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Professor XXX Course Name / #. Efficient Risky Portfolios. Variance of return - a poor measure of risk. Investors can only expect compensation for systematic risk Asset pricing models aim to define and quantify systematic risk. - PowerPoint PPT PresentationTRANSCRIPT
Chapter 6Risk and Return: The CAPM
and Beyond
Professor XXX
Course Name / #
22
Efficient Risky Portfolios
Variance of return - a poor measure of risk
Investors can only expect compensationfor systematic risk
Asset pricing models aim to define andquantify systematic riskBegin developing pricing model by asking:Are some portfolios better than others?
33
E(RP)
P
Expanding The Feasible Set On The Efficient Frontier
EF including domestic & foreign assets EF including domestic
stocks, bonds, and real estate
EF for portfolios of domestic stocks
44
Two – Asset Portfolios
E(RP)
P
Stock A•
• Stock B
MVP (75%A, 25%B)
C (50%A, 50%B)
inefficient portfolios
efficient portfolios
•
•
Are Some Portfolios Better Than Others?
efficient portfolios
•MVP
D
F•
•
E
• • •• •
• ••
•
• ••
•
N – Asset Portfolios
Efficient portfolios achieve the highest possible return for any level of volatility
What happens when we add a risk-free asset to the picture?
55
Expected Return (per month) and Standard Deviation for Various Portfolios
66
Riskless Borrowing And Lending
Return: 6%Risk-free asset Y
Buying asset Y = Lending money at 6%
interestHow would a portfolio with $100 (50%) in asset X and
$100 (50%) in asset Y perform?
Portfolio has lower return but also less volatility than 100% in XPortfolio has higher return and higher volatility than 100% in risk-free
Three possible returns:
-10%; 10%; 30%
Risky asset X
Expected return = 10%Standard deviation =16.3%
$100 Asset X
$100 Asset Y
Three possible returns:
-2%; 8%; 18%
Expected return = 8%Standard deviation =8.16%
77
Riskless Borrowing And Lending (Continued)
What if we sell short asset Y instead of buying it?Borrow $100 at 6%Must repay $106
Invest $300 in XOriginal $200 investment plus $100 in borrowed funds
%18$200
$200-$106-$270 Investment $200on Return Net When X Pays –
10%
%12$200
$200-$106-$330 Investment $200on Return Net When X Pays 10%
%42$200
$200-$106-$390 Investment $200on Return Net When X Pays 30%
Expected return on the portfolio is 12%. Higher expected return comes at the expense of greater volatility
88
Riskless Borrowing And Lending (Continued)
PortfolioExpected Return
Standard Deviation
50% risky, 50% risk-free 8% 8.16%
100% risky, 0% risk free 10% 16.33%
150% risky, -50% risk free 12% 24.49%
The more we invest in X, the higher the expected return
The expected return is higher, but so is the volatility
This relationship is linear
99
Portfolios Of Risky & Risk-Free Assets
•
••
•RF=6%
0 30% 52%
12%
16.5%
E(RP)
P
9%
15%
A
MF
B
1010
New Efficient Frontier
1111
The Market Portfolio
Only one risky portfolio is efficient
Equilibrium requires this to be the Market Portfolio
Suppose investors agree on which portfolio is efficient
Market Portfolio: value weighted portfolio of all available risky assets
The line connecting Rf to the market portfolio - called the Capital Market Line
1212
Finding the Optimal Risky Portfolio
If investors can borrow and lend at the risk-free rate, then from the entire feasible set of risky portfolios, one portfolio will emerge that maximizes the return investors can expect for a given standard deviation.
To determine the composition of the optimal portfolio, you need to know the expected return and standard deviation for every risky asset, as well as the covariance between every pair of assets.
1313
Finding the Optimal Portfolio
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The Capital Market Line
The line connecting Rf to the market portfolio is called the Capital Market Line (CML)
CML quantifies the relationship between the expected return and standard deviation for portfolios consisting of the risk-free asset and the market portfolio, using
1515
Capital Asset Pricing Model (CAPM)
Only beta changes from one security to the next. For that reason, analysts
classify the CAPM as a single-factor model, meaning that just one variable explains differences in returns across securities.
1616
The Security Market Line
Plots the relationship between expected return and betas
In equilibrium, all assets lie on this lineIf stock lies above the line
Expected return is too highInvestors bid up price until expected return
fallsIf stock lies below the line
Expected return is too lowInvestors sell stock, driving down price until
expected return rises
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The Security Market Line
i
E(RP)
RF
SML
Slope = E(Rm) - RF = Market
Risk Premium (MRP)
•A - Undervalued
•
•
•RM
=1.0
•B
•A
• B - Overvalued
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Beta
2m
imi
The numerator is the covariance of the stock with the market
The denominator is the market’s variance
In the CAPM, a stock’s systematic risk is captured by beta
The higher the beta, the higher the expected return on the stock
1919
Beta And Expected Return
Beta measures a stock’s exposure to market risk
The market risk premium is the reward for bearing market risk:
• Rm - Rf
E(Ri) = Rf + ß [E(Rm) – Rf]
• Return for bearing no market risk
• Stock’s exposure to market risk
• Reward for bearing market risk
2020
Calculating Expected Returns
E(Ri) = Rf + ß [E(Rm) – Rf]• Assume
• Risk–free rate = 2%• Expected return on the market = 8%
If Stock’s Beta Is Then Expected Return Is
0 2%
0.5 5%
1 8%
2 14%When Beta = 0, The Return Equals The Risk-Free ReturnWhen Beta = 1, The Return Equals The Expected Market
Return
2121
Scatterplot for Returns on Sharper Image and S&P500
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
-0.3 -0.2 -0.1 0 0.1 0.2 0.3
S&P500 Weekly Return
Sh
arp
er Im
age
Wee
kly
Ret
urn
Slope = Beta = 1.44
R-square = 0.19
2222
Scatterplot for Returns on ConAgra and S&P500
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
-0.15 -0.1 -0.05 0 0.05 0.1 0.15
S&P500 Weekly Return
Co
nA
gra
We
ek
ly R
etu
rn
beta = 0.11
R-square = 0.003
2323
Scatterplot for Returns on Citigroup and S&P500
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2
S&P500 Weekly Return
Cit
igro
up
We
ek
ly R
etu
rn beta = 1.20
R-square = 0.50
2424
r%
12.4%
10
5
Rf = 2%
1 2GEP&G
SML
6.8%
Using The Security Market Line
15
•
slope = E(Rm) – RF =
MRP = 10% - 2% = 8% = Y ÷ X
The SML and where P&G and GE place on it
2525
r%
11.1%
10
5
Rf = 2%
1 2GEP&G
SML1
6.2%
Shifts In The SML Due To A Shift In Required Market Return
15
Shift due to change in market risk premium from 8% to 7%
••
SML2
2626
r%
14.4%
10
5Rf = 4%
1 2GEP&G
SML1
8.8%
Shifts In The SML Due To A Shift In The Risk-Free Rate
15
•Shift due to change in
risk-free rate from 2% to 4%, with market risk
premium remaining at 8%. Note all returns
increase by 2%
SML2
2727
Alternatives To CAPM
Arbitrage Pricing Theory
Fama-French Model lowhigh3bigsmall21 RRRRRRRR iifmifi
Betas represent sensitivities to each source of riskTerms in parentheses are the rewards for bearing each type of risk.
2828
The Current State of APT
Investors demand compensation for taking risk because they are risk averse.
There is widespread agreement that systematic risk drives returns.
You can measure systematic risk in several different ways depending on the asset pricing model you choose.
The CAPM is still widely used in practice in both corporate finance and investment-oriented professions.