**Essay Instructions**: Read the article below and do some of your own research using the CyberLibrary and Internet search engines. Then write a five page paper answering the following question:

Do you think APT or the CAPM is the best approach for a financial professional to use?

Defend your answer rigorously. And don't cop out by saying "I like both approaches", take a side and defend it.

Abstract:

The capital asset pricing model (CAPM) states that the return on a stock depends on whether the stock's price follows prices in the **market** as a whole. The more closely a stock follows the **market**, the greater will be its expected return. A technique called mean-variance analysis can be used to construct a series of portfolios that are efficient. Instead of looking at the covariances among stocks in a portfolio, the CAPM divides a stock's **risk** into 2 parts: systematic and unsystematic. The CAPM assumes that no investor has better information than another and that, if a stock's beta is known, its long-run return can be predicted. Researchers found that the CAPM works only in the long run. Despite doubts, the CAPS passed most of its early tests. The arbitrage pricing theory (APT) divides systematic **risk** into smaller component **risks**. Recent research has suggested that the 4-factor version of the APT is better at predicting the return on a stock than the simplest version of the CAPM. In some of its basic ideas, but not in its details, the APT builds on rather than replaces the CAPM.

Full Text:

Copyright Economist Newspaper Group, Incorporated Feb 2, 1991

MODERN portfolio theory has changed the way investors think about equities --though most investors would consider its starting-point other-worldly. The theory assumes that financial **markets** are "efficient", meaning that the price of any stock incorporates all publicly available information about that stock. The main task of the theory is to say what determines the stock's rate of return. (If it can do that, it will be allowed its assumptions.)

According to the theory's most famous offspring, the capital-asset pricing model (CAPM, pronounced CAP-M), the return on a stock depends on whether the stock's price follows prices in the **market** as a whole: the more closely a stock follows the **market**, the greater will be its expected return. This theory has stood up to the facts quite well.

The correlation between the price of an individual stock and the price of the **market** as a whole is known by a Greek letter; by the late 1960s hardly a securities house in London or New York did not use, or know about, beta.

Safety in numbers

The difficult road to beta and CAPM starts with Harry Markowitz, now a professor at the City University of New York. In 1952 Mr Markowitz published a path-breaking article called "Portfolio Selection". This paper (like many before) argued that investors demand a high return from risky investments. A risky stock, or a risky portfolio, is simply one whose returns tend to vary a lot.

Before Mr Markowitz, economists had been aware that a portfolio with lots of stocks was less risky than one with only a few. Stocks that perform badly tend to be offset by stocks that perform well, so the return on the portfolio as a whole varies less than the return on smaller lots of individual stocks. But Mr Markowitz also saw that the key to diversifying a portfolio lay not simply in the number of stocks it contained, but in the correlation of their returns.

If returns are highly correlated, then the portfolio, in effect, will not be diversified. If the correlation is low, the portfolio will be highly diversified and the **risk** much less.

An investor can easily calculate the past correlations -- or co-variances, to be precise --among the stocks in a portfolio, and the average return on each individual stock. With this information, Mr Markowitz showed that a technique called mean-variance analysis could be used to construct a series of portfolios that were "efficient" -- yet another use for that over-used word. Efficient portfolios are those which, in the past, yielded the highest return for any given **risk**.

Chart 1 should make the idea clearer. **Risk** is measured on the horizontal axis, and returns on the vertical axis. The crosses represent combinations of **risk** and return for individual stocks. The tinted area represents combinations of **risk** and return that can be achieved by mixing different stocks together in portfolios. The curved line represents the set of efficient portfolios. Any portfolio below and to the right of the line is "inefficient" because it offers a lower return for any given **risk**.

From this set of efficient portfolios, the investor would pick his preferred portfolio according to his appetite for **risk**. If the investor wanted a high return, no matter the **risk**, he might pick portfolio A in chart 1. If he preferred a middling amount of **risk**, he might choose portfolio B; if he was **risk**-averse he would pick portfolio C.

It turns out, however, that much more can be said about the desirability of these different portfolios -- even though all of them may be efficient. In 1958 James Tobin, of Yale University, extended the Markowitz model. He asked what happens if all investors can lend or borrow at the same rate of interest. The answer was surprising: all investors ought to choose the same portfolio of assets, regardless of their attitude to **risk**.

To see why Mr Tobin reached this startling conclusion, turn to chart 2, and imagine that an investor prefers the level of **risk** given by point C. He could simply buy the portfolio at C. Or, instead, he could put some of his money in B, and spend the rest on a safe, interest-bearing asset (treasury bills, say). But this would enable him to reach point D in chart 2 -- an investment as safe as C, but paying a higher return. So that is what he will do.

Equally, if he preferred the riskiness of A, he could borrow at the **market** rate of interest to buy B. By "leveraging" (borrowing against) his investment, the investor's **risk** would rise, but so would the return -- to point E. Just as D was unambiguously better than C, so E is unambiguously better than A.

The chosen investments all lie on a straight line that cuts the vertical axis at the **market** rate of interest -- the return on a riskless asset. And it touches the efficient-portfolio line, in this example, at B. If the investor prefers no **risk**, he can choose the fixed rate of interest and buy no shares; otherwise, he will buy portfolio B and either lend or borrow. The investor's job has two parts: first, find the point of tangency that defines the best portfolio; second, borrow or lend to adjust the balance between **risk** and return.

Evidently, investors behave like this only in models. But theorists were unwilling to abandon the trail -- and rightly so. There is no such thing as perfect competition, but in many ways **market** economies behave as if firms are perfectly competitive: the model is a revealing simplification. In the same way, investors do not all choose the same efficient portfolio -- but perhaps, in some respects, financial **markets** behave as if they do.

Before the model in chart 2 can be put to the test, it needs to be calibrated. The **market** rate of interest (where the straight line in chart 2 cuts the vertical axis) is known. But how to measure **risk**? And how to find B, the chosen portfolio? This is where the CAPM -- developed independently by William Sharpe of Stanford University, and by the late James Lintner of Harvard University -- comes in.

Instead of looking at covariances among stocks in a portfolio, the CAPM takes an ingenious short-cut. It divides a stock's **risk** into two parts: systematic and unsystematic. Systematic **risk**, or **market** **risk**, is the extent to which the share price is correlated with the **market** as a whole; it is measured by beta. A stock with a beta of one tends to rise by 10% for every 10% rise in the stockmarket; a stock with a beta of two tends to rise by 20% for every 10% rise in the stockmarket, and so on. A stock's unsystematic **risk** is the variation that is left after stripping out the systematic **risk**.

This distinction is extremely fruitful. In a diversified portfolio, unsystematic **risks** cancel each other out. Since investors can eliminate this sort of **risk**, it ought to have no bearing on a stock's return. But investors cannot eliminate systematic **risk** merely by diversifying: a fully diversified portfolio (eg, the stockmarket as a whole) has a beta of one. So the CAPM focuses on the relationship between systematic **risk** -- the beta of a stock or a portfolio -- and returns.

Since betas can be calculated, the model has a usable measure of **risk** to place on the horizontal axis in chart 2. What about B, the chosen portfolio? The CAPM assumes, among other things, that no investor has better information than another. It also accepts the framework of chart 2, which concluded that investors will all choose the same portfolio. Together these imply that the chosen portfolio is none other than the **market** itself.

From this comes a way to price stocks. The straight line in chart 2 passes through the so-called **market** portfolio, which, by definition, has a beta of one. As the discussion above showed, that straight line also reveals the the returns that will be required of stocks (or portfolios) with higher or lower betas. Nobody will hold a stock that is below the line; such stocks will fall in price until the expected return rises to the line. Stocks above the line will be in great demand; they will rise in price.

In equilibrium, all stocks will lie on the line. Individual investors need not worry about the **market** portfolio: they need only decide how much systematic **risk** they wish to take on. **Market** forces then ensure that any stock can be expected to yield the appropriate return for its beta.

Does it fit?

The CAPM says that if you know a stock's beta, you can predict its long-run return. It is a model -- a simplification. Some of its assumptions are questionable; but instead of asking whether the model is "true", ask whether it works. Most tests of the CAPM have concluded that it does: as predicted, stocks with high betas yield high returns.

In 1972 three researchers (Fischer Black, Michael Jensen and Myrton Scholes) divided the stocks listed on the New York Stock Exchange into ten portfolios. The first portfolio contained 10% of the securities with the lowest betas, the second the 10% with the next lowest betas, and so on. The study found that over 35 years there was an almost exactly straight-line relationship between a portfolio's beta and its average return, just as predicted by the CAPM (see chart 3).

However, niggling doubts remain. Stocks with a beta of zero tended to have a higher return than treasury bills, contrary to the CAPM's predictions. This suggests that investors do expect to be compensated for taking on unsystematic **risk**. Also, stocks with high betas tended to do slightly worse than predicted by the CAPM.

The CAPM works only in the long run. As Burton Malkiel of Princeton University shows in his excellent book, "A Random Walk Down Wall Street", the returns of America's mutual funds in the 1980s bore no relation to their betas; if anything, in fact, there was a slight tendency for low-beta funds to outperform high-beta ones. And the betas of individual stocks vary a good deal over time. (The beta of a portfolio of stocks is more stable, though, because changes in the betas of individual stocks tend to cancel each other out.)

Roll's rocket

Despite these doubts, the CAPM passed most of its early tests with honours. Then in 1977 it was dealt a more serious blow, by Richard Roll of the University of California at Los Angeles.

Recall that, according to the original CAPM, all investors choose to hold the **market** portfolio. Taking this idea literally, the **market** portfolio would include every financial asset in the world. The trouble with tests of the CAPM, suggested Mr Roll, is that they use a bad proxy for this **market** portfolio -- eg, the 500 biggest companies listed on the New York Stock Exchange.

Mr Roll showed that the CAPM will always look true if the **market** proxy (such as the S&P 500) is "efficient" in the sense defined by Mr Markowitz --ie, if no combination of the shares would give a higher return for the same **risk**. But this does not prove that each share's expected return is affected only by its correlation with the true **market** portfolio. Conversely, even if share returns were unrelated to betas derived from the S&P 500, shares might still be correctly priced in relation to the true **market** portfolio.

This objection might look like a quibble. But Mr Roll showed that a small change in the **market** proxy (eg, from the S&P 500 to the Wilshire list of 5,000 listed stocks) can completely alter the expected returns of a stock as predicted by the CAPM. Since nobody knows what the true **market** portfolio is, nobody can say whether the CAPM holds.

This attack on the CAPM sat comfortably with an alternative model of asset prices, developed by Stephen Ross of Yale University. Known as arbitrage pricing theory (APT), it now demands a chapter in just about every finance textbook.

Unlike the CAPM, the APT divides systematic **risk** into smaller component **risks**. It does not specify in advance what these are. In principle, any factor that might affect the return from a group of assets qualifies. An unexpected change in interest rates, for instance, might affect lots of companies' share price --not to mention bond prices, commodity prices and so on.

In practice, Mr Ross found that returns depend on: (a) inflation; (b) industrial production; (c) the investor's appetite for **risk**; and (d) interest rates. The APT says that the expected return on a stock is directly proportional to its sensitivity to each of these factors.

Recent research has suggested that the four-factor version of the APT is better at predicting the return on a stock than the simplest version of the CAPM. The model has the further advantage of explaining the pricing of assets in relation to each other, rather than in relation to an unidentifiable **market** portfolio. Also, the APT can be used to eliminate any specific **risks** that may worry a particular investor. For instance, a pension fund may want a portfolio that is immune to the inflation rate.

In some of its basic ideas, though not in its details, the APT builds on rather than replaces the CAPM. It may be a "truer" model and in many ways a more fruitful one -- but it is far harder to grasp and use, not least because it requires lots of complicated mathematics. If for no other reason, the CAPM will remain every investor's introduction to portfolio theory for many years to come.

Efficiency: the search goes on

THE CAPM assumes that stockmarkets are efficient. Is this true? The belief that a stock's price takes into account all information (about dividends, earnings and so on) as soon as this information becomes publicly available was once the bedrock of financial economics. Recently, it has begun to be challenged.

* If **markets** are efficient, no investors would look for new information, because they would not profit from acquiring it. So some inefficiency in a stockmarket is necessary to encourage investors to look for information.

* When assets have no close substitutes (a whole stockmarket, for instance, may have no substitute), investors may be unable to spot when they are under- or over-valued.

* Stock prices tend to move about much more than changes in their dividend payments would suggest.

* Big movements in share prices often fail to happen when there are major public announcements, or big changes in information.

* There are many smaller anomalies. Small stocks tend to do well in January; all stocks do well at the beginning of the month; most do badly on Monday mornings. Stock returns tend to be mean-reverting -- ie, bad days, and even bad years, are more often than not followed by good days, or good years.

Does this mean economists are abandoning clever models to explain how **markets** move? Not a bit of it. They are using their new mathematical techniques to explore sentiments, fashions, fads and speculative bubbles.

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Finance 6335 Managerial Finance Rodney Boehme

Page 1

CHAPTER 11: Arbitrage Pricing Theory (APT):

Coverage of this chapter is intended to be brief. However, it is important to understand both the

differences and similarities between the CAPM and APT, and also that an asset's required return

should be a linear function of that asset's sensitivities to the nondiversifiable or systematic **risk**.

The first task is to revisit what we define as relevant **risk**. From Chapter 10, we can define the

total **risk** of any one individual security as:

Total **Risk** = Systematic **risk** + unsystematic (diversifiable) **risk**

The Capital Asset Pricing Model assumes any asset's systematic or macroeconomic **risk** is

captured by one **risk** factor - the **market** **risk** factor. In a well-diversified portfolio, firm specific

or diversifiable **risk** of the various stocks cancel out one another (they are random and

independent among the firms) and is essentially eliminated in any well-diversified portfolio.

Adding one new stock to a well-diversified portfolio affects the **risk** of the portfolio depending

upon the asset's degree of **market** **risk**, as measured by its Beta. The asset's firm specific **risk**

won't contribute to portfolio **risk**. The CAPM is represented as:

E(Ri) = Rf +Bi[Rm - Rf] , where:

E(Ri) = expected or required return on the asset "i".

Rf = **risk**-free rate of return (typically U.S. Treasury Bills, although many use the 5 to 7 year

Treasury bond yield).

Bi = the Beta of the asset's returns, i.e., its sensitivity with respect to some well diversified

portfolio or **market** basket of stocks such as the Standard and Poors 500 Index. The **market**

portfolio should actually consist of a Global Wealth Portfolio of all the world's investment

assets, but such a portfolio is not observable or measurable. This Beta is to serve as a

measurement of the asset's level of **market** or systematic (non-diversifiable) **risk**.

Rm = the required return on a **market** basket of stocks such as the S&P 500 Index or Morgan

Stanley World Index of stocks (since we cannot accurately measure the returns to any Global

Wealth Portfolio).

The CAPM also assumes that the systematic or **market** **risk** of any security is captured by only

one **risk** factor; its Beta. The CAPM also assumes that:

1. Investors will hold the **market** portfolio as their portfolio of risky assets.

2. Investors have homogeneous expectations about securities and their relationship to each

other.

3. Asset returns are multivariately normally distributed.

4. The only relevant or priced **risk** factor is the asset's level of **market** or Beta **risk**.

5. A linear relationship exists between Beta and expected return.

6. Firm specific or diversifiable **risk** is not relevant, since it is easily eliminated.

Finance 6335 Managerial Finance Rodney Boehme

Page 2

The Arbitrage Pricing Theory or APT assumes that:

1. Only the systematic **risk** is relevant in determining expected returns (similar to CAPM).

However, there may be several non-diversifiable **risk** factors (different from CAPM,

since CAPM assumes only one **risk** factor) that are systematic or macroeconomic in

nature and thus affect the returns of all stocks to some degree.

2. Firm specific **risk**, since it is easily diversified out of any well-diversified portfolio, is not

relevant in determining the expected returns of securities (similar to CAPM).

The APT model:

1. Does not require investors to hold any particular portfolio. There is no special role for

any **market** portfolio.

2. Only systematic or non-diversifiable **risk** matters, but there may be several of these

macroeconomic **risk** factors that affect the returns of well-diversified portfolios. It is up

to the researcher to identify the **risk** factors. Such **risk** factors might happen to be

unexpected changes in industrial production, inflation, real interest rates, etc.

3. Investors must agree on what the relevant **risk** factors are. There must be a linear

relationship between the **risk** exposure or sensitivity (its loadings on the **risk** factors) and

expected return of a security.

4. If any asset offers an expected return that is out of equilibrium with respect to the **risk**

factors, then investors can build a zero wealth portfolio in order to exploit the mispricing

of the security. This is known as an arbitrage in expectations.

Zero wealth portfolio: requires that some assets be sold short and the proceeds used to purchase

(go long on) other assets. Short selling is the borrowing and selling of an asset that you do not

own. You must later repurchase and return the asset. You make a profit when you are able to

buy back the asset for a lower price than you sold it for.

A representation of a three factor APT model for IBM common stock (this one assumes that

there are three economy-wide or systematic **risk** factors driving the returns of stocks in a well

diversified portfolio) would look like the following:

E(RIBM) = Rf + BIBM,1[R1 - Rf] + BIBM,2[R2- Rf] + BIBM,3[R3 - Rf] , where

E(RIBM) = expected or required return on IBM common stock.

Rf = **risk**-free rate of return (typically Treasury Bills)

BIBM,1 = IBM's sensitivity (its "loading" or "Beta" with respect to **risk** factor number 1.

Analogous definitions exist for BIBM,2 and BIBM,3.

[R1 - Rf] = the **risk** premium of any asset having a Beta = 1 with respect to **risk** factor number 1

and Beta = 0 with respect to **risk** factors number 2 and 3. An analogous definition exists for the

other two **risk** premium terms [R2 - Rf] and [R3 - Rf].

In statistical terminology, the APT **risk** factors are orthogonal to each other.

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APT - Arbitration Pricing Theory

Arbitration pricing theory is based on a much lesser number of assumptions about the stock **market** character as compared to CAPM. The "arbitration" concept suggests earning guaranteed no-**risk** profit from **market** speculation. As arbitration example can serve a situation when a stock is traded in different **markets**, while the current **market** price of this stock in those **markets** is different. In that case the following sequence of actions is apparent: sell the stock short (sale of borrowed securities) in the **market** where the stock price is higher and buy the same amount of stock in another **market** where it costs less. Imagine now that such an opportunity really exists. Since there are many participants in the stock **market**, it is hardly worth hoping that nobody else would notice such an opportunity - notice they will, and start capitalizing on it. But "unexpected" demand increase in one **market** with lower stock prices, and offer increase in another **market** with higher stock prices, will inevitably result in the leveling of prices: higher demand stimulates price increase, while higher offer brings it down. The situation described is an example the simplest arbitration. However, there might be other, more complex types (multi-stage, distributed in time).

Arbitration pricing theory is based on one assumption: arbitration (of any kind) is impossible in balanced **market** conditions. If such an opportunity exists, **market** will quickly "liquidate" it.

Further reasoning on impossibility of arbitration portfolio creation leads to basic equation of asset pricing, which can be considered as a practical result of this theory. It is interesting to note the fact that APT equation is a generalization of CAPM equation, although the arbitration theory has been created as its alternative.

According to this equation, asset value fluctuation is influenced not only by the **market** factor (**market** portfolio value), but by other factors as well, including non-**market** **risk** factors - national currency exchange rate, energy prices, inflation and unemployment rates, etc. If only one factor is considered as **risk** factor - **market** portfolio value - the equation will coincide with that of CAPM.

What is multi-factor modeling?

Taking several factors into account allows creating a stricter model. It results in:

More precise asset price change forecasting;

Reduction of non-systematic **risk**, even without portfolio creation.

Classic CAPM model takes into account only one factor, and asset is characterized by two parameters: "beta" sensitivity coefficient, describing **risk** associated with this coefficient, and average residual yield E responsible for specific **risk**, i. e. **risk** not explainable with the selected factor influence. APT model provides for a possibility of taking into account several factors. Now asset is characterized with a number of "beta" parameters, each of them representing asset sensitivity to a particular factor and characterizing systematic **risk** associated with this factor, and, as before, residual yield E. However, now the amount of specific (not factor explained) **risk** has become lesser.

Any problems?..

Transition from single-factor CAPM model to multifactor APT model provides not only advantages, but raises new problems as well.

How many and what factors should be selected for a multifactor model?

This is a really big problem not only for APT model, but for any multifactor model describing the stock **market** as well. It is absolutely clear that not all parameters available for analysis influence asset price behavior. However, it is not so easy to understand, which and how many of them do. It is not constructive to build a model of all factors available at once - insignificant factors will play a role of noise and may considerably distort any results received with the model.

Are **risk** factors identical for all assets alike?

The second question is more delicate than the first one. And more complicated. While intuitive decision could be offered for solving the first problem - select some basic macroeconomic or industry parameters influencing, according to intuitive perception, the stock prices - that could not be done for solving the second problem. Because behavior of each asset is, generally speaking, individual. Therefore, each asset has his own composition and number of **risk** factors. What reasons should decide, which set of factors match one asset, and which set of factors match another one?

Is composition and number of **risk** factors changing with time?

Assume that somehow one could manage to find composition and number of factors influencing a concrete asset. Can that factor composition change over a certain period of time? Our research results demonstrate an unsteady character of interrelations in the stock **market**. It means that the model is applicable only during a limited period, after which it becomes necessary to rebuild it. The **risk** factors may be different, too.

Can factors influence the price not immediately, but after a certain period of time?

The question bears the answer in itself - they certainly can. Thus, increase in oil prices may have an effect on transportation stock prices not at once, but some time later. If there are several factors, each factor may have its individual timing. How do we determine it?

How to rank companies by several parameters at once?

Having constructed a CAPM model for several assets, you could sort them out by sensitivity, systematic or non-systematic **risk**, with the aim of selecting the most attractive assets. In a multifactor case, asset is characterized by a number of systematic **risks** associated with each factor. How to analyze them all?

No Problem !

We will solve all these uneasy problems for you. Our methods and technologies are specially developed to solve such problems. Service complex offered within the framework of a multifactor model contains integrated mechanisms to solve most of the problems listed above.

Services offered within APT model framework:

Selection of significant factors for an asset or groups of assets;

Selection of significant factors for portfolio;

Taking into consideration factor interaction;

Definition of factors' specific time of influence on the asset;

Calculation of "Beta" parameters for an asset or list of assets;

Calculation of "Beta" parameters for portfolio;

"Beta" parameter absolute error evaluation;

Systematic **risk** calculation;

Non-systematic **risk** calculation;

Estimation of overevaluation/underevaluation;

Yield forecast;

Asset ranking by "beta" set of parameters;

Asset ranking by set of systematic **risks**.

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