Skip to content
All library documents

Choosing a Treasury Benchmark for Quarterly Excess Returns

Article Quant Q&A · Author: Jason008
Read the original

Summary

The document considers which Treasury rate to use as the risk-free proxy when calculating quarterly excess returns for an asset typically held over a longer horizon. It contrasts using a maturity aligned with the asset’s holding period against the commonly used short Treasury yield, and asks whether the rate should come from the same quarter or the preceding quarter. The stated use is an arithmetic Sharpe ratio based on simple excess returns.

The answer emphasizes matching the benchmark to the asset’s expected cash-flow pattern and duration. A lump-sum payoff and a self-amortizing asset can call for different benchmark instruments even if both span the same total period. It also notes that a rolling investment horizon may make benchmark total returns more appropriate than yields, since longer-maturity fixed-income prices can move with interest rates. The document gives conceptual guidance but no universal yield tenor or timing rule; the choice depends on the asset’s cash flows and measurement design.

Key ideas

  • The benchmark maturity should reflect the asset’s cash flows and duration, not just its stated holding period.
  • A lump-sum payoff and a self-amortizing asset can require different benchmark instruments.
  • A rolling horizon may call for benchmark total returns rather than yields.
  • Longer-maturity fixed-income benchmarks can fluctuate as interest rates change.
  • The document does not prescribe a universal Treasury maturity or observation date.

Tags

Fixed incomeStatisticsRisk management
Full text
# What maturity Treasury yield to use for risk free rate to compare against asset typically held for 10 years?


# What maturity Treasury yield to use for risk free rate to compare against asset typically held for 10 years?












I have a quarterly return in quarter i for an asset which is typically held for 10 years. Which maturity Treasury yield should I use as a risk free rate in this context, and from what period? I initially think quarter i-1, but that thinking may be flawed.

My thinking is I use the 10Y Treasury yield and divide by 4 to make quarterly. I’ve also been told to use the 3M Treasury yield as it’s most often used in literature.

There are mixed answers out there, so I’m hoping to answer this. Typically I’m reading one should use a Treasury yield as a proxy for the RFR with maturity roughly equal to the typical holding period of the asset, but others have different answers. Also getting different answers about whether to use Treasury yield from same quarter, or previous quarter, as RFR rate for quarterly return in quarter i.

Edit: I’ll be using the resulting excess returns for an arithmetic Sharpe ratio (simple excess returns then Sharpe ratio scaled by sqrt(4)) so I am effectively ignoring the effects of compounding for the sake of using the formal Sharpe ratio.

## Answer by Si Chen (score 1)

https://quant.stackexchange.com/a/68140

This is a very deep and interesting question. Actually I think the answer depends on the cashflows for your asset and how they will be reinvested.

For example, if your asset is held for 10 years but will be returned to you at one lump sum with all the principal and interest at the end of the 10 years, then a different benchmark rate should be used than an asset which is held for 10 years, but returns its principal and interest in a self-amortizing way, so that by year 10 there is no principal left to return.

In both cases, you will need to figure out how you expect the cash flows to come back, and calculate its duration. Then you need to find a similar duration instrument as its benchmark.

The next step is once you have this benchmark, and you roll forward in time, are you getting closer to your 10 year horizon? In other words, a year from now, are you 9 years from the end of your holding period? If so, then you should not be using the yield but rather the total return of your benchmark. This is important because 10 year fixed income instruments, especially a zero coupon one to match a lumpsum payment, will have a lot of fluctuations due to interest rate changes.

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.