Portfolio Management - Classroom

8/8/2019 Portfolio Management - Classroom

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PortfolioManagement


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Table of Contents

Portfolio Management

Asset Allocation Decision

Introduction to Portfolio Management Introduction to Asset Pricing Models

2


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Daily cash managementEnsure sufficient cash

(target balance)Avoid keeping excesscash balances because ofthe interest foregone bynot investing the cash inshort-term securities toearn interest.

3

Firms also use short-term

borrowings, typically from

banks or from issuingcommercial paper, to

manage their daily cash

positions.


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Asset Allocation Decision


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Steps In The Portfolio ManagementProcess

5

serves as a road map valuable to both

investors andportfolio managers

why construct a

policy statement? to understand and

articulate investorgoals

to create a portfolioperformancestandard


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Investment Objectives &Constraints

Investment objectives must be stated in terms of bothrisk and return. Return objectives may be stated in absolute ($) terms

or percentages and may be stated in terms of: capital preservation capital appreciation

current income total return

Return only objectives may lead to inappropriate, high-risk investments and excessive trading.

Risk tolerance is a function of investors psychological

makeup and covers personal factors such as age,family situation, existing wealth, cash reserves andincome.

6


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Return Objectives

7


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Investment Constraints

8


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The Importance of AssetAllocation

process of dividingfunds into asset classes

concerned with funds

variability

concerned with the riskassociated with

different assets

concerned with

relationship among

investments returns

9

In general, fourdeterminations are made

when constructing an

investment strategy:

asset classes

policy weights

allocation ranges

security selection

First two provide 85-95%

of overall investmentreturn.


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The Investor Life Cycle

10

Accumulation phase

Long-term:

retirement

childrens college needsShort-term:

house

car

Consolidation phase

Long-term:

retirement

Short-term:

vacations

childrens college needs

Spending phase

Gifting phase

Long-term:

retirement

Short-term:

vacations

childrens college needs

25 35 45 55 65 75Age

Phases of Wealth Accumulation


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11

Pop Quiz 2.1

The return objective of an investor who is relatively risk averse yet has along time horizon and little need for liquidity would most likelybe

described as:

A. capital preservation.

B. capital appreciation.

C. total return.

D. long-term appreciation.

A total return strategy is appropriate for an investor with a longer-terminvestment horizon who is very risk tolerant. The inclusion of a

significant allocation to income producing securities such as bonds andhigh-dividend stocks makes this a less risky strategy than that for anobjective of capital appreciation.


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Introduction toPortfolio

Management


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13

Risk Aversion

Individuals prefer less risk to more risk. given two asset with the same return, they choose less

risky

they will only accept a riskier investment if they are

compensated in the form of greater expected return

Evidence could be seen from the promised yield

on bonds. The promised yield on bonds increases as one goes

from AAA (the lower risk class) to AA to A, and so on

as such, risk aversion implies a positive

relationship between expected return and risk.


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Markowitz Portfolio Theory:Assumptions


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Markowitz Portfolio TheoryApplied

MarkowitzPortfolioTheory


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Expected Return (QMRefresher) For an individual investment

n

E(R) =PiRi = P1R1 + P2R2 + + PnRn i=1

Where: Pi = probability that state iwill occur

Ri = asset return if the economy is in state I

For a portfolio

E(Rp) = w1E(R1) + w2E(R2)

Where: E(R1

) = expected return on asset 1

E(R2) = expected return on asset 2

w1 = %age of total portfolio value invested in asset 1

w2 = %age of total portfolio value invested in asset 2


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Variance & Standard deviation (QMRefresher)

Variance = Pi[Ri - E(R)]2 = 0.0025 + 0.0000 + 0.0025= 0.0050

Standard deviation = (0.0050)1/2 = 0.0707 = 7.07%

State i Pr

Ex ansion

Variance and Standard Deviation Computation


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Covariance & CorrelationCoefficientCovariance Measures the extent to which two variables move together Measures the degree to which two variables move together

relative to their individual mean values over time For two assets, i and j, the covariance of rates of return is defined

as:Covij = E{[Ri,t - E(Ri)][Rj,t - E(Rj)]}

Correlation Coefficient Standardized measure of the linear relationship between two variables considers variability of two individual return series range of values = from -1 to +1

+1 = perfect positive relationship -1 = perfect negative relationship

0 = no linear relationship

rij = Covij/(sisj)

Covij= covariance of returns for securities i and jsi= standard deviation of returns for security i

sj= standard deviation of returns for security j


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Standard Deviation of aPortfolio

port ijj

n

i

n

j

in

i

ii Covwwwport = ==

+=1 11

22

port = Standard deviation of portfolio

= Weights of individual assets in the portfolio2

i = Variance of rates of return for asset i

= Covariance between rates of return for assets i and j.

Wi

Covij

2

= Portfolio variance

2

port

Key point of LOS (and of Markowitz analysis): The risk of a portfolio of riskyassets depends on the asset weights, the standard deviations of theassets returns, and (crucially) the correlation (covariance) of the assetreturns.


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The Optimal Portfolio

)E( port

)E(Rport

X

Y

U

3 U

2 U

1

U3U2 U1

The optimal portfolio has the

highest utility for a given investor It lies at the point of tangency

between the efficient frontier andthe utility curve with the highestpossible utility

A relatively more conservative

investor would perhaps choosePortfolio X

On the efficient frontier and onthe highest attainable utilitycurve

A relatively more aggressive

investor would perhaps choosePortfolio Y

On the efficient frontier and onthe highest attainable utilitycurve


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Pop Quiz 3.1

A and B are efficient portfolios. Then,

A. A and B must have the same risk.

B. A and B have the same risk-to-reward ratio.

C. if A has a higher expected return, it must have a lower risk.

D. A combination of investments in A and B is necessarily anefficient investment.

E. None of the above.

An efficient frontier is made up of portfolios which have the highest expected

return for a given level of risk and the lowest level of risk for a given level ofexpected returns. Hence, if A has a higher expected return, it must have a higher

risk. However, this does not mean that A cannot have a higher risk-to-reward

ratio. Finally, a combination of two efficient portfolios is always efficient

(property of the frontier).


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Pop Quiz 3.2Given that the covariance between two assets is zero, the standard

deviation on asset 1 is 35, and the standard deviation on asset 2 is 15,what is the standard deviation on a portfolio in which asset 1 accounts

for 60%, and asset 2 accounts for 40% of portfolio value?

A. 20.5

B. 24

C. 21.8

D. 421

E. 477

The standard deviation of a portfolio with two assets is equal to the square root

of the following: weight of asset 1 squared multiplied by the standard deviation of

asset 1 squared, plus the weight of asset 2 squared multiplied by the standarddeviation of asset 2 squared, plus two times the weigh of asset 1 multiplied by

the weight of asset 2 multiplied by the covariance. In this example, the standard

deviation of the portfolio is equal to [(0.6)^2] x [35^2)] + [(0.4)^2] x [15^2] + [2 x

0.5 x 0.5 x 0] = 477. The square root of 477 is 21.8.


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Introduction to

Asset Pricing Models


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Capital Market Theory:Assumptions


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Risk Free Assets

Risk-free asset = asset with zero variance

one from which future returns are certain rate of return = risk-free rate of return (RFR)

Risky asset = an asset from which future returns are uncertain.

What would happen if risk-free assets are combined with a

portfolio of risky assets?

dilemma: What happens to average rate of return and the standarddeviation of returns?

expected return standard deviation ...risk-return combination (w/ sample graph)risk-return with leverage

return ...

risk .

E(port ) = (1-WRF )i

E(Rport ) = WRF (RFR) + (1-WRF ) E(Ri )

E(Rport ) = WRF (RFR) + (1-WRF ) E(RM )

E(port ) = (1-WRF )M


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Risk-Return Combination

E(Rport )

RFR

E(port )

CB

A

MD

Capital market line

Efficient frontier

Lendi

ng

Borro

wing


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CML & Market Portfolio

Capital Market Line (CML) Markowitz efficient frontier

generates a set of straight line

portfolio possibilities dominant line is the one tangent

to the efficient frontier, the CML

dominant line and all portfolioson CML are perfectly positively

correlated portfolios on CML combine risky

and risk-free assets investors target this line

depending on their riskpreferences

Market Portfolio in the CML world, all investors will

hold some combination of the RFR

and portfolio M (the market portfolio) portfolio that includes all risky assets

common stocks, non-US stocks

US and non-US bonds options, real estate coins, stamps, art, or antiques

market portfolio is a completely

diversified portfolio unique risk is offset by unique

variability


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Security Market Line (SML)

SML: represents the relationship

between systematic risk and the

expected or required rate of return on

an asset.

Differs from the CML: SML relies

on the systematic risk (beta) while

CML uses the variance to representrisk.

Equation:

E(Ri) = RFR + Betai(RM RFR)

estimated rates of return should beconsistent with levels of systematicrisk

above SML line = underpriced below SML line = overpriced

S

M

L

RFR

RM

M

2

MCoviM

E(Rit)


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Security Market Line (SML)

Stock

A

B

CD

E

Beta

0.70

1.00

1.151.40

-0.30

E(Ri)

12.2

14.0

14.916.4

6.2

Est. Ret.

12.0

8.1

24.25.3

10.0

4 less 3

-0.2

-5.9

9.3-11.1

3.8

Valuation

Properly

Over

UnderOver

Under

1 2 3 4

E(Ri) = required return


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Capital Asset Pricing Model

CAPM calculates theexpected or required rates ofreturn on risky assets.

CAPM providescomparability option

you compare your estimatedrate of return to the required rate ofreturn implied by the CAPM

then, you determine whetherthe asset is

undervalued overvalued properly valued

Beta is a measure of systematic risk.

Standardized because it divides an assetscovariance with the market portfolio bythe variance of the market portfolio.

Thus, the market portfolio has a beta of 1.

If the beta is greater than 1, then anasset has more systematic risk (i.e., itis more volatile) than the marketportfolio and has an expected returngreater than the expected return on themarket


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Characteristic Line

The characteristic line is the regression line thatresults from a regression of an individual asset orportfolios return against the return to the marketportfolio.

The estimated slope coefficient (beta) from this

regression is a measure of the asset or portfoliossystematic risk.

Beta measures how the returns on the stock movein reaction to changes in the overall market

(definition of systematic risk).


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Pop Quiz 4.1

According to capital market theory, the only relevant risk measurefor a security is

A. its range of returns.

B. its covariance with the market portfolio.

C. its standard deviation

D. its standard deviation / variance.

E. its average covariance with other securities its portfolio.

According to the Markowitz portfolio model, the only relevant risk measure for a

security is its average covariance with all the other assets in the portfolio.

According to capital market theory, the only relevant portfolio is the market

portfolio. Combining the two models results in the conclusion that the only relevant

risk measure for a security is its average covariance with the securities in the

market portfolio, or rather its covariance with the market portfolio.


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Pop Quiz 4.2

If the estimated return on your portfolio is higher than the requiredrate of return dictated by your assumed model of security returns

(like CAPM), then in your model, the portfolio is ________.

A. under-priced

B. fairly priced

C. overpriced

D. under- or overpriced

E. None of the above.

If the expected return is higher than that implied by its risk, then the extra

return can come only through an under-pricing of the portfolio that will

get corrected by the time the portfolio cash flows are realized.

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Portfolio Management - Classroom