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Using Constant or Time-Varying Risk-Free Rates in Performance Analytics

Article Quant Q&A · Author: Raghu Ramachandran
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Summary

The document clarifies how a performance analytics workflow can treat the risk-free rate when calculating or plotting portfolio risk and return. A scalar input represents a constant rate, while a vector can associate a different rate with each return period. The question arises because passing a rate vector to a risk-return scatter chart makes its Sharpe ratio guide lines disappear.

The response identifies this as behavior consistent with a changing risk-free rate: each period’s returns can have its own corresponding rate. This distinction matters when calculating excess returns and interpreting performance measures across time. The brief answer does not explain the chart’s exact plotting implementation or how the vector should be aligned or annualized, so users should consult the relevant package behavior for those details.

Key ideas

  • A scalar risk-free rate represents a constant assumption across periods.
  • A vector can represent rates that vary over time, with a rate associated with each return period.
  • The chart’s Sharpe ratio guide lines disappearing with a vector is described as expected behavior for a time-varying rate.
  • The response does not specify vector alignment or annualization conventions.

Tags

Risk managementStatisticsPortfolio construction
Full text
# Risk free rate for Performance Analytics


# Risk free rate for Performance Analytics












In [R] one can pass either a vector or scalar as the risk free rate. What is better? If I pass a vector to (for example) chart.riskreturnscatter then the sharpe ratio lines disappear.

```
chart.RiskReturnScatter(managers[,c(1,2,3)],0.01)
chart.RiskReturnScatter(managers[,c(1,2,3)],managers[,10])
```

So is this a feature?

Thanks, Raghu

## Answer by Kyle Balkissoon (score 1)

https://quant.stackexchange.com/a/16140

This is a feature, when you pass a vector it's because the risk free rate has changed over time. E.g. you can assume a constant or changing risk free rate as each period of returns can have an associated risk free rate.

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.