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Good afternoon everyone! I have a question regarding the risk free rate of my two asset portfolio. For my course, we have to create a two asset portfolio with the time frame of 2015-2020 with monthly returns. For the risk free rate, I have utilised the 5 year T-Bill because it has the same maturity as the project and also does not have any reinvestment risk since the T-Bills are zero-coupon bonds. However, I am unsure about my approach for the monthly risk-free rate, which I need since all of my returns of my assets are also monthly.

As of now, I took the yield of a 5-year T-Bill calculated the average yield of a 5-year T-bill from 2015-2020. Since the yield of the T-Bills are denoted in yearly terms, I took the caculated average yield of those five years and plotted the number in the following formula:

monthly rf yield = LN(1+avg. annual rf yield)/12

This gave me the avg. monthly rf rate. Is this approach appropiate or should I approach this problem in a different way? Kind regards

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    $\begingroup$ U.S. treasury only issues zero-coupon bonds ("T-bills") with maturities < 1 year. Some other countries treasuries issue zero-coupon bond with >1 year maturities. Still, assuming the existence of a 5-year zero-coupon bond doesn't sound realistic. $\endgroup$
    – Dimitri Vulis
    Commented Apr 28, 2021 at 15:34
  • $\begingroup$ Thank you for your response. Sorry for that rookie mistake, I am very new to this topic. In order to receive the monthly risk-free return for a 5-year time horizon, is it still applicable to utilise a 5 year US-Treasury which pays coupons? I realised that the "T-Bills" I was refering to in my question are actually the Yield of the 5-year US Treasuries. I have calculated the average return of the adjusted prices and then used the formula stated above. Is this approach appropiate or should I try a different approach? Sorry for that "silly" question but I am stuck with this issue $\endgroup$
    – Sam0512
    Commented Apr 28, 2021 at 15:43
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    $\begingroup$ As a quick solution, why not use this 1mo CMT fred.stlouisfed.org/series/GS1M divided by 12 to put it on a monthly basis. $\endgroup$
    – nbbo2
    Commented Apr 28, 2021 at 16:09

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