I have found finance books very decisive on this issue, such that some of them prefer short term maturity and some of them chose long term. I would be very glad if anyone can provide me with an intuition for the case for choosing either of them.
A six month treasury bill rate, while default free, will not be risk
free, because there is the reinvestment risk of not knowing what the treasury bill
rate will be in six months.
Even a 5 year treasury bond is not risk free, since the
coupons on the bond will be reinvested at rates that cannot be predicted today.
The risk free rate for a five year time horizon has to be the expected return on a
default free (government) five year zero coupon bond.
In summary, an investment can be riskfree only if it is issued by an entity with no default risk, and the specific instrument used to derive the riskfree rate will vary depending upon the period over which you want the return to be guaranteed.
Remember that the risk-free rate actually doesn't exist., There are only proxies for risk-free rate. An often accepted proxy is domestically held short-dated (one-year) government bond. I don't know what you need it for, but for paper or chapter you can choose proxy most often cited in your literature (remember about your target journal). Than provide some insights into other proxies (with references) and explain your choice. Remember about country-specific risk.
Agree with Anna, none of the financial assets has zero-risk free(rf). Therefore, the results may vary according to the maturity. In the literature, they usually use 3-month treasury bills (3tb) as a proxy for rf. Additionally, in order to be able to compare your results with previous studies you have to be in line with those studies.
However, the issue with CAPM is not to use 1TB, 3TB or 6TB or even 12TB, but rather it is with the factors that may work well in predicting returns, as return on market RM (such as FTSE100) included in the CAPM model does not represent the market, hence we have to consider other factors such as HML and SMB ( Fama-French 3Factor model) or consumption growth (C-CAPM), etc
Agree with other resercher there is not risk-free assets, inflation rate is another economic cost no considerated and it is as a risk rate; however the beterr asset risk-free is five years trasure-bond. Mario
Note that, while considering inflation, the selected financial instrument must be very liquid. This is NOT usually the case for many emerging market economies, but for SOME developed countries like US and UK, that is the case. Therefore, for US and UK economies, I agree a 5-year treasury bond is usually a good choice.