For (1) and (2)
Nominal risk-free rate = real risk-free rate + expected inflation rate …(approximately)
Now, a required rate of return must consider all the following:
Required rate of return = real risk-free rate + expected inflation rate + liquidity risk premium + maturity risk premium + default risk premium
So, any rate of return from a risky asset contains a nominal risk-free rate inside it. This is benchmark of what to expect from a security given a level of risk. CAPM model builds over this.
Real rates of return can be nominal rates of return after deducting expenses like taxes, investment fees and inflation, so they are like the “real” gain to the investor.
Hope this helps,
Would it be correct to say that real risk-free rate is the same as real rates of return?
Real risk-free rate is a real rate of return, but from risk-free assets only.
The most common rates of return are those from risky assets (stocks, bonds and others) and can be real or nominal.
Remember that risk-free assets are theorical, because virtually speaking they have no historical default, but that does not guarantee 100.00% safe investment, there is always a probability of default.
Got it! Thanks again for your eagerness to help me out.