Risk premium – What does it mean?

Different stocks offer different levels of expected return. What causes stock A’s expected return to be higher than stock B’s expected return? How does the expected return of a risky asset relate to the risk-free rate of return? In this post, we answer both questions by introducing the concept of risk premium.

Learning objectives

• Define the risk premium for an asset and interpret how it relates to that asset’s expected return and the risk-free rate of return.
• Understand why risk premiums vary across both between and within asset classes.

The formal definition of risk premium

The formal definition of risk premium π on a risky asset is easy enough to understand. It is simply the difference between that asset’s expected return E[R] and the risk-free rate of return Rf

π = E[R] − Rf

The same equation can be rewritten as:

E[R] = Rf + π

This tells us that a risky asset’s expected return is the risk-free rate PLUS a risk premium. It implies that we would invest in a risky asset only if it offers a return higher than the risk-free rate. That markup constitutes the risk premium. This is a direct consequence of investors’ aversion towards risk: Risk-averse investors would bear risk only if they are rewarded for doing so. And, the risk premium is the reward.

In general, the riskier the asset, the higher the risk premium should be. So, if asset A is riskier than asset B, we have πA > πB. If that is the case, we can deduce that asset A’s expected return, which is E[RA] = Rf + πA, should be higher than asset B’s expected return, which is E[RB] = Rf + πB, as well: E[RA] > E[RBsinceπA > πB. This answers the question we posed at the start of this post: The difference between the expected returns of stock A and stock B is down to the difference between their πs. That is, the riskier stock will command a higher risk premium and, thus, will have a higher expected return.

The fact that risk and (expected) return goes hand-in-hand is known as the risk-return tradeoff, which is a fundamental principle in finance. An investor can expect to earn a higher level of expected return only if the investor agrees to bear a higher degree of risk.

Note that the risk premium of the risk-free asset must be zero by definition. Therefore, the expected return on the risk-free asset is E[R] = Rf + π  = Rf, which is of course the risk-free rate of return. This makes intuitive sense. While the risk-free asset has π = 0, risk-averse investors would not invest in risky assets if they didn’t offer a positive risk premium.

Let’s wrap up with a simple, numerical example. Suppose that the risk premium for the Tesla stock is 8% per year and the risk-free rate of return is 2% per year. This would imply that the expected return on Tesla shares is 8% + 2% = 10%.

What is next?

This post is part of the series on investments. The next post in the series explains how to calculate the return of a portfolio of assets. The previous post explained the meaning of the “risk aversion coefficient” and discussed the methods of measuring risk aversion.

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