Risk Managent

Risk Management - Part D

Manolis Anastopoulos @ University of Leicester - Risk Management

3. Capital Asset Pricing Model

William Sharpe in 1964, and others, took the previous work further, by formalizing the Capital Asset Pricing Model (CAPM), which showed how the market must price individual securities in relation to the market portfolio. More specifically, their model – the CAPM – as stated in (Friedman 1987), ‘describes the relationship between the expected risk and expected return’. This model – the CAPM, can be used both as apricing model that predicts an asset’s required rate of return, and as a technique in the cost of equity analysis[1], as well.

The formula that generally describes the aforementioned relationship-the CAPM, is the following:

Rk = Rf + (Rm – Rf ) x beta

Rk = The required (expected) rate of return

Rf = The rate of a risk-free investment, i.e. cash

Rm = The market return

Beta =The price of the beta coefficient


Assuming we have a stock with a beta of 0.8, we would expect a rate of return (Rk) of 12.6% if the rate of the risk-free investment (Rf) is 7% and the market return (Rm) is 14%. It is worth noticing that because the stock’s beta is 0.8 (less than zero) the stock’s expected rate of return (Rk) is 12.6%, which is less compared to the market’s return (Rm = 14%). Conversely, if the beta is greater than 1, say 1.4, which determines a more risky stock than the market (beta =1), then the Rk would be 16.8%, which is higher compared to the market’s return (Rm = 14%).

The above mentioned higher rate compared to the market rate, is what such an investor actually requires because of the extra risk that he undertakes when choosing a stock with a beta greater than 1.

3.1 Beta Coefficient

The beta coefficient, as stated in their book (Gitman & Madura 2001), ‘Is a relative measure of non-diversifiable risk’. The beta is the covariance of a stock’s return in relation to the whole stock market’s return and it is measured by the R-square. As it is known, the R-square measures the degree of response between the independent and dependant variable, e.g. between the whole market return and a company’s share return.

When we consider ‘the whole stock market’s return’, we can refer, for example, to the General Index of the Athens Stock Exchange (with a beta coefficient of 1), which is a good indicator of the whole stock market’s behavior.

Stocks with beta higher than 1, are more volatile than the market and, consequently, are more risky. Conversely, stocks with beta lower than 1, are less volatile than the market and less risky, as well.

As a result, it can be argued that high-beta shares, due to their potential of higher-than-market returns, usually ‘attract’ investors willing to risk. Unfortunately, the expected higher-than-market return would be worked against the investor, i.e. a- less- than market return, should the stock market decline.

In conclusion, beta can be used to predict the volatility of a stock’s price related to the market risk, i.e. the systematic or the non-diversifiable risk. However, we should not forget that in order to find the beta coefficient, we have actually relied on past comparisons between company’s share return and the market return, which does not necessarily  predict accurately the future behavior of the company’s share.

4. Usefulness and Limitations of the Portfolio Theory and CAPM

Undeniably, the Portfolio Theory that later evolved into Modern Portfolio Theory introduced significant tenets of modern finance. The concepts below mentioned are still regarded as dominant tools for the current portfolio managers.

  1. The concept of diversification clarified to potential investors that by increasing the number of stocks or assets in their portfolios, they are actually reducing the non-systematic risk that is associated with each individual asset or, in other words, they are reducing their uncertainty. As a result, the overall risk of their portfolio can approach more closely the systematic risk, i.e. the market’s risk.
  2. Diversification is attainable, not only by increasing the number of shares, but also by including different assets in portfolios. In such a case, the result would be the same, i.e. to change in the investor’s favor the relationship between return to risk.
  3. Another important rule that followed the introduction of diversification was the concept of correlation, which enables prospective fluctuations of individual securities to cancel each other to a satisfactory extent.
  4. The Portfolio Theory by using statistical tools - standard deviation or coefficient of variation – managed to measure the volatility. Thus, both the risk-averse investors and those willing to risk were able to trace, through quantitative data, those portfolios that matched their desire for the undertaken risk in respect to the expected return.
  5. As a result, the efficient portfolio that succeeds the highest average rate of return for a given level of risk or, in other words, portfolio that ‘optimally’ balance risk and return, had been born. Thus, investors, for any given value of volatility (risk) can choose an optimal portfolio that gives them the greatest possible rate of return.
  6. Finally, through the analysis of the efficient frontier and the capital market line, the ‘target’ of all investors was determined as the point where the capital line touches the ‘original’ efficient frontier, which represents an identical portfolio - the market portfolio.

Undoubtedly, Markowitz was the first who actually quantified the risk. William Sharpe, Lintner, Mossin, and Famma in 1964 took the Markowit’z work further, by formalizing the Capital Asset Pricing Model (CAPM), which showed the relationship between individual securities in relation to the market portfolio.

More specifically, the CAPM contributes to the following:

  1. The introduction of the CAPM separated the non-systematic risk- the risk incorporated in each individual security, and the systematic risk, or market risk- the risk that affects all equities.
  2. According to CAPM, all investors should hold the market portfolio, leveraged or deleveraged with positions in the risk-free assets.
  3. The formula that describes the CAPM introduced the beta coefficient which actually is the covariance of a stock’s return in relation to the whole stock market’s return.
  4. Since it had already been proved that a number of about 20 shares were sufficient to significantly reduce the risk that was possible to eliminate, i.e. the non-systematic risk, leaving only the systematic risk to affect the diversified portfolio.
  5. Finally, the CAPM offers to investors a ‘quantified’ relationship between risk and return and thus enables them to ‘require’ an expected rate of return for any given level of risk, also offering companies a useful ‘tool in the cost of equity analysis.

Despite the usefulness of the aforementioned concepts, there have been many necessary assumptions in order to conclude to the aforesaid results.

More specifically, we can refer to the following assumptions:

  1. The theory in question, as well the associated models, are based on the hypothesis of an efficient market, which, among others, prerequisite:
    • The existence of many small investors, that is to say, ‘price takers’.
    • All investors have the same level of economic knowledge. They also all have free access to all information, which is not the case.
    • There is no restriction on investments, no taxes, and no transaction cost, which certainly does not respond to the real business environment.
    • All investors make their decisions under the principle of the ‘rational’ behavior or, in other words, they are all behaving as risk-averse investors who prefer higher return and lower risk. However, this is contentious. To give an example, we can refer to those people who like to bet, which indisputably does not characterize a risk-averse investor.
  2. Investors have the same investment horizon, which is far from certain. For example, we can refer to investors who are ‘expecting’, say a 15% return from a share, while others would be satisfied having such a return after 2 or 3 years time.
  3. Investors’ target is to maximize the utility of wealth. This is not unrealistic as it is known from the economic theory – consumer behavior.
  4. All the investors use the same ‘tools’ in order firstly, to measure the volatility (risk), i.e. the standard deviation of return, and secondly, to measure the return. However, this is implausible because investors are likely to have different ‘opinion’ about the future rates of the ‘tools’ in question.
  5. The likelihood that all investors can lend and borrow any desired amount of funds at the risk-free interest rate. Certainly, this is not case. For example, a huge multinational company can, undoubtedly, much more easily, negotiate the terms of a loan, e.g. the interest rate, than a small domestic one.
  1. In practice, investors take into consideration the historically determined betas, which does not necessary reflect their future value. Therefore, it would be better to consider the required return, which is specified by the model, as a rough estimation of the actual one.

[1] The CAPM return is a good indicator regarding the company’s cost of equity capital (having first deducted the relevant taxes).


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