Transcript Investment Analysis Eco/Bus350

Investment Analysis
Bus350
Return and Risk Calculation
• Professor Tao Wang
• Tel: x5445
• E-mail: [email protected]
• Room: PH154
• Office Hour: W, F 12:15pm – 1:15pm
• Coursepage:
http://www.qc.edu/~twang/course/350/i
nvestments.html. Announcements,
homework, cases, exam dates are all on
the webpage.
Course Overview
• Book: Investment Analysis and Portfolio
Management by Reilly and Brown
• CFA-designated Textbook
• Group case (10%), three homework
(5%), two midterms (50%) and one final
(30%). Class participation is 5%.
Contents
• Calculate return and risk based on distribution
for a single asset
• Calculate return and risk for a portfolio of
assets
• Holding Period Return
• Real life indices
• Calculate return and risk from index example,
geometric mean and arithmetic mean
comparison
Probability Distributions of
Returns
• Assume that there are two stock
available, GENCO and RISCO, and each
responds to the state of the economy
according to the following table
Returns on GENCO & RISCO
State of Return on Return on ProbEconomy RISCO
GENCO
ability
Strong
50%
30%
0.20
Normal
10%
10%
0.60
Weak
-30%
-10%
0.20
•Probability Distributions of Returns of GENCO and RISCO
•0.6
•0.5
•0.4
•Probability •0.3
•0.2
•0.1
•0
•50%
•GENCO
•30%
•Return
•10%
•RISCO
•-10%
•-30%
Observation
• Both companies have the same expected
return, but there is considerably more
risk associated with RISCO
Equations: Mean
 r  E r   P1r1  P2 r2  P3r3  ...Pn rn
 P r
n
  Pi ri
i 1
r
 0.2  0.3  0.6  0.10  0.2  (0.10)
r
 0.10  10%
GENCO
GENCO
Also :
 rRISCO  10%
Equations: Standard Deviation

 r  E r  E r 2

 P1 r1   r   P2 r2   r   ...  Pn rn   r 
2

n
2
2
 Pi ri   r 
2
i 1
r
 0.2  0.30  0.10   0.6  0.10  0.10   0.2  (0.10  0.10) 2
r
 0.016  0.1265
GENCO
GENCO
2
Also :
 rRISCO  0.2530
2
Observation
• The expected returns of GENCO and
RISCO happen to be equal, but the
volatility, or standard deviation, of RISCO
is twice that of GENCO’s
• Which stock would a typical investor
prefer
Example
1. Calculate the expected return and standard
deviation of the following stock A:
State
Probability
Return
1
20%
15%
2
60%
10%
3
20%
-8%
The mean is 0.2*0.15+0.6*0.1+0.2*(-0.08) = 7.4%
The standard deviation is:
S.D. = Sqrt[0.2*(0.15-0.074)^2+0.6*(0.10.074)^2+0.2*(-0.08-0.074)^2] = 7.9%
Portfolio Return and Risk
• Suppose you invest in two assets: stocks
and bonds.
• Stocks offer a return of 10% with
standard deviation of 15%
• Bonds offer a return of 6% with standard
deviation of 8%
Portfolio weight
• If the investment weight on stocks is
50%, on bonds is 50%, what’s the return
on the portfolio?
• What about the risk of the portfolio?
Holding Period Return
Ending Price - Beginning Price  Dividend
HPR 
Beginning Price
$220  200  10

 0.15
$200
Measures of
Historical Rates of Return
Arithmetic Mean :
AM   HPR/ n
where :
 HPR  the sum of annual
holding period yields
Measures of
Historical Rates of Return
• Geometric Mean
GM 
 (1  HPR) 
1
n
1
where :

 the product of the annual
holding period returns as follows :
1  HPR 1  1  HPR 2  1  HPR n 
• Arithmetic mean is used for forecasting
future returns
• Geometric mean is used to calculate real
past returns
• Geometric mean has upward bias
Measure volatility
• Historical volatility
– Standard deviation
– Realized volatility
• Future volatility
Stylized facts
• Stock/Bond returns are fairly difficult to
predict
• But return volatilities are predictable to a
degree
Yahoo finance
• Most indices historical data can be
downloaded from
http://finance.yahoo.com