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The relationship between trading frequency and achievable alpha

Published in Automated Trader Magazine Issue 42 Q1 2017

Some of the most successful investors have long holding periods and investors are often advised to "buy and hold". We investigate how the average holding period of an optimal trading strategy relates to the alpha it can generate. Is longer really better?

AUTHOR'S BIO

Paul Buiges

Paul Buigues is the founder of XR Research, an investment research company based in Paris. XR designs engines that autonomously generate, select and allocate to a large variety of trading systems.

A common belief amongst investors is that long-term investing is preferable to short-term trading. The great Warren Buffett, whose favourite holding period is "forever", is often cited as evidence to support this point of view.

On the other hand, it is fairly obvious that increasing trading frequency, at least hypothetically, enables capturing more variance and should therefore be more profitable overall.

In this article, we first show the difficulty of generating significant alpha at low trading frequencies. After that, we quantify the relationship between trading frequency and maximum theoretically achievable alpha.

Figure 01: Maximum return strategy with 7 trades on the S&P 500 (since 1871)

Figure 01: Maximum return strategy with 7 trades on the S&P 500 (since 1871)

Figure 02: Maximum alpha strategy with 6 trades on the detrended S&P 500 (since 1871)

Figure 02: Maximum alpha strategy with 6 trades on the detrended S&P 500 (since 1871)

THE MAXIMUM RETURN STRATEGY AT A LOW TRADING FREQUENCY

We will start our analysis at a very low trading frequency, with an average period of 25 years between two trades (corresponding to so-called 'secular' bull/bear markets). Between 1871 and 2016 (145 years), this average trading period would have allowed about six trades.

Figure 01 shows the maximum return directional strategy (long or short 100% assets) that can be generated on the S&P 500 with seven trades (green = 100% long position, red = 100% short position). Here, we look at excess returns (i.e. total returns including dividends above the risk-free rate). Note that we use seven trades instead of six, as an odd number of trades yields the optimal strategy in this case. (We will later consider a maximum alpha strategy for which an even number of trades is optimal instead.)

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