I have a time series of the three month interbank rate each month and I suppose that the rate is has yearly frequency.

I need these interbank rates to be on a monthly basis because I want to us these rate as a proxy for the risk- free rate, so I can subtract the rates from my monthly return to get the excess rate.

Let's consider an example:

by assuming the monthly return of stock x in April is 6%. The interbank rate at the end of April is 3% annually. Can I simply subtract o.25%(3/12) from 6% resulting in 5.75% of excess return.

Any help would be much appreciated.


To get one-month rate X from three-month rate Y, you use this formula:

1 + X = (1 + Y)^(1/3)

To get one-month rate X from annual (12-month) rate Y, you use this formula:

1 + X = (1 + Y)^(1/12)

To get three-month rate X from annual (12 month) rate Y, you use:

1 + X = (1 + Y)^(3/12)

0.25% is annual 3% converted to a monthly rate, i.e. (1+0.03)^(1/12) - 1

By the way, multiplying by 1/12 or 3/12 etc. is just a linear approximation of raising numbers like 1.03 (that are close to 1) to the power of 1/12 and 3/12 respectively.


I think you are on the right track... To double check I tried to get the Monthly return by using the following formula:

Monthly Return = [(1 + Annual Rate)^(1/12)]-1

by using this formula with the stated 3% Annual Return, the Investor receives approximately 0.25% per month....


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