Download - Group 4 Sapm
-
8/2/2019 Group 4 Sapm
1/41
-
8/2/2019 Group 4 Sapm
2/41
CAPM
CAPMOverview:
CAPM Model:Assumptions
CAPMformulae
SecuritiesMarket line
Limitations
of CAPM
Practical Useof the CAPM
conclusions
-
8/2/2019 Group 4 Sapm
3/41
Markowitz, William Sharpe, John Linter and Jan Mossim provided basic structure
for CAPM model.
The Capital Asset Pricing Model(CAPM) helps us to calculate investment risk
and what return on investment we should expect.
This model describes the relationship between risk and expected return
This model starts with the idea that individual investment contains two types of
risk:
Systematic Risk (or Market risk)
Unsystematic Risk (or Specific risk)
Click here
-
8/2/2019 Group 4 Sapm
4/41
CAPM considers only systematic risk and assumes that unsystematic risk can be
eliminated by diversification. In more technical terms, it represents the
component of a stock's return that is not correlated with general market moves.
No of shares.
Beta
Click Here
-
8/2/2019 Group 4 Sapm
5/41
Beta is used as a measure of systematic risk
In this theory, The required rate of return of an asset is having a linear
relationship with assets beta value
All investor hold only the market portfolio and riskless securities.
Market portfolio consists of the investment in all securities of the market.
Each assets is held in proportion to its market value to the total value of all
risky assts.
For Say if Reliance industry share represents 20% of all risky assets, then the
market portfolio of all individual investors contains 20% of Reliance industry
shares
CAPM is based on the idea that investors demand additional expected return(called the risk premium) if they are asked to accept additional risk.
This model tells us the fair (risk-adjusted) expected return for every individual
asset.
Click Here
-
8/2/2019 Group 4 Sapm
6/41
A market equilibrium model i.e SML equation.
Finally to sum up:
It explains how assets should be priced in the capitalmarket.
Click Here
-
8/2/2019 Group 4 Sapm
7/41
-
8/2/2019 Group 4 Sapm
8/41
The perfect market assumption
There are no taxes or transaction costs or information costs
Stocks can be bought and sold in any quantity (even fractions)
There is one risk-free asset and all investors can borrow or lend at
that rate
-
8/2/2019 Group 4 Sapm
9/41
Capital Asset Pricing Model CAPM formulae
The standard formula remains the CAPM, which describes the relationship between
risk and expected return.
Rs =
CAPM's starting point is the risk-free rate - typically a 10-year government bond yield. To
this is added a premium that equity investors demand to compensate them for the extra
risk they accept. This equity market premium consists of the expected return from themarket as a whole less the risk-free rate of return. The equity risk premium is multiplied
by a coefficient that Sharpe called "beta."
Click Here
-
8/2/2019 Group 4 Sapm
10/41
According to CAPM, beta is the only relevant measure of a stock's risk. It measures a
stock's relative volatality - that is, it shows how much the price of a particular stockjumps up and down compared with how much the stock market as a whole jumps up
and down.
If a share price moves exactly in line with the market, then the stock's beta is 1.
A stock with a beta of 1.5 would rise by 15% if the market rose by 10%, and fall by 15%if the market fell by 10%.
Beta :
Interpreting F
ifF!
asset is risk freeifF!
asset return = market return
ifF"
asset is riskier than market index
Fasset is less risky than market index
Click here
-
8/2/2019 Group 4 Sapm
11/41
The Security market Line:
The SML line helps to determine the expected return for a given Security beta.
In other words, when beta are given, we can generate expected return for the
given securities.
Positive relationship between systematic risk and return of a portfolio
The line which gives the expected returns-systematic risk combinations of assets
is called the security market line
The overvaluation and undervaluation of stock can be seen.
CAPM is called a single-factor model because the slope of the SML is caused by asingle measure of risk the beta.
Click here
-
8/2/2019 Group 4 Sapm
12/41
Plot the Risk-Free Rate
Beta Coefficient1.0
Return
%
Rf
-
8/2/2019 Group 4 Sapm
13/41
Plot Expected Return on the
Market Portfolio
Beta Coefficient1.0
Return
%
Rf= 4%
km =12%
-
8/2/2019 Group 4 Sapm
14/41
Draw the Security Market Line
Beta Coefficient1.0
Return
%
Rf= 4%
km =12%
SML
-
8/2/2019 Group 4 Sapm
15/41
Plot Required Return(Determined by the formula = Rf+ Fs[kM - Rf]
Beta Coefficient1.0
Return
%
Rf= 4%
km =12%
SML
1.2
R(k) = 4% + 1.2[8%] = 13.6%
R(k) = 13.6%
-
8/2/2019 Group 4 Sapm
16/41
Limitations ofCAPM
It is not realistic in the world.
This assumes that all investors are risk averse and higher the risk, the higher is the
return.
Investors ignore the Transactions cost, information cost. Brokerage, taxes etc and
make decision on single period time horizon.
The investor are given a choice on the basis of risk- return characteristics of an
investment and they can buy at the going rate in the market.
There are many buyers and sellers and the market is competitive and free forces of
supply and demand determine the prices.
CAPM Empirical tests and analyses used ex-post i.e Past data only.
The historical data regarding the market return, risk free rate of return and betas vary
differently for different periods. The various methods used to estimate these inputs
also affect beta value. Since the inputs cannot be estimated precisely, the expected
return found out through the CAPM model is also subjected to criticisms.
-
8/2/2019 Group 4 Sapm
17/41
CAPM establishes a measure of risk premium and is measured by F(Rm Rf)
Beta coefficient is the non diversifiable risk of the asset, relative to the risks of
the asset.
Suppose Tisco company has a beta equal to 1.5 and the risk free rate is say 6%
.The required rate of return on the market (Rm) is 15%. Then adopting this
equation, we have
If the market rate is 15% then the return on Tisco should 19.5% because the
larger risk on tisco than on market.
When return on market is zero this model doesnt work accurately .
-
8/2/2019 Group 4 Sapm
18/41
Practical Use of the CAPM
It is helpful for finance manager has to keep in mind the expected return to the shareholdersand the returns he provides should be commensurate with the risk. This risk is reflected in his
investment and financing decision.
Used to price initial public offerings (IPOs)
Used to identify over and under value securities
Used to measure the riskiness of securities/companies
Used to measure the companys cost of capital. (The cost of capital is then used to evaluate
capital expansion proposals).
The model helps us understand the variables that can affect stock pricesand this guides
managerial decisions.
SML provides a benchmark reflecting the equilibrium position in the relationship between
the risk and return.
-
8/2/2019 Group 4 Sapm
19/41
Focuses on the Market Risk. Thus makes investors to think about riskiness of the
assets in general.
It has been useful in the selection of securities and portfolios. Securities withhigher returns are considered to be undervalued and attractive for buy. The below
normal expected return yielding securities are considered to be overvalued and
suitable for sale.
In the CAPM it has been assumed that investor consider only the market risk ,
Given the estimate of the risk free rate, the beta of the firm, stock and requiredmarket rate of return, one can find out the expected returns for the firms security.
This expected return can be used as an the cost of retained earnings.
-
8/2/2019 Group 4 Sapm
20/41
Conclusions: CAPM
It is called a pricing model because it can be used to help us determine appropriateprices for securities in the market.
The CAPM suggests that investors demand compensation for risks that they are
exposed toand these returns are built into the decision-making process to invest
or not.
The CAPM is a fundamental analysts tool to estimate the intrinsic value of a
stock.
The analyst needs to measure the beta risk of the firm by using either historical or
forecast risk and returns.
The analyst will then need a forecast for the risk-free rate as well as the expected
return on the market.
These three estimates will allow the analyst to calculate the required return that
rational investors should expect on such an investment given the other
benchmark returns available in the economy.
-
8/2/2019 Group 4 Sapm
21/41
Introduction Assumptions ArbitragePortfolio
The APT
model
Factorsaffecting the
return
Arbitage One
Factor Model
APT and CAPM
-
8/2/2019 Group 4 Sapm
22/41
Introduction
This model developed in asset pricing by Stephen Ross
Arbitrage pricing theory is one of the tools used by the investors and portfolio
managers.
The capital asset pricing theory explains the returns of the securities on the basis oftheir respective betas.
The investor chooses the investment on the basis of expected return and variance.
Click here
-
8/2/2019 Group 4 Sapm
23/41
Arbitrage: Meaning
Arbitrage is a process of earning profit by taking advantage of differential pricing
for the same asset. The process generates riskless profit.
In the security market , it is of selling security at a high price and the
simultaneous purchase of the same security at a relatively lower price.
The profit earned through arbitrage is riskless.
The buying and selling of the arbitrageur reduces and eliminates the profit
margin. Thus bringing the market price to the equilibrium level.
-
8/2/2019 Group 4 Sapm
24/41
24
For same risks
Asset U has higher return than Asset O
Asset U is underpriced and assets O is overpriced.
Sell asset O or go short on O
Buy asset U or go long on U
@Investor makes Riskless profit
Impact
Demand on asset U goes up and supply of O also goes up
@Price of U increases and price of O decreases
Thus, Arbitrage goes on till prices are traded at same level.
Arbitrage Mechanism
Arbitrage Pricing Theory
-
8/2/2019 Group 4 Sapm
25/41
Assumptions
The investors have homogeneous expectation.
The investors are risk averse and utility maximizes.
Perfect competition prevails in the market and there is no transaction cost.
-
8/2/2019 Group 4 Sapm
26/41
Arbitrage doesnt assume
Single period investment horizon.
No taxes
Investors can borrow and lend at risk free rate of interest.
The selection of the portfolio is based on the mean and variance analysis.
-
8/2/2019 Group 4 Sapm
27/41
Arbitrage Portfolio
According to the APT theory an investor tries to find out the possibility toincrease return from his portfolio without increasing the funds in theportfolio. He also likes to keep the risk at the same level.
For eg:-, the investor holds A, B and C securities and he wants to changethe proportion of the securities without any additional financial
commitment. Now the change in proportion of securities can be denotedby by XA , XB , and XC. The increase in the investment in security A could becarried out only if he reduces the proportion of investment either in B or Cbecause it has already stated that the investor tries to earn more incomewithout increasing his financial commitment.
Thus, the changes in different securities will add up to zero. This is thebasic requirement of an arbitrage portfolio.
-
8/2/2019 Group 4 Sapm
28/41
If X indicates the change in proportion,
XA+ XB+ XC=0
The factor sensitivity indicates the responsiveness of a securitys return to a
particular factor. The sensitiveness of the securities to any factor is the weighted
average of the sensitivities of the securities, weights being the changes made in
the proportion
For eg:-bA, bB, Bc are the sensitivities, in an arbitrage portfolio the sensitivities
become zero.
bA XA + bB XB + bC XC =0
-
8/2/2019 Group 4 Sapm
29/41
The APT model:
According to Stephen Ross, returns of the securities are influenced by a number of
macro economic factor.
The macro economic factors are:
Growth rate of industrial production,
Rate of inflation,
Spread between long term and short term interest rates and
Spread between low grade and high grade bonds.
Click here
-
8/2/2019 Group 4 Sapm
30/41
30
APT
Ri = P0 + P1 Fi1 + P2 Fi2 + P3 Fi3 + . + Pk Fik
Where,
Ri = Expected Return on asset i.e. on well diversified portfolio
P0 = Expected Return on asset with zero systematic risk
P1 = The risk premium related to each of the common factor e.g. the risk premium
related to interest rate risk.
Fij = the pricing relationship between the risk premium and asset i i.e. how
responsive asset i is to this common factor j i.e. sensitivity or beta coefficient
for security i that is associated with index j
Arbitrage Pricing Theory
The arbitrage theory is represented by the equation:
-
8/2/2019 Group 4 Sapm
31/41
If the portfolio is well diversified one, unsystematic risk tends
to be zero and systematic risk is represented by F 1 and F 2 F
n in the equation.
-
8/2/2019 Group 4 Sapm
32/41
Factors Affecting The Return
The specification of the factors is carried out by many financial analysts. Chen, Roll
and Ross have taken four macro economic variables and tested them. According tothem the factors are
Inflation,
Inflation affects the discount rate or the required rate of return and the size of the
future cash flows.
The term structure of interest rates,
Risk premia and
Industrial production.
-
8/2/2019 Group 4 Sapm
33/41
Burmeister and McElroy have estimated the sensitivities with some other factors. They
are
Default risk
Time premium
Deflation
Change in expected sales
The market return not due to the first four variables.
-
8/2/2019 Group 4 Sapm
34/41
The default risk is measured by the difference between the
return on long term government bonds and the return onlong term bonds issued by corporate plus one half of one %.
Time premium is measured by the return on long term
government bonds minus one month treasury bill rate one
month ahead.
Deflation is measured by expected inflation at the beginning
of the month minus actual inflation during the month.
Contn.
-
8/2/2019 Group 4 Sapm
35/41
Salomon Brothers identified 5 factors in their fundamental factor model.
Growth rate in gross national product
Rate of interest
Rate of change in oil prices
Rate of change in defence spending.
-
8/2/2019 Group 4 Sapm
36/41
36
Arbitrage Pricing TheoryONE FACTOR MODEL
Assume, there is only one factor which generates returns on asset i, APT Model boils down
to
E(ri) = Fio +FijP1
Fio = Risk Free Return or Zero Beta Security
Slope of arbitrage price line is P and intercept is Fio. The arbitrage price line shows the
equilibrium relation between an assets systematic risk and expected return.
In a single factor model, the linear relationship between the return Ri and
sensitivity bi can be given in the following form.
Click here
-
8/2/2019 Group 4 Sapm
37/41
The risk is measured along the horizontal axis and the return on the vertical axis.
The A, B and C stocks are considered to be in the same risk class. The arbitrage
pricing line interests the Y axis on lamda 0, which represents riskless rate of
interest i e the interest offered for the treasury bills. Here, the investments involve
zero risk and it is appealing to the investors who are highly risk averse.
Lamda i stands for the slope of arbitrage pricing line. It indicates market price of
risk and measures the risk return trade off in the security markets. The beta i is thesensitivity coefficient or factor beta that shows the sensitivity of the asset or stock
A to the respective risk factor.
-
8/2/2019 Group 4 Sapm
38/41
APT and CAPM
-
8/2/2019 Group 4 Sapm
39/41
In APT model, factors are not well specified . Hence investors finds it difficult to
establish equilibrium relationship.
The well defined market portfolio is a significant advantage of the CAPM leadingwide usage in the stock exchange.
Lack of consistency in the measurements of the APT model.
Further , the influence of factor are not independent to each other because it is
difficult to identify the influence that corresponds exactly to each factor.
Click here
-
8/2/2019 Group 4 Sapm
40/41
Click here
-
8/2/2019 Group 4 Sapm
41/41