## What is Equity Risk Premium in CAPM?

Equity Risk Premium is the return offered by individual stock or overall market over and above the risk-free rate of return. The premium size depends on the level of risk undertaken on the particular portfolio and higher the risk in the investment higher will be the premium. This risk premium also changes over time with respect to the fluctuations in the market.

### Equity Risk Premium Formula in CAPM

For calculating this, the estimates and judgment of the investors are used. The calculation of the Equity risk premium is as follows:

Firstly we need to estimate the expected rate of return on stock in the market, then the estimation of risk-free rate is required and then we need to deduct the risk-free rate from the expected rate of return.

**Equity Risk Premium Formula:**

**Equity Risk Premium Formula = Market Expected Rate of Return (R _{m}) – Risk Free Rate (R_{f})**

The stock indexes like Dow Jones industrial average or the S&P 500 may be taken as the barometer to justify the process of arriving at the expected return on stock on most feasible value because it gives a fair estimate of the historic returns on stock.

As we can see from the formula above that the market risk premium is the excess return that the investor pays for taking the risk over the risk-free rate. The level of the risk and the equity risk premium are correlated directly.

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Let’s take the example of a government bond which is giving a return of 4% to the investor, Now in the market the investor will definitely choose a bond which will give a return greater than 4%. Suppose an investor chose a stock of the company giving a market return of 10%. Here the equity risk premium will be 10%- 4% = 6%.

### Interpretation of Equity Risk Premium in CAPM

- We know the level of risk associated with the debt investment like investment in bonds is usually lower than that of the equity investment. Like that of preferred stock, there is no surety of receiving the fixed dividend from the investment in equity shares as the dividends are received if the company earns the profit and the rate of dividend keeps on changing.
- People do investment in the equity shares in the hope that the value of the share will increase in near future and they will receive higher returns in long term. Yet there is always a possibility that the value of a share may decrease. This is what we call the risk which an investor takes.
- Moreover, if the probability of getting a higher return is high then the risk is always high and if the probability of getting a smaller return is high then the risk is always lower and this fact is generally known as risk-return trade-off.
- The return that can be received by an investor on a hypothetical investment without any risk of having financial loss over a given time period is known as the risk-free rate. This rate compensates the investors against the issues arising over a certain time period like inflation. The rate of the risk-free bond or government bonds having long term maturity is chosen as the risk-free rate as the chance of default by the government is considered to be negligible.
- The riskier the investment, the more is the return required by the investor. It depends upon the requirement of the investor. Risk-free rate and equity risk premium help in the determining of the final rate of return on the stock.

### Equity Risk Premium for US Market

Each country has a different Equity Risk Premium. This is primarily denotes the premium expected by the Equity Investor. For the United States, Equity Risk Premium is **6.25%.**

source – stern.nyu.edu

- Equity Risk premium = Rm – Rf = 6.25%

### Use of Equity Risk Premium in the Capital Asset Pricing Model (CAPM)

The model of CAPM is used for establishing the relationship between the expected return and the systematic risk of the securities of the company. CAPM model is used for pricing of risky securities and also for calculating the expected return on investment with the use of risk-free rate, expected rate of return in the market and the beta of the security.

The equation for CAPM:

Expected Return on security = Risk-free rate + beta of security (Expected market return – risk-free rate)

= R_{f} +(Rm-Rf) β

Where R_{f} is the risk-free rate, (R_{m}-R_{f}) is the equity risk premium and β is the volatility or systematic risk measurement of the stock.

In CAPM, to justify the pricing of shares in diversified portfolio, It plays an important role in as much as for the business wanting to attract the capital it may use a variety of tools to manage and justify the expectations of the market to link with issues such as stock splits and dividend yields etc.

### Example

Suppose the rate of return of the TIPS (30 years) is 2.50% and the average annual return (historical) of S&P 500 index be 15%, then using the formula equity risk premium of the market would be 12.50% (i.e., 15% – 2.50%) = 12.50%. So here the rate of return which the investor require for investing in the market and not in the risk-free bonds of the Government will be 12.50%.

Apart from the investors, the managers of the Company will also be interested as the equity risk premium will provide them with the benchmark return which they should achieve for attracting more investors. Like for instance, one is interested in XYZ Company’s equity risk premium whose beta coefficient is 1.25 when the prevailing equity risk premium of the market is 12.5% then he will calculate Company’s equity risk premium using the details given which comes to 15.63% (12.5% x 1.25). This shows that the rate of return which XYZ should generate should be at least 15.63% for attracting investors towards the Company rather than risk-free bonds.

### Advantages and Drawbacks

Using this premium one can set the expectation of portfolio return and also determine the policy related to asset allocation. Like, the higher premium shows that one would invest a greater share of his portfolio into the stocks. Also, CAPM relates the expected return of the stock to equity premium which means that stock which has more risk than of market (measured by beta) should provide an excess return over and above equity premium.

On the other side, the drawback includes the assumption used that stock market under consideration will perform on the same line of its past performance. No guarantee is there that prediction made will be real.

### Conclusion

This gives the prediction to the stakeholders of the company that how the stocks with high risk will outperform when compare with less risky bonds in the long-term. There is a direct correlation between risk and the Equity risk premium. Higher the risk is higher will be the gap between the risk-free rate and the stock returns and hence premium is high. So it is a very good metric to choose stocks which are worth for the investment.

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