Leading Economic Index Exploitable for Sector Rotation?

A subscriber asked about a strategy that rotates among equity sectors according to the Leading Economic Index (LEI), published monthly by the Conference Board (see "Leading Economic Index and the Stock Market"). To assess LEI usefulness for sector rotation, we consider the following nine sector Standard & Poor’s Depository Receipts (SPDR) exchange-traded funds (ETF):

Materials Select Sector SPDR (XLB)
Energy Select Sector SPDR (XLE)
Financial Select Sector SPDR (XLF)
Industrial Select Sector SPDR (XLI)
Technology Select Sector SPDR (XLK)
Consumer Staples Select Sector SPDR (XLP)
Utilities Select Sector SPDR (XLU)
Health Care Select Sector SPDR (XLV)
Consumer Discretionary Select SPDR (XLY)

We consider two LEI-based variables: (1) monthly change in LEI; and, (2) 3-month average change in LEI (average of current value, revised value for prior month and twice-revised value for two months ago) for signal smoothing. For each variable and each sector ETF, we consider two tests: (1) correlation of the variable with ETF return each of the next three months; and, (2) average next-month ETF returns across ranked fifths (quintiles) of the LEI variable. The first test looks for linear relationships, and the second test looks for non-linear relationships. Monthly measurements employ closes on LEI release dates, generally after the market open about three weeks after ends of calendar months reported. Using monthly changes in LEI from archived Conference Board press releases and contemporaneous dividend-adjusted daily levels of the above sector ETFs and of SPDR S&P 500 (SPY) from mid-July 2002 (limited by LEI press releases) through mid-November 2021 (233 monthly LEI observations), we find that: