Friday, January 30, 2009


The Capital Asset Pricing Model.(CAPM).
CAPM – CONCLUSIONSSummaryThis chapter has explored most aspects of the capital asset pricing model in the detail likely to be required in examination questions.
However, you may simply be required to explain the model in outline, and discuss its advantages and limitations. For this sort of question, you do not need to get bogged down in details. A suggested brief description goes as follows.
The CAPM shows how the minimum required return on a quoted security depends on its risk. For simplicity, various assumptions are made.
a) A perfect capital market;
b) Unrestricted borrowing or lending at the risk- free rate of interest
c) Uniformity of investor expectations
d) All forecasts are made in the context of one time period only.

From this it is deduced that all investors will hold a well- diversified portfolio of shares, known as the market portfolio, which is really a ‘slice’ of the whole stock market. Although the market portfolio is not really held by investors, in practice even a limited diversification will produce a portfolio which approximates its behavior, so it is a workable assumption.

The attractiveness of any individual security is therefore judged in relation to its effect when combined with the market portfolio.

A security whose returns are highly correlated with fluctuations in the market is said to have a high level of systematic risk. It does not have much risk – reducing potential on the investor’s portfolio and therefore a high return is expected of it. On the other hand, a security which has a low correlation with the market (low systematic risk )is valuable as a risk reducer and hence its
required return will be lower. The measure of the systematic risk of a security relative to that of the market portfolio is referred to as its beta factor.

The CAPM shows the linear relationship between the risk premium of the security and the risk premium of the market portfolio.
Risk premium of share = market risk premium

The same formula can be applied to computing the minimum required return of a capital investment project carried out by a company, because the company is just a vehicle for the shareholders who will view the project as an addition to the market portfolio.

In practice many of the assumptions underlying the development of CAPM are violated. However, rather than nit-pick it is more sensible to ask dose the theory work? Ie. Dose it explain the returns on securities in the real world?
Fortunately, the answer is yes. Practical empirical tests, whilst showing that betas are not perfect predictors of rates of returns on investments, do show a strong correspondence between systematic risk and rate of return. Certainly CAPM outperforms other models in this area, and in particular it gives a for better explanation of the rate of return on a security that is obtained by looking at its total risk.
advantages of the CAPM
a) risk and rates of return a) it provisos a market based relationship between risk and return, and assessment of security given that risk.
b) It shows why only systematic risk is important in this relationship
c) It is one of the best methods of estimating a quoted company’s cost of equity capital.
d) It provides a basis for establishing risk – adjusted discount rates for capital investment projects.
limitations of the CAPM.
a) By concentrating only on systematic risk, other aspects of risk are excluded; these unsystematic elements of risk will be of major importance to those shareholders who do not hold well- diversified portfolios , as well as being of importance to managers and employees. Hence it takes an investor – orientated view of risk.
b) The model considers only the level of return as being important to investors and not the way in which that return is received. Hence, dividends and capital gains are deemed equally desirable. With differential tax rates the ‘packaging ‘ of return between dividends and capital gain may be important.
c) It is strictly a one – period model and should be used with caution, if at all, in the appraisal of multi-period projects.
d) Some of the required data inputs are extremely difficult to obtain or estimate


Logic and weaknesses.

The capital asset pricing model was originally developed to explain how the returns earned on shares are dependent on their risk characteristics. However, its greatest potential use in the financial management of a company is in the setting of minimum required returns (IE, risk- adjusted discount rates ) for new capital investment projects.
The great advantage of using the for project appraisal is that it clearly shows that the discount rate used should be related to the project’s risk. It is not good enough to assume that the firm’s present cost of capital can be used if the new project has different risk characteristics from the firm’s existing operations. After all, the cost of capital is simply a return which investors require on their money given the company’s present level of risk, and this will go up if risk increases.
Also, in making a distinction between systematic and unsystematic risk, it shows how a highly speculative project such as mineral prospecting may have a lower than average required return simply because its risk is highly specific and associated with the luck of making a strike, rather than with the ups and downs of the market (IE, it has a high overall risk but a low systematic risk).

It is important to follow the logic behind the use of the CAPM as follows.
a) The company assumed objective is to maximize the wealth of its ordinary shareholders.
b) It is assumed that these shareholders all hole the market portfolio (or a proxy of it).
c) The new project is viewed by shareholders, and therefore by the company, as an additional investment to be added to the market portfolio.
d) Therefore, its minimum required rate of return can be set using the capital asset pricing mode formula.
e) Surprisingly, the effect of the project on the company which appraises it is irrelevant. All that matters is the effect of the project on the market portfolio. The company’s shareholders have many other shares in their portfolios. They will be content if the anticipated project returns simply compensate for its systematic risk. Any unsystematic or unique risk the project bears will be negated (‘diversified away ‘) by other investments in their well diversified portfolios.
In practice it is found that large listed companies are typically highly diversified anyway and it is likely that any unsystematic risk will be negated by other investments of the company that accepts it, thus meaning that investors will not require compensation for its unsystematic risk.
Before proceeding to some examples it is important to note that there are tow major weaknesses with the assumptions.

a) The company’s shareholders may not be diversified. Particularly in smaller companies they may have invested most of their assets in this one company. In this case the CAPM will not apply. Using the CAPM for project appraisal only really applies to quoted companies with well diversified shareholders.
b) Even in the case of such a large quoted company, the shareholders are not the only participants in the firm. It is difficult to persuade directors an employees that the effect of a project on the fortunes of the company is irrelevant. After all, they cannot diversify their job.

In addition to theses weaknesses there is the problem that the CAPM is a single period model and that it depends on market perfections. There is also the obvious practical difficulty of estimating the beta of a new investment project.
Despite the weaknesses we will now proceed to some computational examples on the use of the CAPM for project appraisal.
8. certainty equivalents.

In this chapter we have determination of a risk- adjusted discount rate for project evaluation. One problem with building a premium into the discount rate to reflect risk is that the risk premium compounds over time. That is, we implicitly assume that the risk of future cash flows increases as time progresses.
This may be the case, but on the other had risk may be constant with respect to time. In this situation it could be argued that a certainty equivalent approach should be used.

Wednesday, January 14, 2009


The Capital Asset Pricing Model.(CAPM).

1. Introduction.
The relevant risk of a security is not its total risk but the impact it has on the risk of the portfolio to which it is added. CAPM simply allows us to split the total risk of a security into the proportion that may be diversified away, and the proportion that will remain after the diversification process. This remaining risk is the relevant risk for appraising investments.

2. systematic and non-systematic risks.
Initially substantial reductions in total risk are possible: however, as the portfolio becomes more and more diversified, risk reduction slows down and eventually stops.
The risk that can be eliminated by diversification is referred to as non-systematic or unique risk. This risk is related to factors that affect the returns of individual investments in unique ways (eg. The risk that a particular firm’s labour force might go on strike.)
The risk that cannot be eliminated by diversification is referred to as non-systematic or unique risk. To some extent the fortunes of all companies move together with the economy. Changes in macro economic variables such as interest rates exchange rates, taxation, inflation, etc, affect all companies to a grater or lesser extent and cannot be avoided by diversification. That is, they apply systematically right across the market.
The relevant risk of an individual security is its systematic risk and it is on this basis that we should judge investments. Non-systematic risk can be eliminated and is of no consequence to the well diversified investor. Note that it is not necessary- to hold the market portfolio to diversify away non-systematic risk-a portfolio of 15-20 randomly selected securities will eliminate the vast majority of it.

3. systematic risk and return .As non-systematic risk can be diversified away, investors need only concern themselves with (and will only earn returns, for taking) systematic risk. The nest problem is how to measure the systematic risk of investments.
The method adopted by CAMP to measure systematic risk is an index, normally referred to as beta (B ). As with any index we need to establish some base points and then other observations will be calibrated around these points. The two base points are as follows.
a) The risk-free securityThis carries no risk and therefore no systematic risk. The risk-free security hence has a beta of zero.b) The market portfolioThis represents the ultimate in diversification and therefore contains only systematic risk.
We will set beta to 1. 00 for the market portfolio and this will represent the average systematic risk for the market.

4. Establishing beta factors for individual securities.
In theory we need to determine future B factors for the individual company (in order to appraise future investments). In practical terms we will content ourselves with establishing past B s and use these to appraise required returns on fresh investment projects, assuming such fresh projects do not affect overall company risk as viewed by investors.

a) It can be seen that small changes in market returns in the past have been accompanied by much larger changes in the return on this particular security. From this we can infer that security carries more systematic risk than the market portfolio.
b) The exact amount of systematic risk can be determined by establishing the slope of the line of best fit (the security characteristic line). The slope of the line in fact equals the security’s B factor. In this case the line is very steep and its slope (and therefore its B factor) will be greater than. 1 .00. This confirms our observation in (a).
c) The spread of observations around the line is of no great concern to us. This generally represents the non-systematic risk and will be diversified away by well- diversified investors.

5. regression analysis.
regression analysis rather than graphs is normally used to measure B s. the slope of a line in regression analysis can be expressed in several ways, but from our point of view the easiest is probably.
6. aggressive and defensive shares.The expected return on the market portfolio will change in relation to changed economic exceptions this, in turn, will cause a change in the expected return of shares which depends on their beta factors.

Sunday, January 11, 2009


The Diversified Shareholder and The Capital market.
(1). Mixing many risky securities.
Portfolio theory has its roots in the management of investors’ portfolios of stock exchange investments and fixed interest stocks. The following sections show how the attempt to identify an optimal portfolio for investors has led to a comprehensive but simple theory of how the capital market relates risk and return. This, in turn, will assist us in our attempt to adjust discount rates to allow for risk.
The previous section considered portfolios of two securities. It is easy to expend this theory to cover portfolios of many securities, noting that where returns are assessed in percentage terms:
(a) The expected return of a portfolio is equal to the weighted average of the returns of the individual securities in the portfolio.
(b) The risk of the portfolio depends on:
i. The risk of each security in isolation:
ii. The proportions in which the securities are mixed:
iii. The correlations between every pair of securities in the portfolio.
(2). Efficient portfolios.
It is possible to identify which of these portfolios are really worth holding.

A rational risk –adverse investor would define an efficient portfolio as one that has.
a). A higher return than any other portfolio with the same risk; and
b). A lower risk than any other with the same return.

This simple approach is known as the mean-variance efficiency rule (return = mean or expected return; risk = variance or standard deviation).

So, out of all the possible portfolios which an investor could make out of his chosen securities, which are mean variance efficient? (Put another way, which portfolios would the investor select from, given logical assessment of the mean returns and variances of all those available).
You need to be familiar with the following terminology.

(a). Domination an investment dominates another if it provides a better return for the same risk or less risk for the same return.

(b). An efficient investment is one which is not dominated by any other investment, where as an inefficient investment is one which is dominated.

(c). Investor utility curves (or indifference curves) are curves alone which the investor is indifferent between the combinations of risk and return.

(d). Optimal portfolio- the efficient portfolio that has the highest utility for a given investor. This idea was discussed at the start of the chapter & identifying this portfolio requires knowledge of the investor’s indifference curves.
(3). The market portfolio.
The assumptionsA few assumptions are now made, in order to build a simple model:
(a). Investors base their portfolio investment decisions on expected returns, standard deviation and correlations between all pairs of investments.
(b). All investor have the same expectations about future outcomes over a one-period time horizon.
(c). Investors may lend and borrow without limit at the risk-free rate of interest.
(d). There are no market imperfections: investments are infinitely divisible, information is costless, there are no taxes, transaction costs or interest rate charges, and no inflation.
Some of these assumptions are obviously unrealistic, but they greatly simplify the model- building process. Furthermore, even if the assumptions are relaxed, the theory will still hold approximately.
Building the model.

(a). Firstly , consider all the portfolio which could be constructed out of risky securities quoted on the stock market.
(b). Then identify the efficient portfolios from these.
(c). The consider mixing any one of these efficient portfolios, with a risk-free investment, Rf.

Out of all the possible portfolios that could be constructed from risky investment, only one portfolio is worth considering-portfolio M.
A combination of Rf and M produces portfolios which are better than any others in terms of the return which is offered for any given level of risk.
However, given the existence of risk-free investment, investors would choose form those on the revised efficient frontier represented by line RfM.
Portfolios on the line RfM are achieved by mixing portfolio M with risk-free investments. Portfolios on the line M N are achieved by borrowing at the risk-free rate (remember we have assumed that the risk-free rate applies to borrowing as well as lending) and investing our own funds plus borrowed funds in portfolio M.
What is portfolio M.

Because we have assumed that all investors have the same expatiation's about the future outcomes of investments, it follows that:
All investors will come to the conclusion that portfolio M is the best portfolio consisting solely of risky investments to hold.Now, if any quoted share was not in portfolio M, then nobody would with to hold it. It would therefore have not value. We must therefore conclude that:
Portfolio M includes every risky security which is quoted on the market.
Portfolio M is in fact simply a slice of the whole stock market; the proportions of shares held in it are the same as the total market capitalization of the shares on the stock market:

Portfolio M is called the market portfolio.

All rational risk- averse investors will hold the market portfolio, according to the model we have jest constructed. Note that it is not necessary for very investor to hold very share on the stock market. Replicas of portfolio M may be generated by holding as few as fifteen shares. Investment in unit trusts will also achieve the same result.
However, all investors do not have the same attitude to risk. By using the market portfolio, and by either lending or borrowing suitably at the risk-free rate, the investor can choose any level of risk he likes and can predict the return which the market will give him. This return will be the best that he could possibly get for the risk taken.
(4). constructing the capital market line.

We have already seen that combinations of risk-free and investments give a straight line trade-off between risk and return.
To draw the capital market line we therefore need only two observations,
1. Rf- The risk-free rate of interest, which can be approximated by the return on government stock.
2. Rm and sigma m- The risk and return of the market portfolio. As the market portfolio should contain all risk investments, this can be estimated by using the risk and return on a stock market index such as the Financial times all share index.
Value of the Capital market line.

The capital market line tells us for a given level 0 risk the return an investor should expect on the stock exchange. It is often referred to as giving the market price of risk. That is if we choose to take a given level of risk on the stock exchange then we can expect a given level of return.
If this is less than that offered by the project, it is tempting to say that the project should be accepted. However, there is a flaw in this logic.
The problem with this analysis is not in determining the capital market line but in determining the risk of an individual investment.