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Weighting Cash and Derivatives by Total Portfolio Exposure

Article Quant Q&A · Author: Friasco
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Summary

The document considers how to calculate portfolio weights when cash is used to buy a derivative that provides exposure larger than the amount paid. Its example starts with a cash portfolio, spends part of it on a derivative, and asks whether remaining cash should be weighted against the original capital or against the sum of remaining cash and the derivative’s notional exposure. The response recommends the latter when the weights are intended to scale asset returns in a portfolio return calculation: use total exposure as the denominator.

This highlights the difference between cash committed or premium paid and the market exposure represented by a derivative. The answer is brief and does not specify how exposure should be measured for different contracts, account for collateral or changing deltas, or discuss the treatment of nonlinear payoffs. In practice, the chosen exposure measure should match the return convention used for the portfolio calculation.

Key ideas

  • Portfolio weights for return attribution should reflect total exposure when derivatives provide leverage.
  • The amount paid for a derivative can be smaller than the underlying exposure it represents.
  • Remaining cash is weighted against the combined cash and derivative exposure in the example.
  • The document does not prescribe how to measure exposure for different derivative types or nonlinear payoffs.

Tags

Portfolio constructionDerivatives pricingRisk management
Full text
# Calculating portfolio weights of derivatives


# Calculating portfolio weights of derivatives












A rather simple question.

You have a portfolio of USD100 in cash. You now take USD10 and buy a derivative that gives you exposure of USD200 to something.

What is the weighting of cash in the portfolio now: USD90/USD100 or USD90/USD290?

(You want the weight that you would multiply the asset's return by if you were calculating the portfolio's return.)

## Answer by arodrisa (score 1)

https://quant.stackexchange.com/a/20738

You need to calculate your weights using your total exposure, no matter which product you are using. In this case, as you said will be 90/290.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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