# Portfolio Theory by hcj

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```									Vicentiu Covrig                       FIN352

Portfolio Theory
(Jones chapter 7)

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Vicentiu Covrig                                     FIN352

Investment Decisions
nInvolve uncertainty
nFocus on expected returns
- Estimates of future returns needed to consider
and manage risk
nGoal is to reduce risk without affecting
returns
- Accomplished by building a portfolio
- Diversification is key

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Vicentiu Covrig                                    FIN352

Dealing With Uncertainty
nRisk that an expected return will not be
realized
distributions, not just a single return
nProbabilities weight outcomes
- Should be assigned to each possible outcome to
create a distribution
- Can be discrete or continuous

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Vicentiu Covrig                                             FIN352

Calculating Expected Return
n Expected value
- The single most likely outcome from a particular
probability distribution
- The weighted average of all possible return outcomes
- Referred to as an ex ante or expected return

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Vicentiu Covrig                                            FIN352

Example: Given the following probability distribution,
calculate the expected return of security XYZ.
n Security XYZ's     Potential return      Probability
20%                   0.3
30%                   0.2
-40%                  0.1
50%                   0.1
10%                   0.3
Solution:
E(R) = Ripri = (20)(0.3) + (30)(0.2) + (- 40)(0.1) +
(50)(0.1) + (10)(0.3) = 22 percent

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Vicentiu Covrig                                        FIN352

Calculating Risk
nVariance and standard deviation used to
quantify and measure risk
- Measures the spread in the probability
distribution
- Variance of returns: σ² = (Ri - E(R))²pri
- Standard deviation of returns:
σ =(σ²)1/2
- Ex ante rather than ex post σ relevant

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Vicentiu Covrig                                       FIN352

Portfolio Expected Return
nWeighted average of the individual security
expected returns
- Each portfolio asset has a weight, w, which
represents the percent of the total portfolio
value

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Vicentiu Covrig                                            FIN352

Portfolio Risk
n Portfolio risk not simply the sum of individual security risks
n Emphasis on the risk of the entire portfolio and not on risk of
individual securities in the portfolio
n Measured by the variance or standard deviation of the portfolio’s
return
- Portfolio risk is not a weighted average of the risk of the
individual securities in the portfolio

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Vicentiu Covrig                                    FIN352

Risk Reduction in Portfolios
nRandom diversification
- Diversifying without looking at relevant investment
characteristics
- Marginal risk reduction gets smaller and smaller as
nCorrelation drives the diversification benefits
nA large number of securities is not required for
significant risk reduction
nInternational diversification benefits
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Vicentiu Covrig                                     FIN352
Portfolio Risk and Diversification
sp %
35                   Portfolio risk

20
Market Risk
0
10   20      30         40   ......   100+
Number of securities in portfolio
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Vicentiu Covrig                                             FIN352

The benefits of diversification
n Come from the correlation between asset returns

n The smaller the correlation, the greater the risk reduction
potential  greater the benefit of diversification

n If r = +1.0, no risk reduction is possible

§ Adding extra securities with lower corr/cov with the existing
ones decreases the total risk of the portfolio

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Vicentiu Covrig                                     FIN352

Markowitz Diversification
nNon-random diversification
- Active measurement and management of
portfolio risk
- Investigate relationships between portfolio
securities before making a decision to invest
- Takes advantage of expected return and risk for
individual securities and how security returns
move together

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Vicentiu Covrig                                           FIN352

Measuring Portfolio Risk
nNeeded to calculate risk of a portfolio:
- Weighted individual security risks
uCalculated by a weighted variance using the
proportion of funds in each security
uFor security i: (wi × i)2
- Weighted comovements between returns
uReturn covariances are weighted using the
proportion of funds in each security
uFor securities i, j: 2wiwj × ij

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Vicentiu Covrig                               FIN352
Portfolio Risk and Return
n Expected Portfolio Return

n Standard Deviation of Portfolio Returns

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Vicentiu Covrig                                    FIN352

Calculating Portfolio Risk
nEncompasses three factors
- Variance (risk) of each security
- Covariance between each pair of securities
- Portfolio weights for each security
nGoal: select weights to determine the
minimum variance combination for a given
level of expected return

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Vicentiu Covrig                           FIN352
Example: NOT on the EXAM

100%
stocks

100%
bonds

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Vicentiu Covrig                                                 FIN352
Learning objectives
Know the concept of uncertainty
Know how to calculate expected return (probabilities)
Know how to calculate portfolio expected return (weights)
Concept of risk, portfolio risk
Firm and market specific risks; correlation; diversification
Know the concepts of correlation and diversification
NOT on the EXAM:
- covariance section p. 176-177
-calculations with standard deviations p. 178- 183

End of chapter 7.1 to 7.5; 7.23; 7.26; problems 7.1, 7-2

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