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.
- 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 to risk: Risk-averse investors would bear risk only if they are rewarded for doing so. And, the risk premium is the reward.
The risk-return tradeoff
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[RB] sinceπA > 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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