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1996issue C081-12

Evaluating month-end yield gaps for equity regimes

A historical intermarket-regime-filter classified S&P 500 months from a month-end Treasury yield-gap. The evaluation locked that signed gap, reran the same cash switch with lagged closes, and then converted the gap into a split-sample-linear-fit instead of treating a binary equity-or-cash switch as proof.

  • Lock the yield-gap at month-end closes against a six-month-arithmetic-average so the intermarket-regime-filter uses one signed difference for both direction and strength.
  • Rerun the rising-yield-state cash switch as a lagged-yield-implementation, because a same-month yield close is not known until month-end.
  • Keep the yield-gap continuous in a split-sample-linear-fit and judge the predicted-monthly-change on unseen months rather than collapsing the gap into a binary switch.
  • Editorial view: averages by yield state describe association in the archive sample. They do not replace an out-of-sample linear forecast.
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Editorial frame: treat this archive note as an evaluation drill for an intermarket-regime-filter. Lock an objective month-end yield-gap, rerun the same cash-switch rule with lagged closes, and then convert that gap into a split-sample linear forecast instead of treating a binary cash switch as proof.

A locked month-end yield-gap

The evaluation used month-end S&P 500 closes from 1950 through 1995 and recorded only close-to-close monthly percentage change, omitting highs, lows, and dividends.

Yield trend was defined by comparing the month-end 30-year Treasury yield with a six-month-arithmetic-average of month-end yields rather than a 120-day daily average. The yield-gap is that signed difference, and it was used both as the direction of the yield trend and as a gauge of its strength.

How months differed by yield state

Across the sample, an average S&P 500 month rose 0.74% and finished higher 57% of the time. Months with the yield below its six-month-arithmetic-average averaged 1.56%, near-average months 1.43%, and months with the yield above the average lost 0.70%.

Those splits describe how equity months lined up with the sign of the yield-gap. They do not, by themselves, test a trading rule or a forecast.

The binary cash switch and look-ahead

A binary intermarket-regime-filter treated a rising-yield-state as a month in which the 30-year yield stood more than 0.1 percentage points above the six-month-arithmetic-average. In that state the hypothetical book moved from equities into cash represented by the 90-day Treasury yield.

Because a same-month yield close is not known until month-end, the same cash-switch rule was also run as a lagged-yield-implementation on last month's close and on the average of this month's and last month's closes. That second pass is the look-ahead check: the filter cannot be allowed to use a close that arrives only when the month is already over.

Cash switch when the 30-year yield gap exceeds 0.1%

Moving fully to 90-day bills whenever the month-end 30-year yield sat more than 0.1 percentage point above its six-month average raised average annual return and cut the worst 12-month loss versus buying and holding the S&P 500. The five annual statistics are the exact figures printed beside the source chart for January 1950 through December 1995, not heights read off the 3-D bars.
Moving fully to 90-day bills whenever the month-end 30-year yield sat more than 0.1 percentage point above its six-month average raised average annual return and cut the worst 12-month loss versus buying and holding the S&P 500. The five annual statistics are the exact figures printed beside the source chart for January 1950 through December 1995, not heights read off the 3-D bars.S&P 500 · monthly · 1950-01-01T00:00:00.000Z to 1995-12-31T00:00:00.000Z

The rule uses the same month's closing yield, which the source later treated as look-ahead. Dividends are omitted. Cash earns the 90-day Treasury yield.

A split-sample linear forecast

Linear regression treated the yield-gap as the independent variable and monthly S&P 500 percentage change as the dependent variable, rather than collapsing the gap into a binary long-or-cash switch.

The split-sample-linear-fit estimated coefficients on January 1950 through December 1975 and then applied them to 1976-1995 so the predicted-monthly-change would be judged on unseen months rather than on a full-sample fit. The 1950-1975 fit was monthly S&P 500 percentage change equal to 0.859% minus 5.947 times the yield-gap, with an R-squared of 0.0591. Refitting the same inverse linear form on 1950-1995 and on 1976-1995 produced R-squared values of 0.0622 and 0.0823 respectively.

Editorial reading

Editorial reading: keeping the yield-gap continuous, fitting it on the first half of the sample, and scoring the predicted-monthly-change on the second half is the evaluation step that a binary cash switch skips. The archive R-squared values stay small across the original fit and the two refits, so the linear map is a modest association test, not a claim that the intermarket-regime-filter has been proved.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
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