The CAPM has been described as the most widely used model in explaining the relationship between the risk and returns of financial investments. Discuss the theoretical and empirical considerations surroundings the CAPM.
The CAPM has been described as the most widely used model in explaining the relationship between the risk and returns of financial investments. Discuss the theoretical and empirical considerations surroundings the CAPM.
In the 1960's financial researchers working with Harry Markowitz's portfolio theory made a remarkable discovery that would change investment theory and practise throughout the world. William Sharpe based his discovery upon an idealised model of the markets, in which all the worlds risky assets were included in the investors opportunity set and one risk less asset existed, allowing both more and less risk averse investors to find their optimal portfolio.
The capital asset pricing model (CAPM) was a breakthrough in modern finance because for the first time a model became available which enabled academics, financiers and investors to link the risk and return for an asset together, and which explained the underlying mechanism of asset pricing in capital markets. The impact of the CAPM has been immense and it is one of the most influential financial concepts in recent financial history.
All financial decisions contain a risk-element and a return element and that there is always a trade-off between these two elements: the higher the risk, the higher will be the required return and vice versa. The CAPM was the first method of formally expressing the risk-return relationship, it brought together systematic risk and return for all assets.
The total risk of a security or a portfolio of securities can be split into two specific types, systematic risk and unsystematic risk, this can be referred to as risk partitioning:
Total Risk = Systematic Risk + Unsystematic Risk.
Systematic risk cannot be diversified away. It is the risk, which arises from market factors, such as general or macroeconomic conditions (e.g. inflation and interest rates).
Unsystematic risk can be diversified away by creating a large enough portfolio of securities. It is the risk, which relates, or is unique to a particular firm (e.g. factors such as winning a new contract).
The relationship between total portfolio risk and portfolio size can be seen diagrammatically in Figure 1
Figure 1
Figure 1 shows that total risk diminishes as the numbers of securities in the portfolio increases, also it can be seen that unsystematic risk does not disappear completely and that systematic risk remains unaffected by portfolio size.
The CAPM brings together systematic risk and return for a security or portfolio of securities. Only systematic risk is relevant as investor generally create a sufficiently large portfolio of securities and unsystematic risk can be virtually eliminated through diversification. It is the measurement of systematic risk, which becomes critical in the CAPM because the model relies on the assumption that investors will only hold well-diversified portfolios.
The standard deviation (?) is used to measure shares total risk, while the beta coefficient, (?) in contrast is used to measure only part of a share portfolio's risk, which is the systematic risk.
Beta is a measure of the sensitivity or volatility of an individual security's or portfolios return (capital gains plus dividends) in relation to changes in the overall capital market return. In the CAPM market return is the return (capital gain plus dividends) from the market portfolios. The market portfolio is a theoretical concept, which in theory should include every conceivable security traded in the capital market in proportion to its market value.
In practice the market portfolio would be impossible to achieve, so a sufficiently large stock market index such as the FTSE 100 share index is substituted for the market portfolio.
Share can be broadly classified as aggressive, average or defensive according to their beta vales.
Shares with a beta > 1 is described to be aggressive. The shares are more risky than the market average and consequently investor would require a rate of return from the share, which is greater than the market average.
Shares with a beta = 1 is described to be average as their rate return moves in exact harmony with movements in the stock market average return, they are of average risk and yield average returns.
In contrast, shares with a beta < 1 are classed as defensive. A defensive share does not perform well in ...
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Shares with a beta > 1 is described to be aggressive. The shares are more risky than the market average and consequently investor would require a rate of return from the share, which is greater than the market average.
Shares with a beta = 1 is described to be average as their rate return moves in exact harmony with movements in the stock market average return, they are of average risk and yield average returns.
In contrast, shares with a beta < 1 are classed as defensive. A defensive share does not perform well in a bull market,
A share's beta is determined from the historical values of the share's returns relative to market returns, therefore that beta is a relative measure of risk. As individual beta is derived from a common base, beta is a standardised risk measure, i.e. this makes the beta of one share directly comparable with beta of another share.
One way of determining the beta for a share is to plot on a graph the historic relationship between the movement in the share's return and the market returns over a defined period of time. Conventionally the markets returns are plotted on the horizontal (x) axis and the individual share returns on the vertical (y) axis. The result almost certainly will appear in the form of a scatter diagram and by the use regression analysis a regression line can be derived through the data. The regression line is the straight line that best represents the shares return and the return from the market over the period. Beta is the slope of this regression line. Shares with high betas will have steeper sloped regression lines than those with low betas, and the steeper the slope of the line the more volatile are the returns from the share in relation to the returns from the market.
Alternative derivation of beta is by the use of historic data on individual share and market returns over a sufficiently lengthy period. The beta of a share is equal to the covariance between the shares returns and the markets returns divided by the variance of the markets returns, which in turn is the standard deviation of the market returns squared that is:
Beta (BS) = (CovarianceSM/VarianceM)
The return on a suitable stock market index can be used as a proxy for the market returns.
As the covariance of each individual share is divided by a common denominator, the variance of the market or a suitable surrogate market index, we end up with a standardised measure of risk, that is, the shares beta. Being standardised measure we are able to directly compare the beta of one share with the beta of another.
CAPM is one of the most famous equations in finance. The CAPM equation links together risk and the required return for a share. Simply stated, the underlying precept of the CAPM is that the expected return on a secrity is composed of two elements as follows:
Expected return ,E(r) = risk free interest rate + a risk premium
Using a capital asset pricing model (CAPM) this relationship is expressed more formally as :
E(ri) = Rf + ?(ERm -Rf)
Where
E(ri) = required return on asset I
Rf = risk free rate of return
? = Beta coefficient for asset
ERm = Expected market return, that is the return expected on the market portfolio of shares
The risk free rate of return Rf
The risk free rate of return, Rf, is the rate of return that can be carried on a security, which has zero risk. Its beta equals zero and the return is certain. The risk free rate of return is the rate that must be offered to compensate the investor for deferring consumption, it reflects the time value of money.
The risk premium, ?(ERm -Rf)
The market risk premium is the difference between the expected market return ERm and the risk free rate of return Rf. the market risk is converted to a risk premium for an individual share by multiplying it by the share's beta. The risk premium therefore for an individual share is a function of the individual share's beta, ?, and the risk premium for the market.
The market risk premium represents the additional return, over and above the risk-free return, which the investor expects for assuming the risk comparable with investing in the risky market portfolio of shares. The increase in required return is proportional to the amount of risk the investor is willing to assume.
Negative beta
In theory betas can be negative, implying that a share's expected return will go up as the market goes down and vice versa, but in practice negative beta's are extremely rare. If the share's beta is negative, the risk premium for the share will also be negative and the expected return will be less than the risk-free rate.
The Security Market Line.
The CAPM equation is in fact a straight-line equation conventionally the equation for a straight line is usually given as Y = MX + C.
When the CAPM equation is shown in a graph form, the resultant straight line is referred to as the Security Market Line (SML). It is the line, which exhibits the positive relationship (correlation) between the systematic risk of a security and its expected return.
On the security market line (SML) the risk-free Rf is a constant and represents the vertical intercept, i.e the point where the SML crosses the vertical axis, it is equivalent to the constant C in the straight-line equation. The coordinates x represents the systematic of market risk of the share as measured by its beta ?, and coordinates y represents the expected market return. Observe that the gradient of the line m, is represented by the market risk premium (RM - Rf), not beta and indicates the level of risk aversion in the economy. The SML represents the level of return expected in the market for each level of the share's beta (market risk), thus the risk-return trade-off for the share can be plainly seen
GRAPH!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Interpreting the SML
) Notice that the beta associated with the risk-free security is zero, reflecting the securities freedom from risk and its immunity from changes in the market return
2) Point M on the SML represents the market portfolio. The return on the market portfolio (i.e. the average return from all securities on the entire market or a proxy index) is given by ERM and its corresponding level of risk is shown by ?M, where ? = 1.0. The beta for the market portfolio must be 1.0, thus a security with a beta of 1.0 has risk equal to that of the market.
3) The difference between ERM and Rf(ERM - Rf) is the market risk premium thus the risk for an individual asset, I equals the market risk premium multiplied by the share's beta ?I(ERM - Rf).
Underlying assumptions and limitations of the CAPM
The CAPM is a mathematical model, and like any model it is merely a representation of reality. All models are constructed from a set of underlying assumptions about the real world, they inevitably have their limitations. The CAPM is built on the following set of assumptions and limitations.
)
Historic data. CAPM is a future- oriented model yet it essentially relies on historic data to predict future returns. Betas for example are calculated using historic data, consequently they may or may not be appropriate predictors of the variability or risk of future returns. The CAPM is not a deterministic model, the required returns suggested by the model can only be viewed as approximations.
2)
investor expectations and judgements. The model includes the expectations and subjective judgements of investors about future asset or security returns and these are very difficult to quantify. In addition the model also assumes that investor expectations and judgments are homogeneous i.e. identical. If investors have heterogeneous (i.e. varied) expectations about future returns they will essentially have different SML's rather than a common SML as implied by the model.
3)
A perfect capital market. CAPM assumes an efficient or perfect capital market. An efficient capital market is one where all securities and assets are always correctly priced and where it is not possible to outperform the market consistently expect by luck. An efficient capital market implies that there are many small investors (all are price takers), all of whom are rational and risk averse; they each posses the same information and the same future expectations about securities. It also assumes that in the financial markets there are no transaction costs, no taxes and no limitations on investments.
4)
Investors fully diversified. The CAPM also assumes that investors are fully diversified. In practice many investors, particularly small investors, do not hold highly diversified asset portfolios.
5)
Practical data measurement problems. There are also practical problems associated with the model such as difficulties with specifying the risk-free rate, measuring beta and measuring the market risk premium.
6)
One-period time horizon. CAPM assumes investors adopt a one-period time horizon. In practice investors are likely to have differing time horizons and again this would imply varying SML's.
7)
Single-factor model. CAPM is a single factor model: it relies on the market portfolio to explain security returns. The rate of return on a security is a function of the security beta times a risk premium, that is, ?(ERM-RF). Both beta and the risk premium are determined in relation to the market portfolio. Recall that each security's beat (risk factor) is derived by linear regression, plotting its return against the return from the market portfolio- characteristic line.
Comments and criticisms of the CAPM
Some of these assumptions are clearly unrealistic, implying that the CAPM is of very limited value. However, the model should not be dismissed solely on the grounds that it includes some simplifying assumptions. The acid test of its efficacy is : does it work? Can it be used effectively as a predictive tool? Unfortunately the evidence is controversial and inconclusive.
Some researchers have found evidence supporting the model, or certain aspects of it, and others have found evidence to challenge the model. In 1977, in what is now a classic article, Richard Roll questioned if it was even possible to test the model because it is practically impossible to establish the return on the market portfolio. As the market portfolio is theoretically supposed to include all risky assets (shares, bonds, commodities, precious metals, property, works of art, ...etc) it is not feasible to test the model empirically.
Even if a stock market index is used as a surrogate for the market portfolio, this is still a very restricted view of the market portfolio as so many other types of risky assets are omitted.
On the upside, there is substantial empirical evidence supporting the positive linear relationship between an asset's beta (risk) and its return as implied by the model (Levy and Sarnat 1994). This would apparently confirm the model's inference that high beta (risk) shares produce high returns and low beta (risk) shares produce low returns. However, even these findings are not free from controversy.
To date perhaps the most serious challenge to validity of the CAPM has come from research by Eugene Fame and Kenneth French, both from university of Chicago, published in 1992. Fame and French found no correlation between historical betas and historical returns on over 2,000 stocks between 1963 and 1990- thus they concluded that the magnitude of a stock's historical beta bore no relationship to the magnitude of its historical return.
Based on this, and their other findings, Fame and French concluded that 'beta is dead'- at the time a seemingly body blow to the validity of the CAPM. Fame and French found, for example that variations in share returns had more to do with company size ( as measured by the total market value of the firm's equity and the ratio of the company's equity book value to its equity market value) than with beta.
Needless to say, the work of Fame and French has provoked even more controversy and many academics have since rushed to the defence of the CAPM, criticising Fame and French's research methodology and suggesting that their arguments 'theoretically incomplete'.
Roll and Ross (1992) , for example have argued that the use of a stock market index such as the Standard and Poor's (S&P) 500 (a US stock market index analogous to a FTSE index in the UK), as a surrogate or proxy for the true market portfolio may not give an accurate measure of the true market returns. Thus if the surrogate portfolio used by Fame and French is not a correct one, then it may not be reasonable to conclude that there is a positive correlation between betas and rates of return.
Other researchers, such as Chan and Lakonishok (1993) have found that the CAPM is an adequate measure of the risk-return relationship.
Whatever the conclusion of various researchers, it is worth noting that all of the test of the CAPM have by necessity been based on ex post data, whereas the CAPM is an ex ante model. In other words, CAPM is a future oriented equilibrium model linking future required return and risk.
While the academic battling is likely to continue for some time, the CAPM, in the mean time, has not been dethroned. Until it is superseded by a more suitable theory the CAPM remains a valuable expectational model: it is still of value as a predictive tool.
Despite its limitations the CAPM offers the financial manager and investors a very insightful methodology for recognising and making explicit the relationship between risk and return inherent in financial decisions. If forces investors to consider both sides of the coin, not just to focus on return.
In making investment decisions, which are the key wealth- creating decisions, it is clearly important that the financial managers consider both elements, risk as well as return, in evaluating the decision. By recognising that a vital risk-return trade-off is inherent in every investment decision, and by endeavouring to take account of and evaluate risk together with return in such decisions, the financial manager will be guided towards realising the goal of shareholder wealth maximisation.
Recognising that shareholder wealth is reflected in the market price of a company's shares, the financial managers will now realise that the company's share price in the market will fluctuate until investors perceive that it offers a 'fair' return relative to its risk.
In conclusion, the CAPM is a very simple yet powerful financial model which implies that the risk premium for an individual share to the average risk premium in the stock market multiplied by the share's price.
It is important to appreciate the CAPM's major contribution, to our understanding of the linkages between risk and return, and how required rate of return are derived and therefore how securities are valued in the markets.
Clearly there are to be some way of analysing and relating risk to return and until a new king is crowned the CAPM will continue to rule: however the model has to be applied with care.
