Risk Free Rate?

Is there a way to find or derive the risk free rate? I saw something about RiskFreeAveAnnRet. Can I use that in a formula?

You have to define the risk free rate. Usually, this is defined as the expected rate of return on a risk free investment. Since this does not actually exist in real life, you have to first determine what relatively “risk free” means to you. Also, you must determine is your timeframe. Most importantly, you have to have a “use case”.

Is a 3 month US T-Bill risk-free? In other words, is the probably of US default within 3 months exactly 0. If you think so, then you could try “ShowVar(@TBill, (Close(0,#TBILL3M)/100) )”. You’ll see that the current risk free rate is essentially 0. What if you think the chances of a US default over a 12 month timeframe are still 0. In this case, try “ShowVar(@TBill, (Close(0,#TBILL12M)/100) )”.

But what if you define the risk free rate as the guaranteed rate of return of an investment above inflation, i.e., “the real risk free rate”. But measuring YoY inflation, “ShowVar(@Inflation, (Close(0,#CPI)/Close(11, #CPI))-1 )”, you’ll see that 3 and 12 month T-Bills have a negative “real” rate of return.

What I’m getting is that the risk free rate does not actually exist… You have to make it up. How you do this depend on how it will be used, i.e., your “use case”. So… what is your use case?

This has been discussed before, but can someone shed light on how to calculate the monthly risk free rate of return from 3-month T-Bill secondary market rate data? I’m developing my own spreadsheet and want to be able to calculate Sharpe, Sortino, etc.

https://fred.stlouisfed.org/series/TB3MS

https://quant.stackexchange.com/questions/18742/convert-three-months-interbank-rate-into-monthly-rate

Thanks but this isn’t what I was asking for.

What calculation is Damodaran using in this spreadsheet for return on 3-month T Bill and why don’t his return numbers match the ETF BIL?

http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histretSP.html

If you assume that the 3 month T-Bill is risk free, then you just need to convert the annual interest rate into a monthly.

Is this what you’re after?

For example, Damodaran reports a 1.39% return for 3-month T bills in 2017 while the ETF BIL had a 0.69% return for 2017. Why the difference?

Just want to make a reference to a closely related thread: Monthly Return on 10-Year Bond

From the Damodoran link :

Damodoran calculates the returns on 3 mo T-Bills as the simple average of interest rates sampled over discrete quarterly intervals (Jan, Apr, Jul, Oct). This is quite frankly not the best way to do this, nor the canonical way, but it’s close enough for rough approximation.

When I download the raw data on H.15 Selected Interest Rates from the Federal Reserve data system, I can match his results up to 2011 with 100% accuracy. Peculiar is that my results begin to differ from Damodaron’s after 2011. It appears that he changed methodologies since this time. Of note, I get ~.86% returns for 2017 using his legacy method.

However, even when I impute bond returns using a “better” method, my results differ significantly from Damodoran’s. Notably, I get .927% to .931% for 2017 (depending on the convention).

This data corroborates a long held intuition I’ve had about Damodoran… In any case, I would personally not use his data.

Yes, I understand what he did, but if you use that as the risk free rate of return and calculate the sharpe for SPY, you get something way too low (and lower than what P123 reports), so that methodology is not correct or at least doesn’t match what what P123 does. It also doesn’t match the returns for BIL.

How do you know if a Sharpe ratio is too high or low? Are you trying to get your spreadsheet to jive with the results from P123? If so, did you try to impute your own risk free rate from H.15 data (i.e., not use Damodoran)?

According to the Risk Glossary , P123 uses 3 Month T-Bills as a proxy for the risk free rate. Some differences can be had depending on the sampling frequency for risk statistics (e.g., weekly, monthly, annual, etc…), but these should not have a very significant impact.

The monthly return I have for 3MTB in 2017 are

-0.04%
-0.05%
0.02%
0.03%
0.04%
0.07%
0.10%
0.08%
0.08%
0.06%
0.09%
0.09%

which is already higher than the return of the ETF BIL, and your calculated annual return of 0.93% looks liked it would be even higher (0.08% monthly).

and the monthly return I have for S&P 500 total return in 2017 is

2.58%
1.75%
-0.15%
1.69%
1.78%
0.99%
0.25%
1.65%
2.73%
1.59%
2.88%
4.86%

These numbers lead to a Sharpe of 1.107 for 2017. P123 (using monthly statistics data) reports 4.38 Sharpe for SPY in 2017. This leads me to believe that the way that I, you, Damodaran, etc are calculating the return on the 3 month T bill is not correct.

aschiff can probably shed light on this topic.

I agree that aschiff should probably be the one chime in.

But I just wanted to point out that one issue may be that the ##UST3MO you are showing clearly has some variation of returns, whereas the theoretical construct of a risk free rate used in the Sharpe ratio and MPT assumes zero variation. I.e., the return of a riskless security is simply its yield to maturity (and nothing more).

The reason that 3 Month Treasury displays some variation shows us that it is not completely riskless. In fact, there is really no such thing as a risk free security in the real world. It’s usefulness as a construct is mostly relegated to theories about risk neutral pricing, arbitrage mechanisms, and market efficiency.

The answer I believe is on the last page here, but I’m too busy at my day job to figure it out right now.

https://admainnew.morningstar.com/directhelp/Morningstar_UST_Constant_Maturity_Return_Methodology.pdf

The idea is you can calculate the prices at the beginning of the current month and beginning of the next month using the monthly yield data and use those numbers to calculate the monthly return (to simulate if you bought and sold the 3-month T Bill every month, before it’s 3-month maturity).

Other references I’ve found:

Appendix B here: http://fmwww.bc.edu/ec-p/wp409.pdf
Here: http://onlinelibrary.wiley.com/doi/10.1002/9781119203414.app4/pdf

and maybe here: https://www.youtube.com/watch?v=tTOzS_ATu-4

Here’s how we’re adjusting ##UST3MO to a monthly return:

  1. Compute the average per calendar month.
  2. Add 1 (i.e. 100%).
  3. Power it by (1 / 12) * (365.25 / 360). This factor has to do with its convention of using 360 day years.
  4. Subtract 1 (i.e. 100%).