I would go completely to TMF. If there is a clear signal that there is no recession, I would bias the UPRO weights higher than calculated using the inverse-volatility method. In transitions, or if it is ambiguous whether there is a transition, I would stick with the weights calculated using the inverse-volatility method.

As a first approximation, I calculated a biased UPRO weight by increasing it a fraction of the way to 1 (full UPRO). For example, if the UPRO weight from the inverse-volatility calculation is w = 0.5, the biased weight is 1 * f + w * (1 – f), where f is the bias fraction. If f = 0, there is no bias. If f = 1, the UPRO weight is 1 and the TMF weight is 0.

I played with the strategies to some extent. I settled on a 15-month moving average period to detect crossovers, but the exact duration doesn’t seem too important. The best results, in terms of expected CAGR, seem to be dependent on the criterion for ambiguity. Overall, it appears that as soon as the sign changes on unemployment index criterion, the state should be considered ambiguous and no bias applied to the weights. Each succeeding month afterwards can be treated as unambiguous.

The bias fraction f is a matter of taste. Pushing f towards 1 improves the expected overall return by a couple of percentage points, but adds exposure to large dips. Black Monday (1987) is the largest crash that does not show up with the unemployment index. When f is close to 1, the portfolio takes a large dive. When f is close to 0, the portfolio is largely buffered. I would likely tend to split the difference by setting f = 0.5, which buffers the Black Monday drop substantially. One may argue about whether a Black Monday will occur again within the next 20 or 30 years, of course. Note that the volatility weights become unimportant as f goes to 1 (the UPRO weight = 1 regardless of volatility).

To give an example, consider a 15-year rolling calculation, with rebalance frequency between daily and quarterly, starting in 1986. Using the nominal 40/60 approach, the largest CAGR was about 22% (starting late 1990) and the smallest about 7% (starting 1999). Other peaks occurred for simulations starting in the late 1980s and 2001-2003. The spread in CAGR between different rebalance frequencies starting on the same date was generally 1 to 4 percent.

Going to the inverse-volatility approach, with rebalance frequency between daily and quarterly, the patterns of peaks and valleys were similar but maxima were closer to 27 %. The minimum CAGR for daily rebalance was about 16 %; overall the minimum was about 6 %. There was a much wider spread in CAGR between different rebalance frequencies starting on the same date, greater than 10 percent in spots (e.g., 7 % minimum to 17 % maximum).

Adding the unemployment index criterion to the inverse-volatility approach smoothed out the overall returns. For the daily through monthly rebalances, the rolling CAGR ranged from 20 to 31 percent and the overall range was from 15 to 33 percent. Overall this approach would have increased CAGR by as much as 10 percentage points relative to the nominal.

I think that there is something to be said for trend following in this case, using information outside the market to guide confidence in the market behavior. Given how well the method performs, it isn’t so critical to exactly time reentry, which is one of the criticisms of trend following.

As far as conditions other than observed, I’d probably be tracking whether the low/inverse correlation behavior continues in the future. If not, as a pragmatic measure I’d be tempted to try to identify if there is some other index that has low/inverse correlation to UPRO and use that instead.

I think that the ratcheting effect of getting out of UPRO when the unemployment index is unfavorable is likely to be persistent; I might be tempted to investigate additional signals as supplements. If I had the daily data back to 1955 I could check on the "lost decade", but it looks like the index would have signaled exit in 1957, 1960, 1969, and 1973.

If someone can tell me how to post images, I’d be happy to share my plots.