Carry as the Difference Between Static and Forward-Evolving Rates

Summary

The document explains why carry can be described as zero when interest rates evolve along projected forward rates. It distinguishes two conventions for a deterministic passage of time. In derivatives practice, market variables are assumed to age according to their forward values: tomorrow’s rates or implied volatility match today’s corresponding forward levels. Under that convention, realized evolution along forwards leaves no carry contribution in the framing described.

In asset management, the comparison is often instead with rates remaining unchanged from today. Carry then measures the effect of the difference between a static market environment and one in which rates move along the forward curve. The answer relates this distinction to option theta: ordinary theta captures time decay, while modified theta also includes effects such as funding and volatility aging. The passage is conceptual rather than a numerical example, and it does not specify a particular instrument, curve construction, or carry calculation. Its main caveat is that “carry” depends on the convention and field of practice, so an explanation needs to state what is held fixed as time passes.

Key ideas

• Carry can mean different things in derivatives and asset management.
• Under a derivatives convention, market variables age according to their forward values.
• Asset-management carry can compare forward-driven evolution with rates remaining unchanged.
• The distinction resembles ordinary theta versus modified theta, which includes other time-related effects.
• A carry statement is incomplete unless its assumptions about how market variables evolve are clear.

Tags

# Why is there no carry if interest rates follow projected forward rates?


# Why is there no carry if interest rates follow projected forward rates?












"Carry is a function of the shape of the interest rate curve. When the curve is upwardly sloping (ie, longer dated rates are higher than shorter rates, as they are currently), then the market is implying that interest rates are expected to rise in the future. If interest rates follow projected forward rates (and these expected rises materialise), then carry will be zero."

I'm struggling to understand why this would be the case?

Source: redington.co.uk/base/redington/publications/download/id/12 [Note: It auto downloads the PDF]

## Answer by Antoine Conze (score 1)

https://quant.stackexchange.com/a/34692

Carry tends to have different meanings in the derivatives world and in the asset management world. The paper you are referring to comes from the asset management world.

In the derivatives world people tend to think that if the random part is zero the variables "age" according to their forward value: tomorrow's interest rates will be today's 1 day forward interest rates, tomorrow's implied vol will be today's 1 day forward implied vol, etc.

In the asset management world people tend to think that if the random part is zero the variables remain the same: tomorrow's interest rates are the same as today's. So they have introduced a concept of carry that can be thought of as the impact of the difference between rates not changing and rates changing according to their forwards.

In essence it's the same difference than between theta and modified theta in the option world: theta is just the derivative to time, but modified theta includes the various funding effects, volatility aging, etc.

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.