The Stock Market Trend is Still Strong According to Kelly Leverage

Optimal leverage for continuous rebalancing of a passive SPY tracking strategy is still above its longer-term mean and far from trend reversal trigger levels. Technically, this is a strong market despite the recent consolidation.

The Kelly optimal leverage, as defined originally by Edward O. Thorp, is equal to the expected excess return in some time period divided by the expected variance of returns

f = μ/σ2

where f is the optimal leverage for continuous rebalancing, μ is the excess return and σ is the standard deviation. (Note that some traders confuse the Kelly leverage with the Kelly ratio used for optimal position sizing.)

The optimal leverage f requires continuous rebalancing and for this reason it is not practical to use. It also results in excessive leverage levels depending on the period used for calculating the expected return and standard deviation. However, when used as an indicator it may provide valuable information about a market. This indicator is plotted below for SPY for a period of 252 days and with the risk-free interest rate set to 0 for simplicity.


It may be seen that for this specific period of returns, the optimal leverage is 7.17, a value that is still above the longer-term average of 6.37. Actually, the leverage has stayed above the average in the last two and a half years (from about the start of 2013). Note that during the 2000s uptrend, the leverage flirted with a zero value several times. This has not happened since the summer of 2012.

I do not worry about a trend reversal unless this indicator crosses below 6 and then gains momentum towards the zero line, as shown on the above chart. For now, technically this market is still quite strong despite the drop in momentum. Note that this is just one indicator and, as I have stated many times in this blog, no indicator can provide sufficient conditions for price action. We are only looking at loose correlations without any implied causation and we hope that they remain significant in the future.

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