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## Risk Premium Definition

The risk premium is the minimum amount of money that a person is willing to accept as compensation for taking on a risky or volatile investment.

So, in investing, it is **the minimum amount of money by which the expected return on a risky investment exceeds the known return on a non-risky asset. **

A risk premium is a sort of hazard pay for your investments. Riskier investments – typically the more volatile ones – have to provide investors with the potential for higher gains than those that are risk-free, in order to convince the investors the risk is worthwhile.

Please note that the estimated return is not always the same as the returns that will eventually be realized. In some cases, such as zero coupon bonds, the expected return is well defined. In other cases, for example an equity stock, the expected return is implicit in how the market prices the asset.

## Types of Risk Premium

There are a few categories of risk premiums that describe various types of risk.

### Liquidity Risk

This is the premium that investors request in exchange for being given a security that is illiquid – that is, it can’t be easily converted into cash at its market value [see: liquid stocks].

### Default Risk

This is the amount that a borrower has to pay to a lender to compensate them for assuming the risk of the borrower defaulting on their debts. Typically, the U.S. government is exempt from this premium. The US debt obligations are generally treated as risk free due to the ability of the government to freely print additional money to satisfy their obligations.

### Country Risk

The additional risk that an investor assumes by investing in international companies instead of the domestic market. There are a lot of other factors that come into play when dealing with international investments, including political instability, changing exchange rates and more.

### Market Risk

The difference between the expected return on a market stock portfolio and the return on a risk-free option, like government treasury bonds. It’s calculated by looking at the slope of the security market line, which is a graph of the capital asset pricing model.

### Equity Risk

This is the excess return that an investor can hope to get from investing in a given stock over low-risk options like government treasury bonds. It can only be estimated, since no one can entirely predict exactly how well a stock will fare. For example, beta risk.

## Calculating Risk Premium

There are three steps to calculating risk premium:

**1. Estimate the Expected Returns on an asset**

**2. Estimate the Expected Returns on a Risk-Free Bond**

**3. Subtract the Difference Between the Two**

Therefore,

*Risk Premium = E(r) – R _{f}*

where E(r) is the Expected Return and R_{f} is the risk free rate

## Using Risk Premium for CAPM Valuations

Capital Asset Pricing Model or CAPM defines the required return for an equity in terms of the risk premium and risk free rate. The CAPM formula states:

CAPM = R_{f} + β x Market Risk Premium

The CAPM rate can then be used to calculate the value of an asset based on the future cash flows.

An astute reader will take the 2 formulas above and deduce that Expected Return of an Equity = β x Market Risk Premium.

This is correct.

This type of valuation requires accurate estimate of the future cash flows which can be hard to get.

## Implied Cost of Capital to Calculate the Equity Premium

There are alternative methods developed to calculate the expected return, and therefore the equity risk premium. Implied Cost of Capital is one such method. The implied cost of capital (ICC) for a given asset can be defined as the discount rate (or internal rate of return) that equates the asset’s market value to the present value of its expected future cash flows.