The Equity Risk Premium and Risk Free-Rate

Junior (College 3rd year) ・Business ・APA ・6 Sources

Is there a need to have a return on investment? The question posed is among the typical issues that require analyzed answers from all perspectives. Most often investors have an obligation attached to their investment thoughts. The need is looking at what a specific investment will give in return for the sacrifice made. The risk premium adjusts significantly depending on the expected market return on equity assets and the risk-free rate. For a person to calculate the risk premium, various approaches are essential, and the best are those that tend to estimate it through the capital asset pricing model. Likewise, those that do not relate to the beta factor may be useful to implement the cost of capital.

The Historical Excess Returns

The risk premium estimate is either the historical excess returns and the implied cost of equity. The difference between the market returns and the risk-free rate obtained from the governments gives us the risk premium (Damodaran, 2009). The process of estimating the risk premium requires the use of backdating information (Cecchetti, Stephen, Pok-sang, and Nelson, 1993). The report must cover more than ten years. Estimating the annual excess returns, it requires one to obtain the average returns. The need incorporates the use of either the arithmetic mean or the geometric average. The most accurate is the arithmetic mean which requires the use of all the available data. The technical issues relating to the method makes it difficult to have reliable excess returns. The short-term returns would instead not give accurate results hence the use of long-term bonds of over ten years. Therefore, under the capital asset pricing model, it is essential to consider the historical excess returns to estimate the risk premium. The main advantage is that the method uses the excess returns to assess the risk premium. Therefore, if the market return is higher than the normal, then the risk premium is higher. The estimation error is as a result of the bias existing when choosing the data to use.

Estimating the Excess Returns

Evaluating the excess returns of an asset requires the presence of two variables. The first variable is the expected market return which is calculated by comparing the indexed stocks in the market. Secondly, the presence of a risk-free rate especially the rate of a riskless asset which is present. A riskless asset can be the government bond that promises hundred percent returns irrespective of the dynamics in the market. The difference between the return and the risk-free rate results to equity premium. In that case, we can estimate the excess returns using the formula below;

Risk premium= expected market return minus the risk-free rate

The arithmetic mean and geometric average gives an average of the returns over a specific duration, say, ten years. The excess return is as a result of the of the outcome from either arithmetic or geometric calculations.

The market-implied cost of equity

The method is significant and advantageous since it considers the required rate of return and the expected dividends. The Gordon growth model uses various variables including compounding factors to obtain the possible profits (Bansal, Ravi, and Wilbur, 1996). Therefore, the main aim is to achieve the future bonuses to compare them with the required rate of return. As long as the current or past dividends create a basis upon which future dividends have obtained, the calculation of the cost of equity is more straightforward. The presence of the market price and the dividends will affect the use of the method. Additionally, the growth rate helps to estimate the proportion with an inclusion of various factors that would arise in the future. The weighted cost of capital uses proportions hence computed as a percentage.

Estimating the Cost of Equity Using the Implied Cost of Equity Method

To estimate the rate it requires the use of the Gordon growth model that takes into account all the available variables. Such variables are the market price, dividends and the growth rate if the dividends are not constant hence need to grow Geyer, Alois, Stephan, and Stefan, 2004). The formula below devised by Gordon is applicable.

Where; Ke, is the cost of equity, Do, is the dividends previously paid, g, is the growth rate, Po, is the market price.

The growth rate implies that the dividends grow at a constant rate. Hence, the dividends today will not be the same dividends in the future. The market price reflects the factors that would make the economy rise or fall. In the long run, the cost is more reliable than that estimated considering the beta factor. The method does not recognize the existence of the beta factor and the risk-free rate.

Implementation of the Methods

The choice of the method to use depends on the nature of the market. The stocks attract dividends which are a measure of return on investment. In the presence of dividends then it is advisable to use the implied cost of capital to estimate the required rate of return. The Gordon model provides a basis for easy computation of the rate since it requires the presence of the dividends previously paid. Therefore, the cost of equity reflects all the present and future factors that would affect the market. The dividends and the market price give a result of a rate.

The historical excess returns are only applicable in circumstances where we can estimate the beta factor or the factor is already provided. Therefore, it will not be possible to use implied a cost of equity in such a situation. The computation of beta suggests that there is a measure of a particular risk in the investment. The Beta combines with the risk premium to give the required rate of return. The presence of bet is also accompanied by the risk-free rate and the expected market return. The method will only apply in such circumstance. Hence, the cost of equity method will be irrelevant.

The Risk-Free Rate

Return on Government Bonds

It is not easy to determine the risk-free rate due to the nature of the market. The changes bring about the difficulty and require more complex and technical information to be used. Three methods exist for estimation. The return on government bonds is a better estimator where the factors vary (Campbell, John, and Samuel, 2007). The government through its financial analysts decide on the rate based on the various reasons that would accompany the rate. The major drawback is that the risk-free rate may be estimated above or below the normal rate leading to overstatement or understatement. To the government, if it is an overstatement, then it stands to lose more money to the investment. If it is an understatement, then it will have a benefit of losing fewer amounts. If the rate is fixed at a specific point, then it means that irrespective of the changes in the market the investors are subject to constant returns. Similarly, if the changes affect the market negatively, then it would be advantageous to the investors since they have a guarantee on the returns.

The return on government securities method considers the changes that would arise in the market due to various reasons. The interest rates change depending on the factors that would affect the market such as inflations and political instability. The return incorporates the impact of the changes in the interest rates of the bonds. The return is reinvested at the same rate hence promising a higher return. The return is affected by this factors, and the rate includes the changes.

Synthetic Risk-free Rate

The calculation of the rate depends on the market factors and the individual asset. When computing the rate, two variables are important and must be included to give an accurate outcome. The variables are the long stocks and the indices. The difference between the long stock and stock index futures. In other words, the underlying assets provide the basis for the computation of the risk-free rate. The drawback of the method is that the rate has to be computed from the long stock which may not be very accurate due to competition and changes in the stock market.

Yield on Government Bonds

The yield on government bonds can create an efficient risk-free rate. The rate is the return required from the government bond at a future date but discounted to give the equivalent rate at present (McInnis, 2010). The rate gives an accurate proportion that reflects the investor's returns.

The implementation is quite straightforward. The only requirement is to wait for the government to issue the bonds. After that, the organizations can apply the rate in the capital asset pricing model especially to obtain the risk premium and then the required rate of return.

The yield on government securities varies from one country to another. The financial crisis led to many changes in the finance field and the stock markets. The government securities could be overvalued hence creating a big problem. In the United States the yield is 2.33% higher than in the United Kingdom and Germany. Due to the crisis, the interest rates have decreased, and the bond yields have fallen too. Therefore, overvaluation of the bonds is a potential problem.


In conclusion, the choice of the method depends on the target analysis. The implied cost of equity is effective in circumstances where previous dividends and the market price exist. Hence, to determine the cost of equity is the division of the dividends with the market price. The historical excess returns approach will require the inclusion of the beta factor to help in estimating the risk which is a major drawback. In most countries, the recognized risk-free rate is the rate attached to government bonds. The reason is that the state will always compensate the investor hence he will recover his investment. The weighted cost of capital incorporates several variables that must be known with certainty. The cost of each source of finance and the weight of each source of finance are the variables to obtaining the cost of capital.

Works Cited

Bansal, Ravi, and Wilbur John Coleman. ""A monetary explanation of the equity premium, term premium, and risk-free rate puzzles."" Journal of Political Economy 104.6 (1996): 1135-1171.

Campbell, John Y., and Samuel B. Thompson. ""Predicting excess stock returns out of sample: Can anything beat the historical average?."" The Review of Financial Studies 21.4 (2007): 1509-1531.

Cecchetti, Stephen G., Pok-sang Lam, and Nelson C. Mark. ""The equity premium and the risk-free rate: Matching the moments."" Journal of Monetary Economics 31.1 (1993): 21-45.

Damodaran, Aswath. ""Equity Risk Premiums (ERP): Determinants, Estimation and Implications–A Post‐Crisis Update."" Financial Markets, Institutions & Instruments 18.5 (2009): 289-370.

Geyer, Alois, Stephan Kossmeier, and Stefan Pichler. ""Measuring systematic risk in EMU government yield spreads."" Review of Finance 8.2 (2004): 171-197.

McInnis, John. ""Earnings smoothness, average returns, and implied cost of equity capital."" The Accounting Review 85.1 (2010): 315-341.

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