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How Leverage Scaling Affects Long-Short Portfolio Turnover

Article Quant Q&A · Author: KDMS
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Summary

The document asks why a leverage or volatility-scaling factor changes the turnover ratio of a momentum portfolio, citing the approach associated with Barroso and Santa-Clara. It distinguishes the intuitive idea of multiplying portfolio exposures by a scale from the turnover calculation, which may include the scale factor in its numerator or denominator. The question notes that the formula is applied separately to each leg of a long-short portfolio, with one-half accounting for the two legs.

No derivation or answer is provided, so the document does not establish whether doubling the scale must change percentage turnover. The issue depends on the exact turnover definition and how the scaling factor varies over time: a constant scale may cancel in a normalized ratio, while changing exposure can affect the trades required to rebalance. The post raises a useful measurement question but gives no empirical evidence or definitive resolution.

Key ideas

  • The document asks how a portfolio scaling factor enters a turnover ratio.
  • It concerns a scaled momentum portfolio and refers to a published volatility management approach.
  • The question distinguishes scaling exposures from measuring percentage turnover.
  • The formula is described as applying separately to each side of a long-short portfolio.
  • No answer or calculation is supplied to resolve the effect of scaling.

Tags

MomentumPortfolio constructionExecution
Full text
# How to calculate Turnover Ratio of a scaled Portfolio


# How to calculate Turnover Ratio of a scaled Portfolio












I want to calculate the Turnover of my scaled Momentumportfolio (Barroso und Santa-Clara 2015) They described Turnover Ratio with the following formula:

While i understand the general concept (without Lt):

Why does the weighting factor (Lt) impact the Turnoverratio in the shown way.

If i got a scaling factor (Lt) of 2, everything would be scaled by 2 but the percentage Turnover Ratio wouldn't be the same ?

So in this case a lower (higher) weighting would cause a lower (higher) Turnover Ratio.

Any one able to explain this ?

(the 0.5 is because its a Long-Short Portfolio, so the formula is for each leg)

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