I want to flesh out the idea of a confidence index that can be used to adjust the weights in a stock/fund portfolio, in particular UPRO/TMF. The index should enhance weighting to equities under favorable macroeconomic conditions and enhance weighting to low-risk funds under unfavorable macroeconomic conditions.

The idea is to fuss with the UPRO weighting that is determined through other means, such as risk parity. Let U0 be the nominal weight calculated with other means. With the confidence index CI, where -1 <= CI <= 1, the weight U actually applied becomes

U = U0 + F (ULIM0 – U0)

where 0 <= F <= 1 is a weighting factor and ULIM0 is a limit based on the current value of CI. ULIM0 = 1 when CI > 0 and ULIM0 = 0 when CI < 0.

The value F = 1 in the market timing approach favored by willthrill81, which means that the weights for UPRO are 1 with CI > 0 and 0 with CI < 0.

I propose a more gradual approach, adjusting F incrementally according to changes in CI. I propose using an index f, where (i) f_lo <= f <= f_hi, (ii) -1 <= f_lo <= 0, (iii) 0 <= f_hi <= 1, and (iv) F = abs(f). It might be reasonable to use f_lo = -0.5 and f_hi = 0.5, which equally combines the risk parity and market timing approaches.

Updates to f are signaled based on the rate of change in the CI. The value of f is decremented with a signal that economic downturn is occurring or imminent, and incremented with another signal that economic robustness is occurring or imminent. Increments and decrements are made up to a limiting value.

The unemployment index (UEI) has long been recognized as a leading indicator of recessions. Typically recessions occur after the UEI begins to rise after a period of falling UEI, and recovery begins occurs prior to the peak of the UEI. The rise leads the recession by zero to several months. This is the index used by willthrill81.

The confidence index should indicate weighting towards equities during falling or flat UEI, and should transition to weighting towards bonds when the UEI starts to rise.

Typically the UEI maximum has lagged the start of the equity rebound by a substantial fraction of a year. However, it appears that the start of economic recovery is also associated with a reduced rate of increase in the UEI. This is consistent with recovery starting to increase employment, slowing the increase in UEI. So the inflection point in the rate of change in an increasing UEI is an indicator of recovery.

Usually the UEI is a bit noisy from month to month. Also, the initial estimates may be changed once or twice as more data comes in, so the data available for backtesting may not be the same as is available in real time. Accordingly, back testing results may be a little optimistic.

Moving averages are typically used to detect the upswing from the UEI minimum. Subtracting the moving average from the latest monthly UEI value gives a proxy value that has the same sign as the slope of the UEI. The signal for a potential recession is onset of a positive slope. Generally the moving average is over a year, plus or minus a few months.

The inflection point in the rate of UEI increase is a bit more subtle to detect. Again moving averages can be used. In this case, the difference between successive values of the slope proxy is used. The inflection point is the first time when the current slope is less than the previous slope, even when both slopes are positive. The moving average may be a bit shorter for this calculation, at the cost of more noise. Three successive values of the moving average could be used to estimate a curvature and the criterion would be the change in sign of the curvature.

So the updating rules are pretty simple each month.

If both the UEI slope and curvature are positive, decrement f until f_lo is reached.

If either the UEI slope or curvature are negative, increment f until f_hi is reached.

It remains for the user to select the step size. Presumably the step should be large enough that only a few months are needed to go from f = f_hi to f = f_lo. It remains to be explored if there are strategies for using different steps for the increment and decrement, or different steps when going towards F = 0 (return to nominal from an extreme) and away from F = 0 (go to extreme from the nominal).

I have two figures, one for 1x S&P500 and LTT and the other for 3x (UPRO/TMF). Both of these are based on monthly data from siamond’s dataset. For clarity, I consider from January 1982 through January 2019, omitting the much poorer performance prior to 1982.

Leveraged 1x

Leveraged 3x

In the top plot for both figures, I show the total return for several concepts, all with monthly rebalance. The yellow and purple lines are the equity and bond returns. The gray line is a standard equity/bond weighted portfolio (60/40 for 1x, 40/60 for 3x). The red line is a parity line using variance instead of standard deviation. The heavy blue line is the parity case, adjusted by taking into account the UEI information.

I assumed that both the previous month’s returns and unemploymenet rate were available when calculating the weights used for the current month. This may be a little optimistic, because there is typically a few days lag before reporting the index.

The middle and bottom plots are the same in both figures. The middle plot indicates the UEI, with red dots flagged as increasing recession and the blue dots flagged as decreasing recession. The bottom plot is the unadjusted equity weight (red) and the adjusted equity weight (blue).

For these plots, I allowed the equity weights to rise halfway to one and to drop to zero. After playing with possibilities a bit, I selected a drop rate to go from fully optimistic to fully pessimistic in two months. The rise occurs over 20 months for these plots, although good results were obtained from 4 months to 25 months (another good value was a rise over four months). The averaging period for calculating recession start was 16 months, and the averaging period for calculating recession termination was 6 months.

For the 1x case, the overall CAGR values for 1982 to 2019 were

13.2 Variance parity adjusted with UEI index

11.9 Variance parity

11.4 Equity

9.44 LTT

11.1 60/40 weighting

For the 3x case, the overall CAGR values for 1982 to 2019 were

27.3 Variance parity adjusted with UEI index

23.6 Variance parity

14.8 UPRO

14.7 TMF

19.5 40/60 weighting

So there appears to be some merit to using the UEI adjustment. Presumably the improvement over straight parity will be less in the future, without the benefit of hindsight.

I am reluctant to set the maximum UPRO weight to 100%, because of the possibility of events such as Black Monday that are very poorly handled.