CAPM Discount Rates

How they work, and the problems they have

The CAPM, or the Capital Asset pricing Model has long occupied a central place in the field of corporate finance, and in turn discount rates make up a central role in that model.

On a fundamental level the CAPM is used to attempt to determine the appropriate discount rate for a given asset or investment.

How it works

The core idea of any discount rate is that it must match a given risk-free rate plus an appropriate premium:

\(\begin{equation} \text{Discount Rate} = \text{Risk-free Rate} + \text{Risk Premium} \end{equation} \)

You can think of this as the following:

• Risk-free Rate → The return you’ll get for doing nothing

• Risk Premium → The return you must demand to justify the risk you’re taking on

´From a theoretical idea this makes some amount of sense, right? After all, the greater the risk, the greater the return.

But thinking it through this isn’t really the case now is it?

Just thinking on it seriously, In an efficient market wouldn’t this mean that the rate of return will always equal the risk-free rate, regardless of the amount of risk you take on?

I am aware this sounds wrong, but stick with me here.

If you think of “risk” as “likelihood and degree of capital loss in an investment”, wouldn’t you expect that in an efficient market the “Risk Premium” demanded by investors would tend towards the actual risk being taken on?

After all, if the risk premium demanded by the market is higher than the actual risk taken on, wouldn’t other investors simply take on that risk up until the 2 equalize? After all, it’s a “free lunch”.

There’s more to a risk premium than risk

This is an important thing to mention, and what actually explains the discrepancy that results in higher risk investment tending towards higher returns.

In a way the “risk premium” in that equation is a poorly worded variable because out of all the variables that actually impact it, risk is the one that does not.

To be clear, higher risk investments do have a noticeable and calculable premium over low risk investments, even when adjusting for the actual risk taken.

This premium does exist, but it does not come from the increased “likelihood and degree of capital loss in an investment”.

This premium actually comes from variables that are correlated with the increased risk, such as:

• Investor Bias, often as a result of regulatory constraints limiting the level of risk funds can be exposed to

• Liquidity and subsequent spread premium

• Diversification bias

• Information premium

• Variance premium

None of those things are risk of capital loss, even if some investors believe them to be.

They do however tend to be positively correlated with risk, and subsequently are used by investors as a way to measure risk (incorrectly!).

What do I mean by this?

The CAPM Expected Return

The CAPM model uses the following formula to determine an expected return of an investment:

\(\begin{equation} \text{Expected Return} = \text{Risk-free Rate} + ( \text{Beta} * \text{Risk Premium}) \end{equation} \)

You may notice the similarities between this and the previous formula.

In essence what the CAPM model does is it estimates the individual risk premium for a given investment based on:

• The Undiversifiable Risk Premium

• The Beta

The Undiversifiable Risk Premium is a general market risk premium and the Beta is the variance of the asset compared to the general market from which you get the risk premium.

A simple way to understand it would be that if you’re calculating the return of a japanese stock, you simply measure the risk premium that the japanese stock market has, and then the variance of the company versus the japanese stock market.

The problem I have with this is simple:

• How do you calculate the actual “market risk premium”

• Why does variance over the market matter to the risk of that individual company?

The truth is, the “market risk premium” is often calculated as a “look back” estimate that does not really work well as a forward looking metric.

Additionally, I fundamentally do not like the variance as a matric for risk, let alone as a risk over/under a given metric.

The truth is, you can play games with variance, and its totally wrong when it comes to certain types of risk:

So what’s the alternative?

I don’t know.

Maybe you do? If so, do let me know in the comments down below!