Chapter 6 - Asset pricing models

Question 1

CAPM (Capital Asset Pricing Model)

Answer 1

def: introduces assumptions regarding the market & the behaviour of the other investors to allow the construction of an equilibrium model of prices in the whole market.
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CAPM tells us about the relationship between risk & return for security markets as a whole

Question 2

CAPM assumptions

Answer 2

KNATTAD PECOF
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> all e(returns), variances & covariances of pairs of assets are KNOWN
> investors = NON-SATIATED
> investors = risk-AVERSE
> fixed single-step TIME period
> no TAXES / TRANSACTIONAL costs
>assets may be held in ANY AMOUNTS
> investors make their DECISIONS purely on the basis of e(return) & variance
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> market for risky assets are PERFECT
> investors have the same ESTIMATES of E(return), sigma, cov & securities over one-period horizon
> All investors measure in the same CURRENCY
> all investors have the same ONE-PERIOD horizon
> all investors can borrow or lend unlimited amounts at the same risk-FREE rate

Question 3

Consequences of the extra assumptions

Answer 3

1) If investors have homogenous expectations, then they all faced with the SAME EFFICIENT FRONTIER of risky securities
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2) If in addition they are all subject to the same rf rate of interest, the efficient frontier COLLAPSES to the str line in E-sigma space which passes through the rf rate of return on the E-axis & is tangential to the efficient frontier for risky securities
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3) All rational investors will hold a COMBO of the rf asset & M, the portfolio of risky assets. at the point where the str line through the rf return touches the original efficient frontier
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4)Because this is the portfolio held in different quantities by all investors, it must consist of all risky assets in proportion to their market capitalisation - ‘MARKET PORTFOLIO’ which is determined by their risk-return portfolio

Question 4

Separation theorem

Answer 4

fact that the optimal combination of risky assets for an investor can be determined without any knowledge of their preferences towards risk & return

Question 5

Capital market line

Answer 5

def: str line denoting the new efficient frontier
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(Ep-r)/(Em-r) = σp/σm………. sigma
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where
Ep= expected return of any portfolio on the efficient frontier
sigma p = s.d of return on portfolio P
Em= expected return on the market portfolio
sigma m= s.d of the return on the market portfolio
r = rf rate of return

Question 6

Security market line

Answer 6

def: equation relating the expected return on any asset to the return on the market
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Ei-r = βi *(Em-r)
where
Ei = expected return on security i
βi = beta factor of security i defined as Cov[Ri, Rm] / Vm
Em = expected return on the market portfolio
r = return on the risk-free asset
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str line in E-B space which shows the expected return on any security expressed as a linear function of the security’s covariance with the market as a whole. Since the beta of a portfolio is the weighed some of the betas of its constituent securities, the security market line equation applies to portfolios as well as individual securities

Question 7

What does a beta of the market portfolio equal? And that of the rf asset?

Answer 7

βm=1
β rf=0

Question 8

Limitations of the CAPM

Answer 8

i) most of the assumptions of the basic model can be attacked as unrealistic & the empirical studies do not provide strong support for the model
ii) basic problems in testing this model is that account has to be taken of the entire investment universe open to investors not just their capital markets

Question 9

Extension of the basic CAPM

Answer 9

> MULTI-PERIOD models (consumption CAPM & one that allows for the uncertain inflation that will be present in a multi-period context so that investors are concerned with real returns)
Models with TAXES (the basic model means that investors are indifferent between income & capital gains)
ZERO-BETA model (there is no asset which is riskless for all investors so a model has been developed which allows for groups of investors in different countries each of which considers their domestic currency to be risk-free)

Question 10

Uses of CAPM

Answer 10

-PRICE ASSETS (where these could be financial securities or other assets such as capital projects)
-estimate the e(return) on a financial security given its exposure to various risk factors modelled
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if the β can be estimated from past data, then the security market line can be used to estimate the prospective return that the asset should offer given its systematic risk. the return can be used to discount projected future CF’s and so price the security & determine if it appears to be under-valued or over-valued.

Question 11

Estimating parameters for asset pricing models

Answer 11

-STATISTICAL MODEL (past time series & it’s a common approach to exclude outliers & focus on remaining residuals which appear more normal)
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or general-to-specific modelling (include all variables & then reduce o those with a ‘major’ influence)