CAPM: Expected Return of an Asset with Zero Beta

Let’s talk about investing and how we think about the returns we might expect to get. Imagine you are deciding where to put your money. You have different options, some seem safer, like putting money in a government savings bond, and some seem riskier, like investing in a brand new tech company. Naturally, you would expect a higher potential return from the riskier investment to compensate you for taking on that extra risk.

This idea, that higher risk should lead to higher expected return, is fundamental to finance. One way we try to quantify and understand this relationship is through something called the Capital Asset Pricing Model, often shortened to CAPM. Think of CAPM as a kind of map that helps us navigate the world of investment returns, especially when it comes to risk.

A key concept within CAPM is ‘beta’. Beta is a measure of how sensitive an asset’s price is to movements in the overall market. Imagine the market as a whole is like a big wave in the ocean. Some boats, representing individual investments, will move up and down with the wave more dramatically than others. Beta is trying to capture how much each boat bobs up and down in response to the market wave.

A beta of 1 means that, on average, when the market goes up by 1%, this particular asset’s price will also tend to go up by 1%. If an asset has a beta greater than 1, say 1.5, it means it’s even more sensitive to market movements. It will tend to amplify the market’s ups and downs. Conversely, a beta less than 1, maybe 0.5, suggests the asset is less volatile than the market; it will move in the same direction as the market, but to a lesser extent.

Now, what if an asset has a beta of zero? This is where things get interesting. A beta of zero, in theory, means that this asset’s price is completely unaffected by the movements of the overall market. It’s like a boat that is so stable it barely notices the ocean waves around it. Think of it like this: imagine investing in something whose value is determined by factors completely unrelated to the stock market’s performance, perhaps something very niche or specialized.

So, what does CAPM say about the expected return of such an asset, one with a beta of zero? The CAPM formula itself is designed to calculate the expected return of an asset based on its risk relative to the market. The formula essentially says that the expected return of an asset is equal to the risk-free rate plus a risk premium. This risk premium is calculated by taking the market risk premium, which is the expected return of the market minus the risk-free rate, and multiplying it by the asset’s beta.

Let’s break that down for an asset with a beta of zero. If we plug zero into the beta part of the CAPM formula, we are multiplying the market risk premium by zero. Anything multiplied by zero becomes zero. This means the entire risk premium component of the CAPM formula becomes zero when beta is zero.

Therefore, according to CAPM, the expected return of an asset with a beta of zero is simply equal to the risk-free rate. The risk-free rate is the theoretical rate of return you could expect from an investment with absolutely no risk, like a very safe government bond.

The intuition behind this is that if an asset has absolutely no systematic risk, meaning its returns are not correlated with the market’s movements, then investors should not demand any extra return for taking on market risk. They should only expect to be compensated for the time value of their money, which is represented by the risk-free rate.

In essence, CAPM suggests that even if an asset is completely insulated from market fluctuations, it should still offer a return, and that return should be at least the risk-free rate. This is because even with zero market risk, there is still the opportunity cost of investing money rather than, say, consuming it today. The risk-free rate compensates for this opportunity cost.

It’s important to remember that CAPM is a model, a simplification of reality. Real-world asset returns are influenced by many factors beyond just market beta. However, CAPM provides a valuable framework for understanding the relationship between risk and expected return, and it offers a clear and logical implication for assets with a beta of zero: their expected return should align with the risk-free rate.