财务管理Chap012

12-2
Arbitrage Pricing Theory
Arbitrage arises if an investor can construct a zero investment portfolio with a sure profit.


Since no investment is required, an investor can create large positions to secure large levels of profit. In efficient markets, profitable arbitrage opportunities will quickly disappear.

12-4
Risk: Systematic and Unsystematic
We can break down the total risk of holding a stock into two components: systematic risk and unsystematic risk:


The beta coefficient, b, tells us the response of the stock’s return to a systematic risk. In the CAPM, b measures the responsiveness of a security’s return to a specific risk factor, the return on the market portfolio.
Ri Ri βi F
The return on the factor F
12-15
Relationship Between the Return on the Common Factor & Excess Return
Excess return
β A 1.5 βB 1.0
Different securities will βC 0.50 have different betas. The return on the factor F
12-3
Total Risk
Total risk = systematic risk + unsystematic risk The standard deviation of returns is a measure of total risk. For well-diversified portfolios, unsystematic risk is very small. Consequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk.
Chapter 12
An Alternative View of Risk and Return: The Arbitrage Pricing Theory
Key Concepts and Skills


Discuss the relative importance of systematic and unsystematic risk in determining a portfolio’s return Compare and contrast the CAPM and Arbitrage Pricing Theory
R R 2.30 5% 1.50 (3%) 0.50 (10%) 1%
12-11
Systematic Risk and Betas: Example
R R 2.30 5% 1.50 (3%) 0.50 (10%) 1%
Finally, if it were the case that the expected return on the stock was 8%, then:
R Rmε R R β I FI βGNP FGNP βS FS ε β I is the inflation beta βGNP is the GNP beta βS is the spot exchange rate beta ε is the unsystemat ic risk
i
12-14
Relationship Between the Return on the Common Factor & Excess Return
Excess return If we assume that there is no unsystematic risk, then i = 0.
12-8
Systematic Risk and Betas: Example
R R 2.30 FI 1.50 FGNP 0.50 FS 1% We must decide what surprises took place in the systematic factors. If it were the case that the inflation rate was expected to be 3%, but in fact was 8% during the time period, then: FI = Surprise in the inflation rate = actual – expected = 8% – 3% = 5% R R 2.30 5% 1.50 FGNP 0.50 FS 1%
bi
Cov( Ri , RM )
( RM )
2
12-6
• We shall now consider other types of systematic risk.
Systematic Risk and Betas


For example, suppose we have identified three systematic risks: inflation, GNP growth, and the dollar-euro spot exchange rate, S($,€). Our model is:
Ri Ri βi F εi
12-13
Relationship Between the Return on the Common Factor & Excess Return
Excess return
Ri Ri βi F εi
If we assume that there is no unsystematic risk, then i = 0. The return on the factor F
2
Total risk
R R U becomes R Rmε where m is the systematic risk ε is the unsystemat ic risk
n
12-5

Nonsystematic Risk: Systematic Risk: m
12.2 Systematic Risk and Betas

Finally, the firm was able to attract a “superstar” CEO, and this unanticipated development contributes 1% to the return. ε 1%
R R 2.30 FI 1.50 FGNP 0.50 FS 1%
R R 2.30 5% 1.50 (3%) 0.50 FS 1%
12-10
Systematic Risk and Betas: Example
R R 2.30 5% 1.50 (3%) 0.50 FS 1%
If it were the case that the dollar-euro spot exchange rate, S($,€), was expected to increase by 10%, but in fact remained stable during the time period, then: FS = Surprise in the exchange rate = actual – expected = 0% – 10% = – 10%
R 8%
R 8% 2.30 5% 1.50 (3%) 0.50 (10%) 1% R 12%
12Factor Models



Now let us consider what happens to portfolios of stocks when each of the stocks follows a one-factor model. We will create portfolios from a list of N stocks and will capture the systematic risk with a 1-factor model. The ith stock in the list has return:
12-9
Systematic Risk and Betas: Example
R R 2.30 5% 1.50 FGNP 0.50 FS 1%
If it were the case that the rate of GNP growth was expected to be 4%, but in fact was 1%, then: FGNP = Surprise in the rate of GNP growth = actual – expected = 1% – 4% = – 3%