## Executive Summary

Used by investors to establish relationship between expected return on investment in asset or security and the risk. It assumes that taxes do not exist in the market and transaction costs are not incurred. CAPM also assumes that investors borrow at risk free rate and uses the beta coefficient to measure volatility of the security. CAPM has several applications including capital budgeting, portfolio analysis and decision making in strategic planning.

The technique is based on risk which can either be diversifiable or non-diversifiable risk. Several criticisms have been laid out with reference to the assumptions made.

The most important factor is that CAPM considers systematic risk, which reflects the general position of investors who have diversified portfolios. This paper outlines the types of risk and assumptions of the capital asset pricing model as well as demonstrating an application of the CAPM equation using a simple example.

## Introduction

The capital asset pricing model, commonly referred to as CAPM, is a tool used by organizations and investors to analyze returns based on risks taken in certain investments within the market. It provides the rate of return on assets which an investor has interest in. The rate of return represent the value that the organization or investor expects to achieve based on the risk undertaken.

It basically seeks to establish the value of an asset based on risk and returns. The capital asset pricing model is based on several assumptions and equally has many applications with regards to a company or organizations investment options.

## Risk and CAPM

Investment in any financial asset usually presents some level of risk. This risk is classified as either diversifiable or non-diversifiable risk. Diversification is aimed at reducing risks that an investment or asset is likely to experience. This is undertaken by adding more stocks or investment portfolios that have minimal correlation to avoid being affected equally by the same type of risk.

For investors, this tool is particularly important as it is used to calculate the returns on risky investment portfolios. What an investor eventually earns is dependent on the level of systematic risk that they undergo.

## Diversifiable Risk

Diversifiable risk is often referred to as controllable risk as they are company specific risks which are unique to the company. Random occurrences within the firm lead to diversifiable risks. These range from strikes by employees, lawsuits and poor managerial practices.

This implies that the risk that the investor is willing to encounter can be eliminated through diversification as this risk can be easily mitigated due to the fact that it is within the firms’ control. This is attributed to the uniqueness of the risk as opposed to the economy wide or market wide effects. Diversification ensures that the firm develops a portfolio of many assets to eliminate unsystematic risk (Brigham & Houston, 2009).

## Non-diversifiable Risk

A non-diversifiable risk is a risk on an investment that cannot be cushioned by diversification. It is a result of an economy wide effect which is beyond the control of the company hence cannot be easily mitigated. Non-diversifiable risk occurs as a result of uncertainty like war, inflation, foreign investment policies, taxation and recessions hence affecting the value of investments made by investors due to changes in the market (Bogdan & Villiger, 2010).

## Assumptions of CAPM Technique

The capital asset pricing model is based on several assumptions as indicated below. However these assumptions may not always reflect the current state or performance of the market.

- Taxes do not exist: CAPM is calculated under the assumption that there are no taxes. This implies that any form of investment undertaken is free from tax and equally the returns generated are not liable to taxation. However, this is not always the case in the market arena. Most countries subject investments to taxation. The existence of taxes reduces the value of the expected returns.
- Costless transactions: CAPM assumes that transactions are costless hence assuming that assets are divisible without incurring transactions costs. The criticism with this assumption is with regard to the fact that any form of investment will include a certain transaction cost and this is evident even in the acquisition of any business entity.
- Efficiency of markets: CAPM sets prices of assets based on the assumption that markets are efficient. This means that the market is considered competitive in terms of the securities being traded and no investor dictates the prices, rather they are all price takers.
- Similar investor expectations: CAPM assumes that investors within a certain period have similar expectations of returns and the risk of security. This may not always be the case, like in a classic example of an investor who wants to undertake purchase of stocks and another who wants to set up a manufacturing plant for crude oil. Their expectations cannot be considered homogenous. Investors cannot have similar estimates based on investments on assets.
- The quantity of securities is fixed: CAPM assumes that the quantity of securities remains unchanged within a certain period.
- Investors borrow at a risk-free rate: CAPM assumes that investors can borrow and lend funds at a risk free rate. This means that investor portfolios reflect risky assets.
- Use of Beta: CAPM assumes beta as a measure of risk and does not factor in other risks, like devalued investments, arising from inflation.

## Applications of CAPM

There are several applications of the CAPM technique ranging from capital budgeting, analysis of merger acquisitions, strategic planning, portfolio analysis and valuation of securities. CAPM is equally relevant to corporations in terms of the fact that it assists in calculating the equity cost of capital. CAPM serves in pricing assets hence making this tool important for the evaluation of stock corporations (Pahl, 2009).

In the event that a corporation has invested in one project, the risks likely to be experienced will pertain to that specific project. In the event that in engages in more than one investment, risks will emanate from all the investments undertaken by the firm.

Therefore for the sake of investment appraisal, CAPM becomes a handy tool for organizations. CAPM thereby provides investors and corporations empirical evidence pertaining to support their investment moves (Karen, 2003).

## The CAPM Equation

The CAPM equation computes the required return of an asset based on the beta co-efficient, the risk free rate and the expected return on market portfolio as indicated in the formula below (Baker & Powell, 2009).

**Expected Return= r _{f} + β (r_{m}– r_{f})**

Where:

r_{f- }Risk Free Rate

β- Beta

r_{m- }Expected Return on Market Portfolio

The Beta coefficient represents the measure of assets volatility with relation to the market position. It measures non-diversifiable risk. An example of the CAPM Technique is demonstrated below.

Find the expected rate of return on the market portfolio given that the expected rate of return on asset “X” is 12%, the risk-free rate is 4%, and the Beta (β) for asset “X” is 1.2. Subsequently, find the risk-free rate given that the expected rate of return on asset “Z” is 9%, the expected return on the market portfolio is 10%, and the Beta (β) for asset “Z” is 0.8.

### Solution

**Computing the Expected Rate of Return on Market Portfolio**

Expected Return= r_{f} + β (r_{m}– r_{f})

**r**_{f}_{– }4%

**β**– 1.2

Expected Return= 12%

**r**_{m}_{– }?

Substitute

12%= 4% + 1.2 (r_{m}** –**4%)

Finding r_{m} will give 0.11 hence r_{m} is 11%

**Computing the Risk Free Rate**

Expected Return= r_{f} + β (r_{m}– r_{f})

**r**_{f}_{– }?

**β**– 0.8

Expected Return= 9%

**r**_{m}_{– }10%

### Substitute

9%= r_{f} +0.8(10% – r_{f})

Finding r_{f} will give 0.05 hence r_{f} is 5%

## Conclusion

In conclusion, capital asset pricing model as a tool may not be reliable due to the assumptions which it is based on. One major criticism is that in the real market arena, investors cannot borrow at risk free rates. Furthermore, CAPM relies heavily on historical figures of return and this may not always serve as an efficient way to predict the future.

## Recommendations

The CAPM technique is therefore considered reliable for determining which investment portfolio an investor can channel funds based on identification of risk. Furthermore, the senior management of firms can rely on the technique to determine decisions relating to mergers and acquisitions as well as which options the firm can undertake to grow with regards to investment.

## References

Baker, H. K & Powell, G. (2009). *Understanding Financial Management: A Practical Guide*. Massachusetts, USA: John Wiley & Sons.

Bogdan, B. & Villiger, R. (2010). *Valuation in Life Sciences: A Practical Guide*. New York, USA: Springer.

Brigham, E.F. & Houston, J.F. (2009). *Fundamentals of Financial Management*. Ohio, USA: Cengage Learning.

Karen, F.R. (2003). *A Blueprint for Corporate Governance: Strategy, Accountability, and the Preservation of Shareholder Value*. New York, USA: AMACOM.

Pahl, N. (2009). *Principles of the Capital Asset Pricing Model and the Importance in Firm Valuation.* Norderstedt, Germany: Grin Verlag.