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8/8/2019 Intro to Portfolio Management
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The Portfolio Management
ProcessA four step process:
1. Construct a policy statement
2. Study current financial conditions andforecast future trends
3. Construct a portfolio
4. Monitor needs and conditions
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The Portfolio Management
Process1. Policy statement
Specifies investment goals and acceptable
risk levels The road map that guides all investment
decisions
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The Portfolio Management
Process2. Study current financial and economic
conditions and forecast future trends
Determine strategies that should meetgoals within the expected environment
Requires monitoring and updates since
financial markets are ever-changing
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The Portfolio Management
Process3. Construct the portfolio
Given the policy statement and the
expected conditions, go about investing Allocate available funds to meet goals
while managing risk
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The Portfolio Management
Process4. Monitor and update
Revise policy statement as needed
Monitor changing financial and economicconditions
Evaluate portfolio performance
Modify portfolio investments accordingly
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The Policy Statement
Understand and articulate realistic goals Know yourself
Know the risks and potential rewards frominvestments
Learn about standards for evaluating
portfolio performance Know how to judge average performance
Adjust for risk
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The Policy Statement
Dont try to navigate
without a map!
Important Inputs: Investment
Objectives
Investment
Constraints
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Investment Objectives
Need to specify return
and risk objectives Need to consider the
risk tolerance of the
investor
Return goals need to
be consistent with
risk tolerance
These will change
over time
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Investment Objectives
Possible broad goals:
Capital preservation
Maintain purchasing power Minimize the risk of loss
Capital appreciation
Achieve portfolio growth through capitalgains
Accept greater risk
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Investment Objectives
Current income Look to generate income rather than
capital gains May be preferred in spending phase
Relatively low risk
Total return Combining income returns and
reinvestment with capital gains
Moderate risk
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Investment Constraints
These factors may limit or at least impact the
investment choices:
Liquidity needs How soon will the money be needed?
Time horizon How able is the investor to ride out several bad
years?
Legal and Regulatory Factors Legal restrictions often constrain decisions
Retirement regulations
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Investment Constraints
Tax Concerns Realized capital gains vs. Ordinary
income? Taxable vs. Tax-exempt bonds?
Regular IRA vs. Roth IRA?
401(k) and 403(b) plans
Unique needs and preferences Perhaps the investor wishes to avoid types
of investments for ethical reasons
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Investment Education
The type of information necessary to constructa good policy statement is neither commonsense or common knowledge.
Many investors fail to diversify. Many fail to plan completely.
Data indicates that many Americans havegreatly under-invested for the future.
The bottom line: If you do not plan for thefuture, you will likely not be prepared for it.
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Asset Allocation Decisions
Four decisions in an investment strategy:
What asset classes should be
considered?What should be the normal weight for
each asset class?
What are the allowable ranges for the
weights?What specific securities should be
purchased?
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The Importance of Asset
Allocation The asset allocation decision (which classes
and at what weights) is very important. Using
fund data: About 90% of return variability over time can be
explained by asset allocation.
About 40% of the differences between returns can
be explained by differences in asset allocation.
Asset allocation is thus the major factor thatdrives portfolio risk and return.
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Risk/Return History and Asset
AllocationLooking at return data on various asset classes
indicate some important factors for investors: Over long time horizons, stocks have always
outperformed low-risk investments.
So the additional risk of stock investing (higher
return standard deviations) over shorter time
horizons seems to all but disappear over time.
Need to consider real investment returns overtaxes and costs
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Asset Allocation and Cultural
Differences Differences in social, political, and tax
environments influence asset allocation.
For instance, 58% of pension fund assets are
invested in equities in the U.S. 78% in equities in United Kingdom, where high
average inflation impacts this choice
8% in equities in Germany, where generous
government pensions and greater risk aversionseem to play a strong role
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Probability Concept
Random variable
Something whose value in the future issubject to uncertainty.
Probability
The relative likelihood of each possibleoutcome (or value) of a random variable
Probabilities of individual outcomes cannotbe negative nor greater than 1.0
Sum of the probabilities of all possibleoutcomes must equal 1.0
Moments
Mean, Variance (or Standard deviation),
covariance
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Computing the Basic Statistics
A security analyst has prepared thefollowing probability distribution of thepossible returns on the common stockshares of two companies:
Compu-Graphics Inc. (CGI) and DataSwitch Corp. (DSC).
Probability Return onCGI
Return onDSC
0.300.500.20
10%14%20%
40%16%20%
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The Mean
%00.14
%)20(20.0%)14(50.0%)10(30.0
3
1
=
++=
==n
nnxpCGI
For CGI, the mean (or expected) return is:
Similarly, the mean return for DSC is 24.00%
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The Variance and Standard Deviation
( )
( )0012
142020014145001410300222
1
22
.
)(..)(.
xpN
n
xnnx
=
++=
==
%46.300.122 ===xx
The variance of CGIs returns is:
The Standard Deviation of CGIs return is:
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The Covariance
( )( )
0024
24201420200
2416141450024401410300
1
.
)()(.
)()(.)()(.
yxp ynxn
N
n
nCD
=
+
+=
==
The covariance of the returns on CGI and
DSC is:
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The Correlation Coefficient
( )( )655.0
58.1046.3
00.24
=
=
=
yx
xy
xy
The correlation coefficient between CGIand DSC is:
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CGI DSC
Mean
Standard Deviation
14.00%
3.46%
24.00%
10.58%
Correlation Coefficient -0.655
Summary of Results for CGI and DSC
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A portfolio is a combination of two ormore securities.
Combining securities into a portfolio
reduces risk. An efficient portfolio is one that has thehighest expected return for a given levelof risk.
We will look at two-asset portfolios infair detail.
Portfolio Securities
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Portfolio Expected Return andRisk
Expected Return Risk
The Expected
Returns
of the
Securities
The
Portfolio
Weights
The Risk
of the
Securities
The
Portfolio
Weights
The
Correlation
Coefficients
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Portfolio Expected Return andRisk
Portfolio Variance
The square root of variance is standard deviation of theportfolio.
In equation WA = weight of security A, WB = weight of SecurityB
others notation are the standard notations of StandardDeviation and Coefficients of Correlation
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Portfolio Weights Portfolios
CGI DSC ExpectedReturn
StandardDeviation
1.000.750.670.50
0.250.00
0.000.250.330.50
0.751.00
14.00%16.50%17.33%19.00%
21.50%24.00%
3.46%2.18%2.64%4.36%
7.40%10.58%
Portfolio Weights and Expected
Return
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CGI
DSC
10%
15%
20%
25%
0% 5% 10%
Standard Deviation
ExpectedRe
turn
Home
Portfolio Expected Return and Risk
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Diversification of Risk
Note that while the expected return ofthe portfolio is between those of CGI andDSC, its risk is less than either of the twoindividual securities.
Combining CGI and DSC results in asubstantial reduction of risk -diversification!
This benefit of diversification stemsprimarily from the fact that CGI and DSCsreturns are not perfectly correlated.
C l ti C ffi i t d P tf li
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All else being the same, lower thecorrelation coefficient, lower is the
risk of the portfolio.
Recall that the expected return of theportfolio is not affected by the
correlation coefficient.
Thus, lower the correlationcoefficient, greater is the
diversification of risk.
Correlation Coefficient and PortfolioRisk
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Stock X Stock Y
Expected ReturnStandard Deviation
10%12%
25%30%
Consider stocks of two companies, X andY. The table below gives their expectedreturns and standard deviations.
Plot the risk and expected return ofportfolios of these two stocks for thefollowing (assumed) correlationcoefficients:
-1.0 0.5 0.0 +0.5 +1.0
Correlation Coefficient and Portfolio Risk
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5%
15%
25%
0% 5% 10% 15% 20% 25% 30% 35%
Standard Deviation
ExpectedR
etur
Y
Correlation
Coefficient-1.0
-0.5
0.0
+0.5
+1.0X
Correlation Coefficient and Portfolio Risk
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Portfolios with Many Assets
The above framework can be expandedto the case of portfolios with a largenumber of stocks.
In forming each portfolio, we can varythe number of stocks that make up theportfolio,
the identity of the stocks in the portfolio, andthe weights assigned to each stock.
Look at the plot of the expected returns
versus the risk of these portfolios
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All Combinations of Risky Assets
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Efficient Frontier
A portfolio is an efficient portfolio ifno other portfolio with the same expectedreturn has lower risk, or
no other portfolio with the same risk has ahigher expected return.
Investors prefer efficient portfolios overinefficient ones.
The collection of efficient portfolio iscalled an efficient frontier.
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(expect
ed
return
)
F
E
(risk)
Efficient Frontier
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Choosing the Best Risky Asset
Investors prefer efficient portfolios overinefficient ones.
Which one of the efficient portfolios is best?
We can answer this by introducing a risklessasset.
There is no uncertainty about the future value of
this asset (i.e. the standard deviation of returns iszero). Let the return on this asset be rf.
For practical purposes, 90-day U.S. TreasuryBills are (almost) risk free.
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Combinations of a Risk Free and a Risky Asset
(risk)
(expe
cted
retu
rn)
F
E
N
rf
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Best Risky Asset
(expec
ted
return)
(risk)
F
E
M
rf
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The Capital Market Line
Assume investors can lend andborrow atthe risk free rate of interest.
borrowing entails a negative investment in
the riskless asset.
Since every investor hold a part of thebest risky asset M, M is the marketportfolio.
The Market portfolio consists of all riskyassets.
Each asset weight is proportional to itsmarket value.
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The Capital Market Line
p
m
fmfp
rr
+=
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The Capital Market Line
rf
(expe
cted
retu
rn
)
(risk)
F
E
M
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Explain the importance of asset pricingmodels.
Demonstrate choice of an investmentposition on the Capital Market Line (CML).
Understand the Capital Asset Pricing Model(CAPM), Security Market Line (SML) and its
uses.
Next Coverage
Understand the determination of the expected rate of
returnCapital Asset Pricing Model
Decomposition of Risk: Systematic Vs. Unsystematic.
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Asset Pricing Models
These models provide a relationshipbetween an assets required rate of returnand its risk.
The required return can be used for:
computing the NPV of your investment.
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The Capital Asset Pricing Model (CAPM)
It allows us to determine the requiredrate of return (=expected return) for anindividual security.
Individual securities may not lie on the CML.
Only efficient portfolioslie on theCML
The Security Market Line (SML) can be
applied to any securities or portfoliosincluding inefficient ones.
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The Security Market Line (SML)
( )fmjfj rr +=
m
jmj
m
mjmj
m
j
Mr
jrCOV
,
2
,
2
),(
===
where
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What does the SML tell us
The required rate of return on a securitydepends on:
the risk free rate
the beta of the security, and
the market price of risk.
The required return is a linear function of
the beta coefficient.
All else being the same, higher the betacoefficient, higher is the required return on thesecurity.
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Graphical Representation of the SML
Beta
Expected
Returns
rf
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Computing Required Rates of Return
Common stock shares of Gator SprinklerSystems (GSS) have a correlationcoefficient of 0.80 with the market
portfolio, and a standard deviation of28%. The expected return on the marketportfolio is 14%, and its standarddeviation is 20%. The risk free rate is 5%.
What is the required rate of return onGSS?
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Required Return on GSS
First compute the beta of GSS:
Next, apply the SML:
( )( ) 1.1220
280.80
m
GSSmGSS,
GSS
==
=
( )( ) 15.08%5%14%1.125%
rr fmGSSfGSS=+=
+=
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Required Rate of Return on GSS
What would be the required rate ofreturn on GSS if it had a correlation of0.50 with the market? (All else is the
same)Beta = 0.70 and GSS = 11.30%
What would be the required rate of
return on GSS if it had a standarddeviation of 36%, and a correlation of0.80? (All else is the same)
Beta = 1.44 and GSS = 17.96%
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Estimating the Beta Coefficient
If we know the securitys correlation withthe
market, its standard deviation, and thestandard
deviation of the market, we can use thedefinition of beta:
Generally, these quantities are notknown.
m
jmj,
j
=
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Interpreting the Beta Coefficient
The beta of the market portfolio isalways equal to 1.0.
The beta of the risk free asset is always
equal to 0.0
m
m m m
m m mce= = =
,
,sin .1 10
0.0since1,
===f
m
fmf
f
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Interpreting the Beta Coefficient
Beta indicates how sensitive a securitysreturns are to changes in the marketportfolios return.
It is a measure of the assets risk.
Suppose the market portfolios risk premiumis +10% during a given period.
if = 1.50, the securitys risk premium will be+15%.
if = 1.00, the securitys risk premium will be+10%
if = 0.50 the securit s risk remium will be
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Beta Coefficients for Selected Firms
Common Stock Beta
Alex BrownNike Inc. (Class B)
MicrosoftPepsiCo. Inc.McDonalds CorporationBoeing Co.AT&T Corp.
Exxon Corp.
1.901.50
1.401.101.051.000.85
0.60
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Beta of a Portfolio
The beta of a portfolio is the weightedaverage of the beta values of theindividual securities in the portfolio.
where wi is the proportion of valueinvested in security i, and iis the beta of
the security i.
p n nw w w w= + + + +1 1 2 2 3 3
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Applying the CAPM
The CML prescribes that investors shouldinvest in the riskless asset and the marketportfolio.
The true market portfolio, which consistsof all risky assets, cannot be constructed.
How much diversification is necessary to
get substantially all of the benefits ofdiversification?
About 25 to 30 stocks!
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