Intro to Portfolio Management

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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Process1. Policy statement

Specifies investment goals and acceptable

risk levels The road map that guides all investment

decisions


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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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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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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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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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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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p

m

fmfp

rr

+=


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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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