portfolio management - classroom
TRANSCRIPT
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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
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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
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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.
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Return Objectives
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Investment Constraints
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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
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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
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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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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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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.