BUA321 Chapter 8 Class notes
Risk and Return
• If you are thinking of investing in
a stock, what things would you
investigate?
• What is inside trading?
• What does this mean: “There is
no such thing as a free lunch”?
Stock Fraud
• Bernie Madoff
http://www.youtube.com/watch?feature=player
_detailpage&v=s68FR1MXT8Q
HPR
• Calculate the holding period
return for TAP. Dividends totaled
$3.90.
TAP closing prices
Date
Close
4/1/2013
52.65
4/22/2010
44.36
Beginning Value
Ending Value
Investment Cash Flows
Investment Time (Yrs)
$44.36
$52.65
$3.90
3.000
Return
HPR (annualized return)
27.48%
8.43%
Returns
• What does history tell us about
stock returns?
• How would you describe Risk?
Return distribution
• If you purchased a stock for $27 last year and
this year it is worth $45. What was the return?
• Calculate the statistics for this asset.
$45
Next year
Change %
Good economy
Average Economy
Bad Economy
Predicted
price
Predicted
Return
Probability
Return distribution
• If you purchased a stock for $37 last year and
this year it is worth $45. What was the return?
• Calculate the statistics for this asset.
$45
Next year
Change %
Predicted
price
Probability
Good economy
15%
51.75
.30
Average Economy
7%
48.15
.60
Bad Economy
-2%
44.10
.10
Economic Conditions
Very Good
Good
Average
Bad
Very Bad
Total Probabilities
Probability
Asset A
0.300
0.600
0.100
15.00%
7.00%
-2.00%
1.000
Portfolio Weights
Statistics
Expected Return
Variance
Standard Deviation
Coefficient of Var
Asset A
8.50%
0.25%
5.00%
0.59
Risk Example
• Combine your prices with 2 other
people. Create 3 portfolios.
Complete the following table.
Asset
1
2
3
Port1
Port2
Port3
Expected return
Standard Deviation
CV
Portfolio Weights
Statistics
Expected Return
Variance
Standard Deviation
Coefficient of Var
Range
95% Confidence Interval
0.50
Asset A
High
Low
0.30
Asset B
8.50%
0.25%
5.00%
0.59
17.00%
18.31%
-1.31%
0.20
Asset C
12.50%
0.26%
5.12%
0.41
15.00%
22.54%
2.46%
Portfolio
4.70%
0.03%
1.62%
0.34
5.00%
7.87%
1.53%
8.94%
0.19%
4.33%
0.48
17.42%
0.46%
Efficient Frontier
• Combine 2 assets into a portfolio.
Insert the picture of the efficient
frontier of the portfolio.
What can you say about the
information in the following table:
Terminology
• What is meant by “Do Not Put All
Your Eggs in One Basket”
Calculate the return on the following
portfolio:
Asset
A
B
C
D
E
F
G
$ invested
5,000
7,000
1,000
10,000
1,500
2,000
7,000
Return
9%
12%
6%
19%
4%
7%
10%
A
B
C
D
E
F
G
H
Portfolio Investment
Investment ($ or weights)
Weights
5,000.00
7,000.00
1,000.00
10,000.00
1,500.00
2,000.00
7,000.00
Returns
0.149
0.209
0.030
0.299
0.045
0.060
0.209
0.000
9.000%
12.000%
6.000%
19.000%
4.000%
7.000%
10.000%
$33,500.00
Portfolio Return
12.388%
Portfolio
• What does correlation describe?
• What does CAPM describe?
• What things create diversifiable
risk? Non-diversifiable risk?
• What is beta?
Portfolio Beta
Asset
$ invested
Return
Beta
A
5,000
9%
1.25
B
7,000
12%
1.75
C
1,000
6%
.54
D
10,000
19%
2.79
E
1,500
4%
.32
F
2,000
7%
.75
G
7,000
10%
1.95
A
B
C
D
E
F
G
H
Portfolio Investment
Investment ($ or weights)
Weights
5,000.00
7,000.00
1,000.00
10,000.00
1,500.00
2,000.00
7,000.00
Returns
0.149
0.209
0.030
0.299
0.045
0.060
0.209
0.000
Betas
9.000%
12.000%
6.000%
19.000%
4.000%
7.000%
10.000%
1.250
1.750
0.540
2.790
0.320
0.750
1.950
$33,500.00
Portfolio Return
12.388%
Portfolio Beta
1.868
CAPM and SML
• Use the beta of the above
portfolio to calculate the
expected return of a portfolio.
Use the 30 year Treasury yield for
the risk free rate and 12% for the
average return of the market.
CAPM (SML)
Risk Free Rate
Avg Return of Market
Portfolio Beta
Ks (Expected Return)
Market Risk Premium
3.490%
12.000%
1.868
19.387%
Group activity
• Complete the following exercise
– Find the expected returns for your individual asset
using this spreadsheet
• Use the same market and RF returns
– You are given $100,000 to invest in your groups
stocks
– Find the betas for you company and input into the
portfolio beta and return worksheet
– Decide how much to invest in each asset
– Calculate the expected returns for this portfolio
Numbers investors should know.
• http://youtu.be/SXLkP4_gX1Y
BUA321 Chapter 08 Web 80 points
1) calculate the statistics for the following investments:
event
Pr
rx
ry
rz
very good
.30
12
-8
8
good
.20
8
-3
8
Avg
.25
2
6
8
Bad
.15
-5
10
8
Very Bad
.10 -10
19
8
Asset X
E( R)
Variance
Standard
deviation
CV
Asset Y
Asset Z
2) For the above assets, create the
portfolios below
a) 40% X, 35% Y, 25% Z
b) 60% X, 40% Y
c) 35% Y, 65% Z
Portfolio a
E( R)
Variance
Standard
deviation
CV
Portfolio b
Portfolio c
3) Calculate the portfolio statistics for
the following assets:
weight
beta
XYZ
.35
DEF
.25
HIJ
.40
correlation
XYZ
XYZ
1.0
DEF
HIJ
Portfolio A
Portfolio B
Portfolio C
DEF
-.25
1.0
(.35, .25, .40)
(.45, .25, .30)
(.10, .75, .15)
return
variance
12
9
15
7
12
20
HIJ
.75
.45
1.0
1.23
1.98
2.98
Portfolio A
Portfolio B
(.35, .25, .40) (.45, .25, .30)
E( R)
Variance
Standard
deviation
Beta
CV
Portfolio C
(.10, .75, .15)
SML
4) If the risk free rate of return is 3.75%
and the stock market averages 12%,
What is the expected return on the
portfolios using the SML?
A
B
C
5) Go to Yahoo Finance
• find your company.
• Go to historical prices and download the past 5 years
of prices and dividends. (Hint select monthly prices,
download, then select dividends only)
• a) delete all prices except the first month and the last
month.
• b) add all the dividends.
• c) calculate the holding period return for your stock
• d) combine this return with the returns of two other
classmates and insert in the table below.
Stock Ticker
Return
e) Determine the growth and
probabilities you expect in the
upcoming economic conditions.
Economic condition
Very Good
Good
Average
Bad
Very Bad
Growth
Probability
f) Determine the expected returns one
year from today using the above
information
Economic
condition
Very Good
Good
Average
Bad
Very Bad
Stock 1
Stock 2
Stock 3
g) create a portfolio using stocks and
calculate the returns:
1) 1 & 2
2) 2 & 3
3) 1 & 3
Portfolio
1
2
3
Returns
Stand Deviation
CV
h) copy and paste the efficient
frontiers from the worksheet
SML
• What are the betas of the company
stocks?
• Create a portfolio using the three
stocks and calculate the portfolio
beta.
Assets
Betas
Weights
• j) Use the beta above and the 30
year risk free rate and stock
market average return of 12% the
determine the expected return of
the portfolio return.