how to decide on risk free rate to use?
In short u use government 10-years bonds (u can also use 20 year bonds). That is one of shortcomings of CAPM because CAPM never said which rate to use for free rate. In many text books authors use short-term rates, but it is only to show how CAPM works. Not to indulge more in explanation. Just use 10 year government bonds (US and Germany are best countries for that)
Select the risk free that most closely approximates the duration of the cash flows in which you are trying to value. If you are valuing a business, the most appropriate rate is a 10-20 year treasury because this security most closely approximates the duration of a business' cash flow: perpetuity. If you are valuing an investment strategy over 1 year, then use the 1 year treasury. Etc. etc.
Are you asking about the currency or the maturity (short or long term)?
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