How to Calculate The Market Risk Premium?

The market risk premium is the amount by which the market return exceeds the risk-free rate for that reason, sometimes people call it the excess Market return. So it’s calculated as follows.

We take the rate of return that’s expected for the market, and let’s say that it’s 12%. When I’m talking about the market, we’re talking about the market portfolio, the performance of an index. Let’s just say that we’re talking about the S&P 500 and so we think that the Return on the S&P, 500 is going to be 12% and then we will subtract the risk-free rate. So, let’s say that the risk-free rate is 2%. And the risk-free rate would be typically the rate of return on like the US. Treasury bill for one month or a three-month us treasury bill, or it could even be the rate of return for a bank account or something. Something that has basically zero risk.

So we take the expected return for the market then we subtract the risk-free rate that is equal to 10% in this example. That is the reward that investors are demanding for holding a market portfolio with a beta of 1. So if investors hold the entire S&P 500, if that’s the market portfolio we're talking about they were to hold that entire portfolio this is the reward, this 10% is the premium they would expect over and above the risk-free rate. With the risk-free rate of 2%, You don’t have to bear any risk at all but when you hold the market portfolio, you are going to bear the systemic risk and so investors want to be compensated for that risk that they’re bearing. Which is in this case is 10%.

So this market risk premium is telling you something about investors' appetite for risk and we can do a number of things. One, we know the market risk premium so we can actually go and say, "What is the risk premium for a specific stock or for a portfolio?" We can figure that out using the capital asset pricing model. So let me show how that works. So we’ve got our CAPM and so we’ve got the expected return for security Ri. Which is going to be equal to the risk-free rate plus the market premium. So we've got the market premium which is (the expected return for the market the risk-free rate). So, we’ve got our Market premium, and then we multiply that by Beta for that security or for that portfolio. So, beta multiplied by the market risk premium, plus the risk-free rate that's going to give us the expected.

Then also, if we think about the visual representation of the capital asset pricing model, Where we have the betas on the x-axis and then on the y-axis, we have the expected return. Basically, the slope of this line is the market risk premium. So, we’ve got the risk-free rate at point Rf, and then here we’ve got a beta of 1 in the y-axis and then that corresponds to the rate of return that’s expected for the market. If we were to calculate the slope, that would be the (Rm - Rf). Risk premium would be the slope of the security market line.