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Choosing a Buy-and-Hold Benchmark for Variable Position Sizing

Article Quant Q&A · Author: Stat
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Summary

The document asks how to construct a fair buy-and-hold comparison for a strategy that accumulates shares over several days, sells the accumulated position, and later repeats the process with a different trade size. The central challenge is that the strategy’s exposure changes through time, while a simple buy-and-hold equity curve may assume a different initial investment or share count. A meaningful comparison therefore needs a consistent basis for capital, exposure, and return measurement.

The post gives an example of repeated purchases followed by a sale, but offers no proposed benchmark, calculations, or answer. It does not specify whether the intended comparison is against a fixed-share holding, a fully invested portfolio, or the underlying market’s return. Those choices can produce different equity curves. Any comparison would also need to state how cash, transaction costs, and periods with no open position are treated; without those conventions, the resulting curves may not be directly comparable.

Key ideas

  • A strategy with changing position sizes has time-varying market exposure.
  • A buy-and-hold benchmark requires a clearly defined starting capital or share count.
  • Fixed-share and fully invested benchmarks answer different comparison questions.
  • The document supplies an example but no benchmark method or empirical comparison.
  • Cash treatment and transaction costs affect interpretation of the equity curves.

Tags

BacktestingPosition sizingEquitiesPortfolio construction
Full text
# Variable Position Sizing: Equity Curve vs Buy & Hold


# Variable Position Sizing: Equity Curve vs Buy & Hold












I have a trading strategy that can take multiple long positions with different sizes before selling them. For example, buy 5 shares of ABC on days 1, 2, 3 and sell 15 on day 4. Going forward, buy 10 shares on days, 11, 12, 13 and sell 30 shares on day 14 etc. I can plot equity curve for this strategy. But, I don’t know how to fairly plot equity curve for the corresponding buy and hold strategy for the sake of comparing against market. Any comment/suggestion is greatly appreciated.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.