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Portfolio management
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How Finance is organized

Corporate finance

Investments
International Finance
 Financial Derivatives

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Risk and Return
The investment process consists of two broad tasks:
• security and market analysis
• portfolio management
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Risk and Return
Investors are concerned with both
 expected return
 risk
As an investor you want to maximize the returns for a given level of
risk.
The relationship between the returns for assets in the portfolio is
important.
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Risk Aversion
Portfolio theory assumes that investors are averse to risk
 Given a choice between two assets with equal expected rates of
return, risk averse investors will select the asset with the lower
level of risk

It also means that a riskier investment has to offer a higher
expected return or else nobody will buy it
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Top Down Asset Allocation
1. Capital Allocation decision: the choice of the
proportion of the overall portfolio to place in risk-free
assets versus risky assets.
2. Asset Allocation decision: the distribution of risky
investments across broad asset classes such as bonds,
small stocks, large stocks, real estate etc.
3. Security Selection decision: the choice of which
particular securities to hold within each asset class.
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Expected Rates of Return
- Weighted average of expected returns (Ri) for the
-
individual investments in the portfolio
Percentages invested in each asset (wi) serve as the
weights
E(Rport) = S wi Ri
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Portfolio Risk (two assets only)
When two risky assets with variances s12 and s22,
respectively, are combined into a portfolio with portfolio
weights w1 and w2, respectively, the portfolio variance is
given by:
sp2 = w12s12 + w22s22 + 2W1W2 Cov(r1r2)
Cov(r1r2) = Covariance of returns for
Security 1 and Security 2
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Correlation between the returns of two securities
Correlation, : a measure of the strength of the linear
relationship between two variables
 




cov( R1 , R2 )
s 1s 2
-1.0 <  < +1.0
If  = +1.0, securities 1 and 2 are perfectly positively
correlated
If  = -1.0, 1 and 2 are perfectly negatively correlated
If  = 0, 1 and 2 are not correlated
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Efficient Diversification
Let’s consider a portfolio invested 50% in an equity mutual fund
and 50% in a bond fund.
Equity fund
Bond fund
E(Return)
11%
7%
Standard dev.
14.31%
8.16%
Correlation
-1
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% in stocks
Risk
Return
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50.00%
55%
60%
65%
70%
75%
80%
85%
90%
95%
100%
8.2%
7.0%
5.9%
4.8%
3.7%
2.6%
1.4%
0.4%
0.9%
2.0%
3.08%
4.2%
5.3%
6.4%
7.6%
8.7%
9.8%
10.9%
12.1%
13.2%
14.3%
7.0%
7.2%
7.4%
7.6%
7.8%
8.0%
8.2%
8.4%
8.6%
8.8%
9.00%
9.2%
9.4%
9.6%
9.8%
10.0%
10.2%
10.4%
10.6%
10.8%
11.0%
Portfolio Return
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Portfolo Risk and Return Combinations
12.0%
11.0%
100%
stocks
10.0%
9.0%
8.0%
7.0%
6.0%
100%
bonds
5.0%
0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.0% 16.0%
Portfolio Risk (standard deviation)
Note that some portfolios are
“better” than others. They have
higher returns for the same level of
risk or less. We call this portfolios
EFFICIENT.
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The Minimum-Variance Frontier
of Risky Assets
E(r)
Efficient
frontier
Individual
assets
Global
minimum
variance
portfolio
Minimum
variance
frontier
St. Dev.
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return
Two-Security Portfolios with Various
Correlations
100%
stocks
 = -1.0
 = 1.0
 = 0.2
100%
bonds
s
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The benefits of diversification

Come from the correlation between asset returns

The smaller the correlation, the greater the risk reduction
potential  greater the benefit of diversification

If  = +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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Estimation Issues


Results of portfolio analysis depend on accurate statistical inputs
Estimates of
- Expected returns
- Standard deviations
- Correlation coefficients
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Portfolio Risk as a Function of the Number of
Stocks in the Portfolio
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s
Thus diversification can eliminate some, but not
all of the risk of individual securities.
Diversifiable Risk;
Nonsystematic Risk;
Firm Specific Risk;
Unique Risk
Portfolio risk
Nondiversifiable risk;
Systematic Risk;
Market Risk
n
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