© k. cuthbertson and d. nitzsche chapter 13 capm and apt investments
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© K. Cuthbertson and D. Nitzsche
Chapter 13
CAPM and APTInvestments
Quiz
RA = 11.2% βA=.82
RB = 17.6% βB=1.46 What is the risk free rate? What is the return on the market? What is the Market Risk Premium?
© K. Cuthbertson and D. Nitzsche
Learning Objectives
Link between CAPM and mean-variance portfolio theory
Beta as a measure of undiversifiable riskLinear relationship between expected returns
and beta of stocks- SMLUse of CAPM for portfolio construction; for
market risk in a portfolio; for estimation of discount factor in DFCF valuation methods, for market timing strategies
© K. Cuthbertson and D. Nitzsche
Capital Market Theory: An Overview
Capital market theory extends portfolio theory and develops a model for pricing all risky assets, while capital asset pricing model (CAPM) will allow you to determine the required rate of return for any risky asset based on the systematic risk in the asset
2
2
( , )
where return on the market index
variance of the market returns
return on Security
i mi
m
m
m
i
COV R R
R
R i
CAPM
CAPM states that the expected excess return on a stock is defined by the stock’s market risk beta and by the expected excess return on the market:
(ER-r)=β(ERm –r) or ER=r+β(ERm –r)
© K. Cuthbertson and D. Nitzsche
Systematic Risk
Risk factors that affect a large number of assets
Also known as non-diversifiable risk or market risk
Examples: changes in GDP, inflation, interest rates, general economic conditions
6
Portfolio Diversification (1)7
Portfolio Diversification (2)8
Measuring Systematic Risk
Beta (β) is a measure of systematic risk
Interpreting beta: β = 1 implies the asset has the same systematic risk
as the overall market βm=Cov(Rm; Rm)/σm2
but Cov(Rm; Rm)=σm2
β < 1 implies the asset has less systematic risk than the overall market
β > 1 implies the asset has more systematic risk than the overall market
9
High and Low Betas10
Portfolio Betas
Consider the previous example with the following four securitiesSecurity Weight BetaA .133 3.69B .2 0.64C .267 1.64D .4 1.79
What is the portfolio beta? 1.773
11
CAPM and SIM
SIM is statistical relationship (regression of excess returns of a stock and a benchmark)
The intercept of the regression line of SIM is a performance measure Jensen’s alpha
© K. Cuthbertson and D. Nitzsche
Market Index in the SIM
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
-0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08
Excess Return on Market
Ex
ce
ss
Re
turn
on
BA
Sh
are
s
Security Market Line
CAPM is an asset pricing equation that explains the systematic risk and the role of diversification E(Ri) = Rf + βi(Rm-Rf)
Rearrange CAPM in terms of market riskCalculate beta on historical stock returns or
from financial information vendorReturn averages from historical data serve as
estimates of expected returns
© K. Cuthbertson and D. Nitzsche
© K. Cuthbertson and D. Nitzsche
Expected/Average Returns
SML
Beta, βi
Q (buy)
S (sell)
P
Average historic return for S
SML/CAPMreturn, ERP
0.5 1 1.2
T (sell)
M
The larger is βi, the larger is the CAPM expected return ERi
r = 5%
9%
13%
4%
14%
Figure 1 : Security market line (SML)
Matrix
Specific elements of a matrix are often denoted by a variable with two subscripts. For instance, a2,1 represents the element at the second row and first column
© K. Cuthbertson and D. Nitzsche
Applications of CAPM
Market timingPortfolio constructionValue at riskPerformance measure
Treynor measure for excess return (uses market risk β)
Sharpe measure (uses total risk σ) Jansen’s α
© K. Cuthbertson and D. Nitzsche
Two Fund Separation and CML
© K. Cuthbertson and D. Nitzsche
Return and Risk of Two Fund Portfolio
Return is weighted average of Risk free rate and market return; portfolio weights sum to one Rp= wRf (Rf) + (1- wRf )(Rm)
Risk on this portfolio is also weighted average (covariance zero; σRf =0 σRp = wRf (σRf ) + (1- wRf )(σ Rm )
© K. Cuthbertson and D. Nitzsche
Using the CML to Invest: An Example
• How much to invest in the riskless How much to invest in the riskless security?security?
11.5%= w11.5%= wRF RF (4%) + (1-w(4%) + (1-wRFRF )(9%) )(9%)
wwRFRF= -0.5= -0.5
• The investment strategy is to borrow The investment strategy is to borrow 50% and invest 150% of equity in the 50% and invest 150% of equity in the
market portfoliomarket portfolio
Background to Capital Market Theory
Assumptions: All investors are Markowitz efficient investors who
want to target points on the efficient frontier Investors can borrow or lend any amount of money
at the risk-free rate of return (RFR) All investors have homogeneous expectations; that
is, they estimate identical probability distributions for future rates of return
All investors have the same one-period time horizon such as one-month, six months, or one year
Continued…
Background to Capital Market Theory
Assumptions: All investments are infinitely divisible, which
means that it is possible to buy or sell fractional shares of any asset or portfolio
There are no taxes or transaction costs involved in buying or selling assets
There is no inflation or any change in interest rates, or inflation is fully anticipated
Capital markets are in equilibrium, implying that all investments are properly priced in line with their risk levels
Background to Capital Market Theory
Development of the Theory The major factor that allowed portfolio theory to
develop into capital market theory is the concept of a risk-free asset An asset with zero standard deviation Zero correlation with all other risky assets Provides the risk-free rate of return (RFR) Will lie on the vertical axis of a portfolio graph
Risk-Return Possibilities
One can attain a higher expected return than is available at point M
One can invest along the efficient frontier beyond point M, such as point D
Risk-Return Possibilities
With the risk-free asset, one can add leverage to the portfolio by borrowing money at the risk-free rate and investing in the risky portfolio at point M to achieve a point like E
Point E dominates point D One can reduce the investment risk by lending money at the risk-free
asset to reach points like C
Risk, Diversification & the Market Portfolio: The Market Portfolio
Because portfolio M lies at the point of tangency, it has the highest portfolio possibility line
Everybody will want to invest in Portfolio M and borrow or lend to be somewhere on the CML
It must include ALL RISKY ASSETS
Risk, Diversification & the Market Portfolio: The Market Portfolio
Since the market is in equilibrium, all assets in this portfolio are in proportion to their market values
Because it contains all risky assets, it is a completely diversified portfolio, which means that all the unique risk of individual assets (unsystematic risk) is diversified away
Risk, Diversification & the Market Portfolio
Systematic Risk Only systematic risk remains in the market
portfolio Variability in all risky assets caused by
macroeconomic variables Variability in growth of money supply Interest rate volatility Variability in factors like (1) industrial production (2) corporate
earnings (3) cash flow
Can be measured by standard deviation of returns and can change over time
Risk, Diversification & the Market Portfolio
How to Measure Diversification All portfolios on the CML are perfectly positively
correlated with each other and with the completely diversified market Portfolio M
A completely diversified portfolio would have a correlation with the market portfolio of +1.00
Complete risk diversification means the elimination of all the unsystematic or unique risk and the systematic risk correlates perfectly with the market portfolio
Risk, Diversification & the Market Portfolio:
Eliminating Unsystematic Risk
The purpose of diversification is to reduce the standard deviation of the total portfolio
This assumes that imperfect correlations exist among securities
Risk, Diversification & the Market Portfolio
The CML & the Separation Theorem The CML leads all investors to invest in the M
portfolio Individual investors should differ in position on the
CML depending on risk preferences How an investor gets to a point on the CML is
based on financing decisions
Risk, Diversification & the Market Portfolio
The CML & the Separation Theorem Risk averse investors will lend at the risk-free rate
while investors preferring more risk might borrow funds at the RFR and invest in the market portfolio
The investment decision of choosing the point on CML is separate from the financing decision of reaching there through either lending or borrowing
Risk, Diversification & the Market Portfolio
A Risk Measure for the CML The Markowitz portfolio model considers the average
covariance with all other assets The only important consideration is the asset’s
covariance with the market portfolio
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