# Arbitrage Pricing Theory

Compare with Arbitrage Pricing Theory

Graduate Level

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The Capital Asset Pricing Model is not the only asset pricing model around. One of the competing approaches to asset pricing is called the Arbitrage Pricing Theory, which was developed to address some of the criticisms of the CAPM.

The CAPM is not inconsistent with the APT. Although its intellectual foundations differ, the two theories are basically arguments that the expected return of a security (i.e. the appropriate discount rate for its cash flows!) is a linear function of systematic risk. The major difference in practice between the CAPM and the APT is that the CAPM uses one risk variable, the market portfolio, while the APT uses several, which is largely the reason why I'm partial to the APT. The APT factors are typically macro-economic - they are related broadly to the economy. None the less, these factors will also affect the market portfolio. Thus, when you use the CAPM, the one single factor will reflect the variation in the APT factors.

The CAPM is a classical model in finance. It is an equilibrium argument that, if true, answers most important investment questions. It tells us where to invest, how to invest and what discount rate to use for project cash flows. Not only that, it is a disarmingly simple model. The expected return of a security depends upon a simple statistic: à?. The relationship between risk and return is linear. Calculation of portfolio risk is trivial. At the same time, the CAPM is revolutionary. It tells us that the variance of a project is NOT a factor in determining the appropriate, risk-adjusted discount rate. It turns financial research from roll-up-your-sleeves fundamental analysis into a statistics problem. In short, the CAPM turned Wall Street on its head.

Here comes the bad news. Despite twenty years of attempts to verify or refute the Capital Asset Pricing Model, there is no consensus on its legitimacy. There are a few hints that the model is ...

#### Solution Summary

Arbitrage Pricing Theory is used.

Arbitrage Pricing Theory, Risk, Cost of Capital, and Capital Budgeting

Please find the file attached.

Factor Beta factor Expected value Actual value

Growth in GNP 2.04 3.5% 4.8

Interest rate -1.90 14.0 15.2

Stock return 10.0

Suppose a factor model is appropriate to describe the returns on a stock. Information about those factors in the following chart

a. What is the systematic risk of the stock return?

b. B. the firm announced that its market share had unexpectedly increased 23 percent to 27 percent. Investors know from their past experience that the stock return will increase by 0.36 percent per an increase of I percent in its market share. What is the systematic risk of the stock?

c. C. what is the total return on this stock?

Q2

Assume that the following market model adequetly describes the return-generating behavior of risky assets

Where Rit= the return for the ith asset at time t

And Rmt= the return on a portofolio containing all risky assets in some proportion, at time t

Rmt and Eit are statistically independent

Suppose the following data are true

Asset (beta)Bi E(ri) Var(ei)

A 0.7 8.41% 1.00%

B 1.2 12.06 1.44

C 1.5 13.95 2.25

Var (Rmt)=1.21%

a. Calculate the standard deviation of returns for each asset

b. Assume short selling is allowed

i. Calculate the variance of return of three portfolios containing an infinite number of asset type A,B, C respectively.

Ii. Assume Rf=3.3% and Rm=10.6% which assets will not be held by rational investors?

Iii. What equilibrium state will emerge such that no arbitrage opportunities exist? why?

Q3

The following table lists possible rates of return on [Company (C)] stock and debt and on the market portfolio. The probability of each state is also listed

State Probability Return on stock Return on debt Return on the market

1 0.1 3% 8% 5%

2 0.3 8 8 10

3 0.4 20 10 15

4 0.2 15 10 20

a. What is the beta of (C) debt?

b. What is the beta of (C) stock?

c. If the debt -to-equity ratio of (C) is 0.5, what is the asset beta of (C)? assume no taxes.

Q4

Calculate the weighted average cost of capital for the (B) Company. The book value of (B)'s outstanding debt is $60 million. Currently, the debt is trading at 120 percent of book value and is priced to yield 12 percent . the 5 million outstanding shares of stock are trading at $20 per share. The required return on (B)'s stock is 18 percent. The tax rate is 25%