Upload
hafsai
View
223
Download
0
Tags:
Embed Size (px)
DESCRIPTION
Corporate Finance - Risk
Citation preview
An Alternative View of Risk and Return: The Arbitrage Pricing Theory
Chapter 12
Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin
12-2
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
12-3
Chapter Outline12.1 Introduction12.2 Systematic Risk and Betas12.3 Portfolios and Factor Models12.4 Betas and Expected Returns12.5 The Capital Asset Pricing Model and the Arbitrage
Pricing Theory12.6 Empirical Approaches to Asset Pricing
12-4
APT Arbitrage pricing theory (APT) is a well-known method of estimating the price
of an asset. The theory assumes an asset's return is dependent on various macroeconomic, market and security-specific factors.
The general idea behind APT is that two things can explain the expected return on a financial asset: 1) macroeconomic/security-specific influences and 2) the asset's sensitivity to those influences
There are an infinite number of security-specific influences for any given security including inflation, production measures, investor confidence, exchange rates, market indices or changes in interest rates, RND, GNP, Rival Product e.t.c. It is up to the analyst to decide which influences are relevant to the asset being analyzed.
APT may be more customizable than CAPM, but it is also more difficult to apply because determining which factors influence a stock or portfolio takes a considerable amount of research. It can be virtually impossible to detect every influential factor much less determine how sensitive the security is to a particular factor. But getting "close enough" is often good enough
12-5
Bahria Enterprises Any Stock traded in Financial Markets has two parts. A) Normal or Expected return(info available to SH & mkt undstding influence in
next month), B) Uncertain or Risky Return (info that is to be reveled with in a month, list of
such info is endless) News abt Bahria Reraserch Sudden drop in interest Discovery about Rivals product News that sales figure are higher then expected Un expected retirement of Founder and president
R= R+U where R is actual total return, R is expected, U is unexpected part of return
12-6
Expected Part of info and unexpected part of info e.g. GNP diff b/w actual and forecast
Announcement = Expected part + surprise (innovation)
So the expected part is there part of info the mkt uses to form the expectation R and the surprise is the news that influences the unanticipated return on stock U.
Un anticipated part is the true risk of any investment. Because if we got what is expected then there'll be no uncertainty
U is further categorized as Systematic Risk and Unsystematic risk.
S.Risk = is any risk affect large no. of assets, each to a greater or lesser degree.
For e.g GNP, Inflation, interest rates
U.Srisk or idiosyncratic risk = Risk that specifically affects a single asset or small group of assets. For e.g Rivals info, Retirement of CEO, RnD
12-7
U = m+ϵ where m is systematic or market risk, ϵ company unique risk
ϵ is specific to company , is unrelated to specific risk of most other companiesBahria Entp specific risk is unrelated to Xerox stock. If Bahria's stock go up or down because of its new
discovery by RnD probably unrelated to Xerox so it mean both the stocks are uncorrelated with each other i.e.
Corr (ϵb, ϵx)
But companies are influenced by same systematic risk, individual companies systematic risks and therefore total return as well.
Lecture Tip: It is easy to see the effect of unexpected news on stock prices and returns. Consider the following two cases: (1) On November 17, 2004 it was announced that K-Mart would acquire Sears in an $11 billion deal. Sears’ stock price jumped from a closing price of $45.20 on November 16 to a closing price of $52.99 (a 7.79% increase) and K-Mart’s stock price jumped from $101.22 on November 16 to a closing price of $109.00 on November 17 (a 7.69% increase). Both stocks traded even higher during the day. Why the jump in price? Unexpected news, of course. (2) On November 18, 2004, Williams-Sonoma cut its sales and earnings estimates for the fourth quarter of 2004 and its share price dropped by 6%. There are plenty of other examples where unexpected news causes a change in price and expected returns.
12-8
Risk: Systematic and Unsystematic
Systematic Risk: m
Nonsystematic Risk:
n
2
Total risk
We can break down the total risk of holding a stock into two components: systematic risk and unsystematic risk:
risk icunsystemat theis
risk systematic theis
where
becomes
ε
m
εmRR
URR
12-9
Systematic Risk and Betas For example, suppose we have identified three
systematic risks: inflation, GNP growth, and the interest rate change
Our model is:
risk icunsystemat theis
change rateinterest isr
beta GNP theis
betainflation theis
ε
β
β
β
εβrFrFβFβRR
εmRR
GNP
I
GNPGNPII
12-10
Systematic Risk and Betas: Example
Suppose we have made the following estimates:1. I = 2
2. GNP = 1
3. S = -1.8 Finally, the firm was able to attract a “superstar” CEO, and this unanticipated
development contributes 1% to the return.
εFrβFβFβRR rGNPGNPII
%5ε
12-11
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.
12-12
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.
12-13
12.2 Systematic Risk and Betas The beta coefficient, , tells us the response of the stock’s
return to a systematic risk. In the CAPM, measures the responsiveness of a security’s
return to a specific risk factor, the return on the market portfolio.
)(
)(2
,
M
Mii R
RRCov
• We shall now consider other types of systematic risk.
12-14
Systematic Risk and Betas: Example
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%
%150.050.130.2 SGNPI FFFRR
%150.050.1%530.2 SGNP FFRR
ϵ
12-15
Systematic Risk and Betas: Example
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%
%150.050.1%530.2 SGNP FFRR
%150.0%)3(50.1%530.2 SFRR
12-16
Systematic Risk and Betas: Example
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%
%150.0%)3(50.1%530.2 SFRR
%1%)10(50.0%)3(50.1%530.2 RR
12-17
Systematic Risk and Betas: Example
Finally, if it were the case that the expected return on the stock was 8%, then:
%1%)10(50.0%)3(50.1%530.2 RR
%12
%1%)10(50.0%)3(50.1%530.2%8
R
R
%8R
12-18
12.3 Portfolios and Factor 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:
iiii εFβRR
12-19
Relationship Between the Return on the Common Factor & Excess Return
Excess return
The return on the factor F
i
iiii εFβRR
If we assume that there is no unsystematic risk, then i = 0.
12-20
Relationship Between the Return on the Common Factor & Excess Return
Excess return
The return on the factor F
If we assume that there is no unsystematic risk, then i = 0.
FβRR iii
12-21
Relationship Between the Return on the Common Factor & Excess Return
Excess return
The return on the factor F
Different securities will have different betas.
0.1Bβ
50.0Cβ
5.1Aβ
12-22
Portfolios and Diversification We know that the portfolio return is the weighted
average of the returns on the individual assets in the portfolio:
NNiiP RXRXRXRXR 2211
)(
)()( 22221111
NNNN
P
εFβRX
εFβRXεFβRXR
NNNNNN
P
εXFβXRX
εXFβXRXεXFβXRXR
222222111111
iiii εFβRR
12-23
Portfolios and DiversificationThe return on any portfolio is determined by three sets of parameters:
In a large portfolio, the third row of this equation disappears as the unsystematic risk is diversified away.
NNP RXRXRXR 2211
1. The weighted average of expected returns.
FβXβXβX NN )( 2211
2. The weighted average of the betas times the factor.
NN εXεXεX 2211
3. The weighted average of the unsystematic risks.
12-24
Portfolios and DiversificationSo the return on a diversified portfolio is determined by two sets of parameters:
1. The weighted average of expected returns.
2. The weighted average of the betas times the factor F.
FβXβXβX
RXRXRXR
NN
NNP
)( 2211
2211
In a large portfolio, the only source of uncertainty is the portfolio’s sensitivity to the factor.
12-25
12.4 Betas and Expected Returns
The return on a diversified portfolio is the sum of the expected return plus the sensitivity of the portfolio to the factor.
FβXβXRXRXR NNNNP )( 1111
FβRR PPP
NNP RXRXR 11
that Recall
NNP βXβXβ 11
and
PR Pβ
12-26
Relationship Between & Expected Return
If shareholders are ignoring unsystematic risk, only the systematic risk of a stock can be related to its expected return.
FβRR PPP
12-27
Relationship Between & Expected Return
Exp
ecte
d re
turn
FR
A B
C
D
SML
)( FPF RRβRR
12-28
12.5 The Capital Asset Pricing Model and the Arbitrage Pricing Theory APT applies to well diversified portfolios and
not necessarily to individual stocks. With APT it is possible for some individual
stocks to be mispriced - not lie on the SML. APT is more general in that it gets to an
expected return and beta relationship without the assumption of the market portfolio.
APT can be extended to multifactor models.
12-29
12.6 Empirical Approaches to Asset Pricing Both the CAPM and APT are risk-based models. Empirical methods are based less on theory and
more on looking for some regularities in the historical record.
Be aware that correlation does not imply causality. Related to empirical methods is the practice of
classifying portfolios by style, e.g., Value portfolio Growth portfolio
12-30
Quick Quiz Differentiate systematic risk from unsystematic risk. Which type is essentially eliminated with well diversified portfolios? Define arbitrage. Explain how the CAPM be considered a special case of Arbitrage Pricing Theory?