# Why do people invest What is the role of financial securities

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```					  Dr. Gutierrez                                              Portfolio Theory   1
FIN 683

Why do people invest? What is the role of financial securities?

T    E (CFt )
Recall:   P0 = ∑              t
t =1 (1 + k )

Risk Aversion:

Expected return

C
•
•
D
•         •
A         B

Risk

Each individual’s goal is to:

maximize expected return for a given risk level

or       minimize risk for a given expected return
Dr. Gutierrez                                                     Portfolio Theory   2
FIN 683

Standard Deviation (or Variance) is our first measure of risk.

Suppose we form a portfolio p of assets a through N. Then we can
define the return on the portfolio as a weighted average of the returns of
the individual assets.

rp = w a ra + w b rb + w c rc + ... + w N rN

How do we calculate the expected return of a portfolio?
N           N
E(rP ) = E( ∑ w i ri ) = ∑ w i E(ri )
i =1         i =1

How do we calculate the risk of a portfolio?

Var (rp ) = σ 2 = Var ∑ w w ri  = ∑ ∑ w i w j cov ij
N           N N
P                
 i =1      i =1 j=1

Bottomline: When we combine several assets together into a
portfolio of securities, the risk of the portfolio depends on the
interaction between the returns of the component assets.
Dr. Gutierrez                                             Portfolio Theory   3
FIN 683

Each investor’s goal is to maximize return and minimize risk.
Different risk-return combinations can be had for the portfolio by
changing the weights in the assets comprising the portfolio.

frontier when correlation = 1.0

frontier when correlation = - 1.0

frontier when –1.0 < correlation < 1.0
Dr. Gutierrez                                              Portfolio Theory   4
FIN 683

Diversifiable Risk

Assuming all stocks are not perfectly positively correlated, there are
benefits to holding a portfolio of stocks versus holding any one stock.

σp                   Diversifiable Risk

Nondiversifiable Risk

Number of stocks
in portfolio

Total Risk = Diversifiable Risk + Nondiversifiable Risk

Should investors expect to be compensated for the total risk of a
security?
Dr. Gutierrez                                              Portfolio Theory   5
FIN 683

Total return = E(r) + unexpected return

error term

compensation for
nondiversifiable risk

Applications of portfolio theory:

Asset allocation

Asset pricing (CAPM)

1970 - 1995
Average annual
return

100%
13%                                                      stocks

100%
bonds
10%
Standard
deviation
12%                            16%              of returns

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