Market Risk Premium (Formula, Examples) | Calculate Market Risk Premium

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Market risk premium is the additional rate of return over and above the risk-free rate, which the investors expect when they hold on to the risky investment. This concept is based on the CAPM model, which quantifies the relationship between risk and required return in a well-functioning market.

Cost of Equity CAPM formula = Risk-Free Rate of Return + Beta * (Market Rate of Return – Risk-free Rate of Return)
here, Market Risk Premium Formula = Market Rate of Return – Risk Free Rate of Return.

In this article, we look at this in detail –

What is Market Risk Premium?
Formula
Interpretation
Calculation Examples
Limitations

What is the Market Risk Premium?

The difference between the expected return from holding an investment and the risk-free rate is called as a market risk premium.

To understand this, first, we need to go back and look at a simple concept. We all know that greater risk means greater return, right? So, why it wouldn’t be true for the investors who have taken a mental leap from being savers to investors? When an individual saves the amount in Treasury bonds, he expects a minimum return. He doesn’t want to take more risk, so he receives the minimum rate. But what if one is ready to invest in a stock, won’t he expect more return? At least he would expect more than what he would get by investing his money in Treasury bonds!

And that’s where the concept of market risk premium arrives. The difference between the expected rate of return and the minimum rate of return (which is also called risk free rate) is called market premium.

Market Risk Premium Formula

The Market risk premium formula is simple, but there are components we need to discuss.

Market Risk Premium Formula = Expected Return – Risk-Free Rate

Now, let’s take each of the components of the market risk premium formula and analyze them.

First, let’s think about the expected return. This expected return is totally dependent on how an investor thinks. And what is the type of investments he invests in.

There are following options that we can consider from the point of view of the investors –

Risk-tolerant investors: If the investors are players of the market and understand the ups and downs and are okay with whatever risks they need to go through, then we will call them risk-tolerant investors. Risk-tolerant investors won’t expect much from their investments and thus, the premiums would be much lesser than the risk-averse investors.
Risk-averse investors: These investors are usually new investors and have not invested much in risky investments. They have saved over their money in fixed deposits or in savings bank accounts. And after thinking over the prospects of investment, they start to invest in stocks. And thus, they expect much more return than the risk-tolerant investors. So, the premium is higher in case of risk-averse investors.

Now, premium also depends on the type of investments the investors are ready to invest in. If the investments are too risky, naturally the expected return would be much more than the less risky investments. And thus, the premium would also be more than the less risky investments.

There are also two other aspects we need to consider here while calculating the premium

Required Market Risk Premium: This is the difference between the minimum rate the investors may expect from any sort of investment and the risk free rate.
Historical Market Risk Premium: This is the difference between the historical market rate of a particular market, e.g. NYSE (New York Stock Exchange) and the risk free rate.

Interpretation of Market Risk Premium

Market risk premium model is an expectancy model because both of the components in it (expected return and risk free rate) are subject to change and are dependent on the volatile market forces.)
To understand it well, you need to have a basis of computing the expected return so as to find the figure for market premium. And the basis you choose should be relevant and aligned with the investments that you have done.
In normal situations, all you need to do is to go for the historical averages to use as your basis. If you invest in NYSE and you want to calculate market risk premium, all you need to do is to find out the past records of the stocks you have decided to invest in. And then find out the averages. Then you would get a figure that you can bank upon. Here one thing you need to remember is that by taking historical figures as the basis, you are actually assuming that the future would be exactly like the past which may turn out to be flawed.

What would be the right market risk premium calculation which would not be flawed and would be aligned with the current market condition? We need to look for Real Market Premium then. Here’s the Real Market Risk Premium formula –

Real Market Risk Premium formula = (1 + Nominal Rate / 1 + Inflation Rate) – 1

In the example section, we will understand everything in detail.

According to Economists, if you want to base your decision on the historical figures, then you should go for a long-term perspective. Because if the premium is beyond 6%, it is way beyond that the actual figures. That means if you take a long-term perspective, it would help you to find out an average premium which will be closer to the actual one. For example, if we look at the average premium of the USA over the period of 1802 to 2008, we would see that the average premium is mere 5.2%. That proves a point. If you want to invest in a market, go back and look at the historical figures for more than 100 years or as many years as you can and then decide upon on your expected return.

Market Risk Premium Calculation Example

Let’s get started with a simple one and afterward we will go to complex ones.

Example # 1 (Market Risk Premium Calculation)

Let’s have a look at the details below –

In percentage	Investment 1	Investment 2
Expected Return	10%	11%
Risk free rate	4%	4%

In this example, we have two investments and we have also been provided with the information for expected return and risk free rate.

Now, let’s look at market risk premium calculation

In percentage	Investment 1	Investment 2
Expected Return	10%	11%
(-) Risk free rate	4%	4%
Premium	6%	7%

Now, in most of the cases, we need to base our assumptions for expected return on historical figures. That means whatever the investors expect as a return that would decide the rate of premium.

Let’s have a look at the second example.

Example # 2 (Equity Risk Premium Calculation)

Market Risk Premium and Equity Risk Premium is different in scope and conceptually, but let’s have a look at equity risk premium example as well as equity can be considered one type of investment as well.

In percentage	Investment
Large Company Stocks	11.7%
US Treasury Bills	3.8%
Inflation	3.1%

Now, let’s have a look at the equity risk premium. Equity risk premium is the difference between the expected return from the particular equity and the risk free rate. Here let’s say that the investors expect to earn 11.7% from a large company stock and the rate of US Treasury Bill is 3.8%.

That means the equity risk premium would be as follows –

In percentage	Investment
Large Company Stocks	11.7%
(-) US Treasury Bills	3.8%
Equity Risk Premium	7.9%

But what’s about the inflation? What would we do with the inflation rate? We will look at that in the next real market risk premium example.

Example # 3 (Real Market Risk Premium Calculation)

In percentage	Investment
Large Company Stocks	11.7%
US Treasury Bills	3.8%
Inflation	3.1%

Now we all know that it is the expectancy model and when we need to calculate it, we need to take historical figures in the same market or for the same investments so that we can get an idea what to perceive as expected return. There lies the importance of real premium. We will take into account the inflation and then compute the real premium.

Here’s the real market risk premium formula–

(1 + Nominal Rate / 1 + Inflation Rate) – 1

First, we need to compute the nominal rate, i.e. normal premium –

In percentage	Investment
Large Company Stocks	11.7%
(-) US Treasury Bills	3.8%
Premium	7.9%

Now we will take this premium as nominal rate and will find out the real market risk premium.

Real Premium = (1 +0.079 / 1 + 0.031) – 1 = 0.0466 = 4.66%.

It is useful because of two particular reasons –

First, real market premium is more practical from the perspective of inflation and real life data.
Second, there is little or no chance of expectation failure when the investors would expect something like 4.66%-6% as expected return.

Limitations of Market Risk Premium Concept

This concept is an expectancy model, thus it can’t be accurate most of the time. But equity risk premium is much better concept than this if you are thinking of investing in stocks (there are many approaches from which we can calculate this). As of now, let us look at the limitations of this Concept –

This is not accurate model and the computation depends on the investors. That means too many variables and too little basis of proper computation.
When market risk premium calculation is done by taking into account the historical figures, it’s assumed that the future would be similar as the past. But in most cases, that may not be true.
It doesn’t take into account the inflation rate. Thus, the real risk premium is a much better concept that market premium.

Market Risk Premium