“Sell in May” Over the Long Run

April 1, 2013 • Posted in Calendar Effects

Does the conventional wisdom to “Sell in May” (and “Buy in November”, hence also termed the “Halloween Effect”) work over the long run, perhaps due to biological/psychological effects of seasons (such as Seasonal Affective Disorder)? To check, we turn to the long run data set of Robert Shiller. This data set includes monthly levels of the S&P Composite Index, calculated as average of daily closes during the month. This method of calculation deviates from that most often used for return calculations, but arguably suppresses noise in daily data. We split the investing year into two half-years (seasons): May through October, and November through April. Using S&P Composite Index levels, associated dividend yields and contemporaneous long-term interest rates (comparable to yields on 10-year Treasury notes) from the Shiller data set spanning April 1871 through October 2012 (283 six-month returns), we find that:

Modeling assumptions for this backtest are complex, as follows:

  • Funds switch between stocks and cash at the ends of April and October. Since the monthly level is the average daily close for the month, this assumption may be optimistic or pessimistic.
  • Cash earns a monthly baseline risk-free yield estimated as one twelfth the long-term interest rate in the data set less 1.45%, which is the average difference between the 10-year Treasury note yield and the 3-month Treasury bill yield since April 1953 (the earliest month available for both series). This estimate may not be representative for pre-1950s data.
  • Dividends accrue while in stocks, with one half of the annual yield paid during each six-month interval and frictionless reinvestment. This dividend smoothing assumption could bias results, and frictionless reinvestment of dividends is optimistic.
  • Baseline trading friction for moving in and out of the S&P 500 Composite Index is a constant 1% over the sample period. This assumption is very crude, as indicated in “Trading Frictions Over the Long Run”. Given the challenges of constructing a portfolio from index components during much of the sample period, this baseline value may be optimistic. For recent data, it is pessimistic.
  • Ignore the tax implications of trading.

The limitations of these assumptions, as well as those of the interpolation methods used in constructing the early part of the source data set, make this analysis more of a concept exploration than a strategy test.

The following chart compares on a logarithmic scale cumulative values of $1.00 initial investments for three strategies using baseline assumptions over the entire sample period:

  1. Buy and hold stocks.
  2. In stocks (cash) during May-October (November-April).
  3. In stocks (cash) during November-April (May-October).

In support of conventional wisdom, being in stock during November-April mostly beats being in stocks during May-October (terminal values $965 versus $55). However, buying and holding the index substantially outperforms both seasonal strategies.

For another perspective, we compare average six-month return statistics for the strategies.

SPcomposite-total-seasonal-cumulatives

The next chart compares the average six-month total returns for the three strategies using baseline assumptions over the entire sample period, with one standard deviation variability ranges. Average total return for being in stocks during November-April is higher and volatility of returns is lower than for being in stocks during May-October, supporting conventional wisdom. Buying and holding stocks generates a substantially higher average total return, but with much higher volatility.

For a different perspective on time variation of returns, we look at average seasonal total returns by decade.

SPcomposite-total-seasonal-return-stats

The next chart compares average six-month total returns by decade using baseline assumptions. Based on this metric, being in stocks during November-April beats being in stocks during May-October for 10 of 14 decades, consistently after 1950. However, the poor returns for being in stocks during November-April for the 1930s and 1940s weakens the argument for a reliable biological/psychological explanation of seasonal returns.

How sensitive are results to modeling assumptions?

SPcomposite-total-seasonal-return-stats-by-decade

The final two charts compare average six-month total returns (upper chart) and terminal values of $1 initial investments (lower chart with logarithmic scale) in the three strategies over the sample period for different sets of assumptions. Results consistently confirm the superiority of being in stocks during November-April as compared to being in stocks during May-October. However, only by ignoring both trading frictions and dividends does being in stocks only during November-April become competitive with buying and holding stocks.

SPcomposite-total-seasonal-return-stats-sensitivities

SPcomposite-total-seasonal-terminal-values-sensitivities

In summary, evidence from rough modeling over the long run suggests that U.S. stocks mostly do better during November-April than during May-October, but (with reasonable assumptions about return on cash, dividends and trading frictions) buying and holding stocks generally outperforms a “Sell in May” market timing strategy.

Cautions regarding findings include:

  • As noted, the data set establishes monthly S&P Composite Index levels by averaging daily closes during the month rather, thereby blurring seasonal effects.
  • As noted, modeling of trading frictions and return on cash is crude. Precise modeling is intractable.
  • Ignoring taxes materially benefits the timing strategies relative to buy-and-hold.
  • Use of an index, rather than a tradable asset, tends to overstate returns by ignoring the costs of establishing and maintaining a liquid asset. Older data may be less reliable than recent data.
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