Finanças
November 2
QDai for FEUNL
Topics covered
Minimum variance portfolio
 Efficient frontier
 Systematic risk vs. Unsystematic risk
 Seperation principle of investment
 Security market line

QDai for FEUNL
Previously

Single stock



Expected return
Variance
Portfolio



Expected
Variance
Correlation
QDai for FEUNL
Portfolio: diversification effect
Superteck Slowpoke Portfolio with
RA
RB
60% in RA and
40% in RB
Expected 17.5%
return
5.5%
12.7%
SD
0.1150
0.1544
0.2586
Weighted average SD= 0.6*0.2586+0.4*0.1150=0.2012
QDai for FEUNL
Portfolio: diversification effect

2 2
2 2
X


2
X
X


X
Variance of portfolio = A A
A B A, B
B B
=0.36*0.066875
+2*0.6*0.4*(-0.004875)
+0.16*0.013225
=0.023851
OR =
QDai for FEUNL
Portfolio: diversification effect

Conclusion:
QDai for FEUNL
Portfolio Return
The opportunity set of two assets
12.0%
100%
Stock B
11.0%
10.0%
9.0%
8.0%
100%
Stock A
7.0%
6.0%
5.0%
0.0%
2.0%
4.0%
6.0%
8.0%
10.0% 12.0% 14.0% 16.0%
Portfolio Risk (standard deviation)
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return
Two-Security Portfolios with Various Correlations
100%
Stock B
100%
Stock A

Relationship depends on correlation
coefficient
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
return
The Efficient Set for Many Securities
Individual Assets
P
The opportunity set of risk-return combinations of
various portfolios.
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Portfolio Risk as a Function of the Number of Stocks
in the Portfolio

Portfolio risk
n risk of
Diversification can not eliminate all of the
individual securities.
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Risk of a security

Total risk of an individual security =

Systematic risk:

Unsystematic risk:

Why do we care about risk diversification?
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Risk aversion

Example: Suppose you have a saving of
€2,000. There is a gamble with a 50%
chance of doubling your money, and a
50% chance that you will lose all.
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return
Optimal Risky Portfolio with a Risk-Free Asset
rf

In addition to stocks and bonds, consider a world
that also has risk-free securities like T-bills
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Separation Principle

The investor’s investment decision
consists of two separate steps
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Definition of Risk When Investors Hold
the Market Portfolio

Researchers have shown that the best
measure of the risk of a security in a large
portfolio is the beta (b)of the security.
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Security Returns
Return on
market %
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Definition of Risk When Investors Hold
the Market Portfolio

Beta measures
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Capital asset pricing model (CAPM)

Expected market return

Expected return of an individual security

The expected return on a security is linearly
related to its beta.

The relationship also holds for portfolios.
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Expected return
Relationship Between Risk & Expected Return
Ri = RF  βi  ( RM - RF )
RM
RF
1.0
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b