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Bollinger Bands: Buy Low and Sell High?

Posted in Technical Trading

Are Bollinger Bands (BB) useful for specifying when to buy low and when to sell high the overall U.S. stock market? In other words, can an investor beat a buy-and-hold strategy by systematically buying (selling) when the market crosses below (above) the lower (upper) BB? To check, we examine the historical behavior of BBs around the 21-trading day (one month) simple moving average (SMA) of S&P 500 SPDR (SPY) as a tradable proxy for the U.S. stock market. We consider BB settings ranging from 0 to 2.5 standard deviations of daily returns, calculated over the same trailing 21 trading days. Using daily unadjusted closes of of SPY (to calculate BBs), dividend-adjusted closes of SPY (to calculate total returns) and contemporaneous yields for 3-month Treasury bills (T-bill) from the end of January 1993 (SPY inception) through early May 2018, we find that:

Testing assumptions are:

  • When the daily unadjusted close of SPY crosses below (above) its lower (upper) BB, we buy (sell) at that close and hold the position until the next sell (buy) signal. This assumption requires slight anticipation of signals just before the close.
  • Commence testing on 4/2/93, when all BB variations are on buy signals.
  • While out of SPY, funds accrue interest at the T-bill yield (ignoring settlement delays).
  • For the baseline case, switching between SPY and cash bears 0.2% frictions (with a sensitivity test later).
  • Dividend reinvestment is frictionless.
  • Ignore tax implications of trading.

First, we consider SPY behaviors when it is below, between and above BBs. The following chart summarizes average daily total returns when SPY is below the lower BB, between BBs or above the upper BB for BB settings ranging from 0.0 to 2.5 standard deviations below/above the 21-day SMA. It also shows the average daily total return for buying and holding SPY (B&H). Notable points are:

  • Increasing the BB setting mostly increases average return below the lower BB (identifies stronger reversals).
  • Between BBs, average return is mostly a little weaker than that for B&H.
  • Average return is mostly weaker than that for B&H above the higher BB, except for the highest setting (suggesting breakout rather than reversal for this setting).

What about daily return variabilities?

The next chart summarizes daily return variabilities for the same variations. Notable points are:

  • Returns below the lower BB are abnormally variable, with variability mostly increasing with BB setting.
  • Returns between BBs have about the same variability as B&H.
  • Returns above the upper BB are abnormally calm, more so as BB setting increases.

What about frequencies of occurrence?

The next chart summarizes percentages of days spent below, between and above BBs for the same variations. Notable points are:

  • Except for higher settings, observations above the upper BB are more frequent than observations below the lower BB (SPY price generally trends upward).
  • For high settings, switching signals are rare.

How do these behaviors translate to trading strategies?

The next chart summarizes net compound annual growth rates (CAGR) and maximum drawdowns (MaxDD) for a strategy that buys SPY when it crosses below the lower BB and sells SPY when it cross above the upper BB over the sample period for the same variations. In other words, the strategy buys only when SPY is BB-undervalued and holds only until SPY becomes BB-overvalued. Notable points are:

  • CAGR increases with BB setting, but never reaches the CAGR for B&H.
  • MaxDDs for the timing strategy are a little less severe than that for B&H, but there is no systematic relationship between BB setting and MaxDD.

For another perspective we look at cumulative performances.

The next chart compares cumulative values of $1 initial investments in the BB strategy for the three highest settings from above, and for B&H, over the available sample period. The BB strategy mostly cannot keep up with B&H.

How do annual performances for the best BB strategy variations and B&H compare?

The next chart compares annual returns for the BB strategy with 2.0 and 2.5 standard deviation settings, and for B&H, by calendar year (1993 partial). Average annual returns during 1994-2017 for 2.0, 2.5 and B&H are 8.1%, 8.8% and 11.1%, respectively, with standard deviations of annual returns 14.5%, 13.3% and 18.2%. Corresponding return-risk ratios are 0.56, 0.66 and 0.62. The BB strategy variations lose some return in exchange for lower volatility.

How sensitive are the 2.0 and 2.5 BB strategy variations to assumed level of switching frictions?

The final chart shows how net CAGRs of the 2.0 and 2.5 BB strategy variations change with assumed level of switching frictions over the sample period. Because 2.0 switches more frequently than 2.5 (117 versus 43 times), 2.0 deteriorates faster as switching frictions increase.

In summary, evidence from simple tests on SPY over nearly 24 years offers little support for belief that investors can beat the broad U.S. stock market by using Bollinger Bands to buy low and sell high.

Cautions regarding findings include:

  • The number of BB switching signals generated by the 2.5 standard deviation setting is modest, undermining confidence in statistics for that variation.
  • Using a different BB measurement interval, using BB signals in some other way or combining them with some other indicator(s) may work better. However, the more combinations of rules/parameter settings considered, the greater the data snooping bias (luck component) in the best results.
  • Even rules that randomly trade in and out of the market tend to outperform B&H during samples with long and deep bear markets.
  • Applying the same BB specification and settings to other assets may produce different results.
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