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PORTFOLIO ANALYSISIndividual securities, as we have seen, have
risk-return characteristics of their own. Portfolios, which are
combinations of securities, may or may not take on the aggregate
characteristics of their individual parts.Portfolio analysis
considers the determination of future risk and return in holding
various blends (combinations) of individual securities.
*
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PORTFOLIO ANALYSIS (Cont)Security analysis recognizes the key
importance of risk and return to the investor.Most methods
recognize return as some dividend receipt and price appreciation
over a period. But the return for individual securities is not
always over the same common holding period, nor are the rates of
return necessarily time-adjusted. An analyst may well estimate
future earnings and a P/E to derive future price. He will surely
estimate the dividend.*
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PORTFOLIO ANALYSIS (Cont)Given an estimate of return, the
analyst is likely to think of and express risk as the probable
downside price expectation (either by itself or relative to upside
appreciation possibilities).Each security ends up with some rough
measure of likely return and potential downside risk for the
future.*
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Why portfolios?The simple fact that securities carry differing
degrees of expected risk leads most investors to the notion of
holding more than one security at time, in a attempt to spread
risks by not putting all their eggs into one basket.Most investors
hope that if they hold several assets, even if one goes bad, the
others will provide some protection from an extreme loss.*
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DiversificationEfforts to spread and minimize risk take the form
of diversificationDiversification of ones holdings is intended to
reduce risk in an economy in which every assets returns are subject
to some degree of uncertainty.Holding one stock each from mining ,
utility, and manufacturing groups is superior to holding three
mining stocks.The best diversification comes through holding large
numbers of securities scattered across industries.*
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Portfolio ConstructionInvestment decisions are all about making
choices: Will income be spent or saved?If you choose to save, you
face a second decision: What should be done with the savings?Each
saver must decide where to invest this command over resources
(goods and services). This is an important decision because these
assets are the means by which investors transfer todays purchasing
power to the future.
*
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Portfolio Construction(cont)Savings are invested in various
assets that make a portfolio which is a combination of assets
designed to serve as a store of value.The investments constitute a
portfolio. Poor management of these assets may destroy the
portfolios value, and the investor will then not achieve his
financial goals.The composition of a portfolio depends on
investment goals.*
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Possible Investment GoalsThere are many reasons for saving and
accumulating assets:Start a business Funds to meet emergenciesFunds
to finance education expensesFunds to make a specified purchase
(e.g., a home; make a downpayment on a house)Funds for retirementOr
accumulate for the sake of accumulating.For any of these reasons
above, people construct portfolios rather than spend all their
current income.*
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Factors affect the construction of a portfolioSeveral factors
affect the construction of a portfolio. These include but not
limited toGoals of the investorRisks involved in a specific
investmentTaxes that will be imposed on any gainKnowledge of
investment alternatives.The motives for saving should dictate, or
at least affect, the composition of the portfolio.*
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Factors affect the construction of a portfolio -goals of the
investorNot all assets are appropriate for all financial
goals.E.g., savings that are held to meet emergencies, such as an
extended illness or unemployment, should not be invested in assets
whose return and safety of principal are uncertain. Instead,
emphasis should be placed on safety of principal and assets that
may be readily converted into cash, such as savings accounts or
shares in money markets. The emphasis should not be on growth and
high returns. However the funds should not sit idle but should be
invested in safe assets that offer a moderate return.
*
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Factors affect the construction of a portfolio- goals of the
investor (Cont..Financing a retirement or a childs education, have
a longer and more certain time horizon. The investor knows
approximately when the funds will be needed and so can construct a
portfolio with a long-term horizon. Bonds that mature when the
funds will be needed or common stocks that offer the potential for
growth would be more appropriate than savings accounts or
certificates of deposit with a bank.The longer time period suggests
the individual can acquire long-term assets that may offer a higher
yield.*
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Factors affect the construction of a portfolio- goals of the
investor (Cont.In addition to the individuals goals, willingness to
bear the risk plays an important role in constructing a portfolio.
Some individuals are more able to bear risk. E.g., if the saver
wants to build a retirement fund, he or she can choose from a
variety of possible investments. Not all investments are equal with
regard to risk and potential return.Investors who are more willing
to accept risk may construct a portfolio with assets involving
greater risk that may earn higher returns. *
-
Factors affect the construction of a portfolio- TaxesTaxes also
affect the composition of an individuals portfolio. Income such as
interest and realized capital gains are taxed. Such taxes and the
desire to reduce them affect the composition of each investors
portfolio.*
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Factors affect the construction of a portfolio(Cont)Portfolio
decisions are important. They set a general framework for asset
allocation of the portfolio among various types of
investments.Individuals, however, rarely construct a portfolio all
at once but acquire assets one at a time. The decision revolves
around which specific asset to purchase: which mutual fund? Which
bond? Or which stock. Security analysis considers the merits of
individual asset. Portfolio management determines the impact that
the specific asset has on the portfolio.It is impossible to know an
assets effect on the portfolio without first knowing its
characteristics.*
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Factors affect the construction of a portfolio(Cont)Stocks and
bonds differ with regard to risk, potential return, and
valuation.Even within a type of asset such as bonds there can be
considerable variation. For example: a corporate bond is different
from a government bond, and a convertible bond is different from a
straight bond that lacks conversion feature. Investors need to
understand these differences as well as the relative merits and
risks associated with each of these assets. After understanding how
individual assets are valued, then he/she may then construct a
portfolio that will aid in the realization of his/her financial
goals.
*
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Diversification and Asset AllocationTo achieve diversification,
the returns on your investments must not be highly correlated.
Factors that negatively affect one security must have a positive
impact on others. E.g: higher oil prices may be good for ExxonMobil
but bad for Delta Airlines. By combining a variety of disparate
assets, an investor achieves diversification and reduce
risk.Reduction in asset specific riskAsset allocation refers to a
acquiring a wide spectrum of assets. *
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Diversification and Asset Allocation(Cont)Individuals use their
finite (limited) resources to acquire various types of assets. E.g
: Allocation of assets among alternatives such as stocks, bonds,
and precious metals, and real estate.Even within a class as stocks,
the portfolio is allocated to different sectors or geographical
regions. E.g. an investor may own domestic stocks and stocks of
companies in emerging nations. By allocating an investor 'assets
over different types of assets, an investor contributes to the
diversification of the portfolio.*
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Diversification and Asset Allocation(Cont)Asset allocation and
diversification are often used in different contexts. E.g: an
investor may tilt (slope or moving into a sloping position) his/her
allocation towards energy stocks and away from airlines if he/she
anticipate high gas prices. The allocation between stocks, bonds,
and other assets remains the same, but the allocation between two
sectors is altered (changed). The words diversification and asset
allocation are often used in this context. *
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Diversification and Asset Allocation(Cont)Diversification is
important because it reduces the investor s risk exposure.Asset
allocation is important because it has a major impact on the return
the investors portfolio earns.Whenever an investor makes an
investment decision, he/she needs to consider its impact on the
diversification of his portfolio and the allocation of his/her
assets. Both are crucial components of portfolio management.*
-
Portfolio AssessmentPopular press places emphasis on return.
Higher return requires accepting more risk. Assessment should
consider both the return and the risk taken to achieve the
return.*
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Investment philosophyBelief that investment decisions are made
in exceedingly competitive financial markets. Information is
disseminated so rapidly that few investors are able to take
advantage of new information.Investment philosophy: the philosophy
and strategies of different investors and portfolio managers may be
different. Some may have a shorter time horizon and may be less
concerned with current taxes or the cost of buying and selling
securities; others might think differently.*
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Investment philosophy(Cont)Understanding yourself and specifying
goals is important when developing an investment philosophy and
making investment decisions.Available time to make investment
decisions; develop a continuous contact with investment, follow
daily news and TV programs talking about investment; have contact
with people who work in the area and know professionals.
*
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The InternetMajor source of information concerning investments:
http://www.investopedia.com;
http://www.TeachMeFinance.comhttp://www.bloomberg.com;
http://money.cnn.com; http://www.fobes.comhttp://www.google.com;
http://www.marketwatch.comhttp://www.morningstar.com;
http://moneycentral.msn.com/investorhttp://www.investor.reuters.com;
http://finance.yahoo.comhttp://www.cma.org.rwMuch information can
be obtained through the internet free of charge, but some vendors
do charge a fee for the material. However too much information may
be available, or you might obtain contradictory information from
different sites.*
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Portfolio Theory
Portfolio Theory is built around the investor seeking to
construct an efficient portfolio that offers the highest return for
a given level of risk or the least amount of risk for a given level
of return. Of all the possible efficient portfolios, the individual
investor selects the portfolio that offers the highest level of
satisfaction or utility.Harry Markowitz is credited with being the
first individual to use the preceding material to develop a theory
of portfolio construction employing returns and risk as measured by
a portfolios standard deviation.
*
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Portfolio Theory(Cont)
1. A measure of the dispersion of a set of data from its mean.
The more spread apart the data, the higher the deviation. Standard
deviation is calculatedas the square root of variance. 2. In
finance, standard deviation is applied to the annual rate of return
of an investment to measure the investment's volatility. Standard
deviation is also known as historical volatility and is used by
investors as a gauge for the amount of expected volatility.
Standard deviation is a statistical measurement that sheds light on
historical volatility. For example,a volatile stock will have a
high standard deviation while thedeviationof a stable blue chip
stock will be lower. A large dispersion tells us how much the
return on the fund is deviating from the expected normal
returns.
*
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Portfolio Theory(Cont)
The contribution of Markowitz was a major advance in finance and
led to the development of the Capital Asset Pricing Model (CAPM)
and subsequently to the arbitrage pricing model, generally referred
to as arbitrage pricing theory (APT). CAPM was developed by William
F.Sharpe, John Lintner, and Jan Mossin. It reduces the explanation
of stocks return to two variables:1. the market return 2. the
volatility of the stock in response to two variables.*
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Portfolio Theory(Cont)Arbitrage pricing theory(APT), initially
developed by Stephen A.Ross, seeks to add additional variables to
the explanation of security returns.Arbitrage is the act of buying
a good or a security and simultaneously selling it in another
market at a higher price (individuals who participate in these
transactions are called arbitrageurs.E.g, if IBM stock is selling
for $50 in New York and $60 in San Francisco, an opportunity for
riskless profit exists. Arbitrageurs would buy the stock in New
York and simultaneously sell it in San Francisco, thus earning the
$10 profit without bearing any risk.Arbitage also implies that
portfolios with the same risk generate the same returns.*
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The Markowitz Model
The Markowitz model is premised on a risk-averse individual
constructing a diversified portfolio that maximizes the individuals
satisfaction (generally referred to as utility by economists) by
maximizing portfolio returns for a given level of risk.This process
is depicted in Figures 1 through 3, which illustrate the optimal
combinations of risk and return available to investors, the desire
of investors to maximize their utility, and the determination of
the optimal portfolio that integrates utility maximization within
the constraint of the available portfolios.*
-
Figure 1 The Efficient Frontier
*
-
Figure 1 The Efficient Frontier(Cont)Figure 1 illustrates the
determination of the optimal portfolios available to investors. The
vertical axis measures portfolio expected returns expressed as a
percentage. The horizontal axis measures the risk associated with
the portfolio, using the portfolios standard deviation (p).
*
-
Figure 1 The Efficient Frontier(Cont)The shaded area represents
possible portfolios composed of various combinations of risky
securitiesThis area is generally referred to as the attainable or
feasible set of portfolios. Some of these portfolios are
inefficient because they offer an inferior return given amount of
risk.E.g., portfolio A is inefficient since portfolio B offers a
higher return for the same amount of risk. *
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Figure 1 The Efficient Frontier(Cont)Inefficient portfolio is a
portfolio whose return is not maximized given the level of risk.All
portfolios that offer the highest return for a given amount of risk
are referred to as efficient.The line that connects all these
portfolios (XY in Figure 1) defines efficient frontier and is
referred to as the efficient set of portfolios.Any portfolio that
offers the highest return for a given amount of risk must lie on
the efficient frontier.Any portfolio that offers a lower return is
inefficient and lies below the efficient frontier in the shaded
area.*
-
Figure 1 The Efficient Frontier(Cont)Since inefficient
portfolios will not be selected, the efficient frontier establishes
the best set of portfolios available to investors.A portfolio such
as C that lies above the efficient frontier offers a superior yield
for the amount of risk. Investors would prefer that portfolio to
portfolio B on the efficient frontier because C offers a higher
return for the same level of risk.While the efficient frontier
gives all the best attainable combinations of risk and return, it
does not tell which of the possible combinations an investor will
select.*
-
Figure 1 The Efficient Frontier(Cont)That selection depends on
the individuals willingness to bear the riskThe combining of the
efficient frontier and the willingness to bear the risk determines
the investors optimal portfolioThis willingness to bear risk may be
shown by the use of indifference curves, which are often used in
economic theory to indicate levels of an individuals utility (i.e.,
consumer satisfaction) and the impact of trading one good for
another.*
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Figure 1 The Efficient Frontier(Cont)When applied to portfolio
theory, the economic theory of consumer behavior develops the
trade-off between risk and return (instead of trade-off between two
goods).This trade-off between risk and return is also shown by
indifference curves.A set of these indifference curves is
illustrated in the following Figure 2. *
-
Figure 2 Indifference Map
*
-
Figure 2 Indifference Map(Cont)
Each indifference curve represents a level of satisfaction, with
higher curves indicating higher levels of satisfaction.Movements
along a given curve indicate the same level of satisfaction (the
individual is indifferent). E.g., on indifference curve I1, the
investor would be willing to accept a modest return, such as r1 and
bear a modest amount of risk (p1). The same investor would also be
willing to bear more risk for a higher return (e.g., r2 and (p2).
*
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Figure 2 Indifference Map(Cont)
The additional return is sufficient to induce bearing the
additional risk, so the investor is indifferent between the two
alternatives.All the points on the same indifference curve
represent the same level of satisfactionThe indifference curves in
Figure 2 are for risk-averse investor; hence, additional risk
requires more return.Notice that these curves are concave from
above; their slope increases as risk increases. This indicates that
investors require ever-increasing amounts of additional return for
equal increments of risk to maintain the same level of
satisfaction.*
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Figure 2 Indifference Map(Cont)
Investors would like to earn a higher return without having to
bear additional risk.A higher return without additional risk
increases total satisfaction.Higher levels of satisfaction are
indicated by indifference curves I2 and I3, which lie above
indifference curve I1.the investor is indifferent between any
combination of risk and return on I2. All combinations of risk and
return on indifference curve I2 are preferred to all combinations
on indifference curve I1. All points on indifference curve I3 are
preferred to all points on I2.*
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Figure 2 Indifference Map(Cont)
The investor seeks to reach the highest level of satisfaction
but is, of course, constrained by what is available. The best
combinations of risk and return available are given by the
efficient frontier. Superimposing the indifference curves on the
efficient frontier defines the investors optimal portfolioThis is
shown in Figure 3, which combines Figure 1& 2.The optimal
combination of risk and return represented by point is the
investors optimal combination of risk and return.*
-
Figure 3 Determination of the Optimal Portfolio
*
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Figure 3 Determination of the Optimal Portfolio(Cont)If the
investor selects any other portfolio with a different combination
of risk and return on the efficient frontier (e.g., A), that
portfolio would not be the individuals best choice. While portfolio
A is an efficient combination of risk and return, it is not the
optimal choice, as may be seen using the following logic.Portfolio
B is equal to portfolio A (i.e., the investor is indifferent
between A and B).B is not efficient and is inferior to portfolio ,
since offers a higher level of return for the same amount of
risk.*
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Figure 3 Determination of the Optimal Portfolio(Cont)Portfolio
must be preferred to B, and because A and B are equal, must also be
preferred to A.Only one portfolio offers the highest level of
satisfaction and lies on the efficient frontier.That unique
combination of risk and return is represented by portfolio , which
occurs at the tangency of the efficient frontier and indifference
curve I2 .*
-
Figure 3 Determination of the Optimal Portfolio(Cont)If an
indifference curve cuts through the efficient frontier (e.g., I1),
it is attainable but inferior, and it can always be shown that the
investor can reach a higher level of satisfaction by altering the
portfolio.If an indifference curve lies above the efficient
frontier (e.g., I3), such a level of satisfaction is not
obtainable.The investor would like to reach that level of
satisfaction, but no combination of assets offers such a high
expected return for that amount of risk*
-
Figure 3 Determination of the Optimal Portfolio(Cont)Different
investors may have varying indifference curves.If the investor is
very risk-averse, the curves tend to be steep, indicating a large
amount of additional return is necessary to induce this individual
to bear additional risk and maintain the same level of
satisfaction.If the curves are relatively flat, the individual is
less risk-averse. Only a modest amount of additional return is
necessary to induce this individual to bear additional risk and
still maintain the same level of satisfaction.However, both
investors are still averse to bearing risk. The difference is the
degree of risk aversion*
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Portfolios Risk and ReturnThe future is uncertain. Investors do
not know with certainty whether the economy will be growing rapidly
or be in recession.Investors do not know what rate of return their
investments will yield.Therefore, they base their decisions on
their expectations concerning the future.The expected rate of
return on a stock represents the mean of a probability distribution
of possible future returns on the stock.*
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Expected ReturnThe table below provides a probability
distribution for the returns on stocks A and BState Probability
Return On Return On Stock A Stock B 1 20% 5% 50% 2 30% 10% 30% 3
30% 15% 10% 4 20% 20% -10%The state represents the state of the
economy one period in the future i.e. state 1 could represent a
recession and state 2 a growth economy. The probability reflects
how likely it is that the state will occur. The sum of the
probabilities must equal 100%. The last two columns present the
returns or outcomes for stocks A and B that will occur in each of
the four states. *
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Expected ReturnGiven a probability distribution of returns, the
expected return can be calculated using the following equation: N
E[R] = S (piRi) i=1Where:E[R] = the expected return on the stock N
= the number of statespi = the probability of state iRi = the
return on the stock in state i.*
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Expected ReturnIn this example, the expected return for stock A
would be calculated as follows:
E[R]A = .2(5%) + .3(10%) + .3(15%) + .2(20%) = 12.5%
Now you try calculating the expected return for stock B!
*
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Expected ReturnDid you get 20%? If so, you are correct.
If not, here is how to get the correct answer:
E[R]B = .2(50%) + .3(30%) + .3(10%) + .2(-10%) = 20%
So we see that Stock B offers a higher expected return than
Stock A.However, that is only part of the story; we haven't
considered risk.*
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Measures of RiskRisk reflects the chance that the actual return
on an investment may be different than the expected return.One way
to measure risk is to calculate the variance and standard deviation
of the distribution of returns. We will once again use a
probability distribution in our calculations.The distribution used
earlier is provided again for ease of use.*
-
Measures of RiskProbability Distribution:
State Probability Return On Return On Stock A Stock B 1 20% 5%
50% 2 30% 10% 30% 3 30% 15% 10% 4 20% 20% -10%E[R]A = 12.5%E[R]B =
20%*
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Measures of RiskGiven an asset's expected return, its variance
can be calculated using the following equation: NVar(R) = s2 = S
pi(Ri E[R])2 i=1Where:N = the number of states pi = the probability
of state i Ri = the return on the stock in state iE[R] = the
expected return on the stock
*
-
Measures of RiskThe standard deviation is calculated as the
positive square root of the variance:
SD(R) = s = s2 = (s2)1/2 = (s2)0.5 *
-
Measures of RiskThe variance and standard deviation for stock A
is calculated as follows:
s2A = 0.2(.05 -.125)2 + 0.3(.1 -.125)2 + 0.3(.15 -.125)2 +
0.2(.2 -.125)2 = .002625
sA = (.002625)0.5 = .0512 = 5.12%
Now you try the variance and standard deviation for stock B!If
you got .042 and 20.49% you are correct.*
-
Measures of RiskIf you didnt get the correct answer, here is how
to get it:
s2B = .2(.50 -.20)2 + .3(.30 -.20)2 + .3(.10 -.20)2 + .2(-.10 -
.20)2 = .042
sB = (.042)0.5 = .2049 = 20.49%
Although Stock B offers a higher expected return than Stock A,
it also is riskier since its variance and standard deviation are
greater than Stock A's.This, however, is still only part of the
picture because most investors choose to hold securities as part of
a diversified portfolio.*
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Portfolio Risk and ReturnMost investors do not hold stocks in
isolation.Instead, they choose to hold a portfolio of several
stocks.When this is the case, a portion of an individual stock's
risk can be eliminated, i.e., diversified away.From our previous
calculations, we know that:the expected return on Stock A is
12.5%the expected return on Stock B is 20%the variance on Stock A
is .00263the variance on Stock B is .04200the standard deviation on
Stock A is 5.12%the standard deviation on Stock B is 20.49%
*
-
Portfolio Risk and ReturnThe Expected Return on a Portfolio is
computed as the weighted average of the expected returns on the
stocks which comprise the portfolio.The weights reflect the
proportion of the portfolio invested in the stocks.This can be
expressed as follows: NE[Rp] = S wiE[Ri] i=1Where:E[Rp] = the
expected return on the portfolioN = the number of stocks in the
portfoliowi = the proportion of the portfolio invested in stock i
E[Ri] = the expected return on stock i*
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Portfolio Risk and ReturnFor a portfolio consisting of two
assets, the above equation can be expressed as: E[Rp] = w1E[R1] +
w2E[R2]
If we have an equally weighted portfolio of stock A and stock B
(50% in each stock), then the expected return of the portfolio is:
E[Rp] = .50(.125) + .50(.20) = 16.25%*
-
Portfolio Risk and ReturnUsing either the correlation
coefficient or the covariance, the Variance on a Two-Asset
Portfolio can be calculated as follows:
s2p = (wA)2s2A + (wB)2s2B + 2wAwBrA,B sAsB ORs2p = (wA)2s2A +
(wB)2s2B + 2wAwB sA,B
The Standard Deviation of the Portfolio equals the positive
square root of the the variance.*
-
Portfolio Risk and ReturnThe variance/standard deviation of a
portfolio reflects not only the variance/standard deviation of the
stocks that make up the portfolio but also how the returns on the
stocks which comprise the portfolio vary together.Two measures of
how the returns on a pair of stocks vary together are the
covariance and the correlation coefficient.Covariance is a measure
that combines the variance of a stocks returns with the tendency of
those returns to move up or down at the same time other stocks move
up or down.Since it is difficult to interpret the magnitude of the
covariance terms, a related statistic, the correlation coefficient,
is often used to measure the degree of co-movement between two
variables. The correlation coefficient simply standardizes the
covariance.
*
-
Portfolio Risk and ReturnThe Covariance between the returns on
two stocks can be calculated as follows: NCov(RA,RB) = sA,B = S
pi(RAi - E[RA])(RBi - E[RB]) i=1Where:sA,B = the covariance between
the returns on stocks A and B N = the number of states pi = the
probability of state i RAi = the return on stock A in state i E[RA]
= the expected return on stock A RBi = the return on stock B in
state iE[RB] = the expected return on stock B *
-
Portfolio Risk and ReturnThe Correlation Coefficient between the
returns on two stocks can be calculated as follows: sA,B
Cov(RA,RB)Corr(RA,RB) = rA,B = sAsB = SD(RA)SD(RB)
Where:rA,B=the correlation coefficient between the returns on
stocks A and BsA,B=the covariance between the returns on stocks A
and B, sA=the standard deviation on stock A, and sB=the standard
deviation on stock B*
-
Portfolio Risk and ReturnThe covariance between stock A and
stock B is as follows:
sA,B = .2(.05-.125)(.5-.2) + .3(.1-.125)(.3-.2) +
.3(.15-.125)(.1-.2) +.2(.2-.125)(-.1-.2) = -.0105
The correlation coefficient between stock A and stock B is as
follows: -.0105rA,B = (.0512)(.2049) = -1.00*
-
Portfolio Risk and ReturnUsing either the correlation
coefficient or the covariance, the Variance on a Two-Asset
Portfolio can be calculated as follows:
s2p = (wA)2s2A + (wB)2s2B + 2wAwBrA,B sAsB ORs2p = (wA)2s2A +
(wB)2s2B + 2wAwB sA,B
The Standard Deviation of the Portfolio equals the positive
square root of the the variance.*
-
Portfolio Risk and ReturnLets calculate the variance and
standard deviation of a portfolio comprised of 75% stock A and 25%
stock B:
s2p
=(.75)2(.0512)2+(.25)2(.2049)2+2(.75)(.25)(-1)(.0512)(.2049)=
.00016
sp = .00016 = .0128 = 1.28%
Notice that the portfolio formed by investing 75% in Stock A and
25% in Stock B has a lower variance and standard deviation than
either Stocks A or B and the portfolio has a higher expected return
than Stock A.This is the purpose of diversification; by forming
portfolios, some of the risk in the individual stocks can be
eliminated.*
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Capital Asset Pricing Model (CAPM) If investors are mainly
concerned with the risk of their portfolio rather than the risk of
the individual securities in the portfolio, how should the risk of
an individual stock be measured?In important tool is the CAPM.CAPM
concludes that the relevant risk of an individual stock is its
contribution to the risk of a well-diversified portfolio.CAPM
specifiesa linear relationship between risk and required return.
The equation used for CAPM is as follows: Ki = Krf + bi(Km -
Krf)Where:Ki = the required return for the individual securityKrf =
the risk-free rate of returnbi = the beta of the individual
securityKm = the expected return on the market portfolio(Km - Krf)
is called the market risk premiumThis equation can be used to find
any of the variables listed above, given the rest of the variables
are known.
*
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CAPM ExampleFind the required return on a stock given that the
risk-free rate is 8%, the expected return on the market portfolio
is 12%, and the beta of the stock is 2.
Ki = Krf + bi(Km - Krf)Ki = 8% + 2(12% - 8%)Ki = 16% Note that
you can then compare the required rate of return to the expected
rate of return. You would only invest in stocks where the expected
rate of return exceeded the required rate of return.*
-
Another CAPM ExampleFind the beta on a stock given that its
expected return is 12%, the risk-free rate is 4%, and the expected
return on the market portfolio is 10%.
12% = 4% + bi(10% - 4%)bi = 12% - 4% 10% - 4% bi = 1.33 Note
that beta measures the stocks volatility (or risk) relative to the
market. *