Bollinger Bands: Buy Low and Sell High?

Are Bollinger Bands useful for specifying low and high levels of the overall stock market? In other words, can an investor beat a buy-and-hold strategy by buying (selling) when the market crosses below (above) the lower (upper) Bollinger Band? To check, we examine the historical behavior of of Bollinger Bands around the 21-trading day (one month) simple moving average of S&P Depository Receipts (SPY) as a tradable proxy for the U.S. stock market. Using daily dividend-adjusted closes of SPY and contemporaneous yields for 13-week Treasury bills (T-bill) for the period 1/29/93 through 11/19/10, we find that…

Assumptions for testing are:

• Consider three sets of Bollinger Bands corresponding to 1.5 (BB 1.5), 2.0 (BB 2.0) and 2.5 (BB 2.5) standard deviations above and below the average.
• When the daily close of  SPY crosses below (above) its lower (upper) Bollinger Band, 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 the test on 4/2/93, when all three sets of Bollinger Bands generate their first buy signal for the data set.
• While out of SPY, accrue interest at the current T-bill yield.
• Trading in and out of SPY incurs one-way trading friction in the range 0.05% to 0.25% (actual trading friction depends on bid-ask spread, actual broker fees and trade size).
• Dividend reinvestment is frictionless.
• Ignore tax implications of trading.

The BB 1.5, BB 2.0 and BB 2.5 sets of Bollinger generate 145, 79 and 24 distinctly tradable buys and sells of SPY over the entire sample period, respectively.

The following chart summarizes average daily total returns for a buy-and-hold strategy and for the three buy-low/sell-high Bollinger Band strategies over the entire 4/2/93-11/19/10 period for various levels of trading friction. Notable results are:

• Even at the gross level (no trading friction), use of Bollinger Bands does not improve upon buy-and-hold.
• There is no progression of average daily returns with “tightness” of bands (suggesting random variation rather than systematic effect).

What about daily return volatility?

The next chart summarizes standard deviations of daily returns for buy-and-hold and the three buy-low/sell-high strategies. Results show that the latter three strategies suppress volatility by being out of the stock market at some times, with volatility decreasing as Bollinger Bands tighten.

What is the combined effect of average daily returns and volatility?

The next chart plots gross (frictionless) cumulative values of $10,000 initial investments at the close on 4/2/93 for buying and holding SPY and for buying SPY low and selling it high based on the three sets of Bollinger Bands. At most points in time, a buy-and-hold strategy produces the best outcome, but the buy-low/sell-high strategies tend to outperform during extended market declines.

What happens to terminal values after incorporating trading friction?

The final chart summarizes terminal values on 11/19/10 for the buy-and-hold strategy and the three buy-low/sell-high Bollinger Band strategies with various levels of trading friction. Results show the material and progressive degradation of outcomes with increasing trading friction.

In summary, evidence from simple tests over the past 17.5 years does not support a belief that investors (especially those with small accounts) can beat a buy-and-hold strategy by using Bollinger Bands to buy low and sell high for the broad U.S. stock market.

Note that:

• Sample size is small relative to the number of round trip trades generated by the 2.5 standard deviation Bollinger Bands.
• Using SPY closing prices unadjusted for dividends to generate the Bollinger Bands improves signaling performance for BB 2.0 but hurts signaling performances for BB 1.5 and BB 2.5.
• Using a different Bollinger Band measurement interval, using Bollinger Band signals in some other way or combining them with some other indicator may work better. However, the more combinations of rules/parameter settings considered, the greater the data snooping bias (luck component) in good results.
• Any rule that uninformatively trades in and out of the market tends to underperform (outperform) a buy-and-hold strategy during bull (bear) markets.

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