Chapter 5

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Chapter 5 –
Support
Risk and Return
5b.1
Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Remember? Determining the
Expected Return/Standard Deviation
Stock BW
Ri
Pi
–0.15
–0.03
0.09
0.21
0.33
Sum
5b.2
0.10
0.20
0.40
0.20
0.10
1.00
(Ri)(Pi)
–0.015
–0.006
0.036
0.042
0.033
0.090
The
expected
return, R,
for Stock
BW is
0.09 or
9%
Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Discrete Distribution: Expected
Return and Variance Calculation
•
As you can see we have recreated the discrete distribution here in Excel.
•
The probabilities must sum to 1 or 100% and when we multiply the individual
expected returns in each state by the associated probability we generate the
contribution that state has to the overall expected return.
•
We then use the expected return to generate the variance of .00703 or a standard
deviation of 8.38% (0.0838) associated with the 9.00% return.
•
Refer to ‘VW13E-05b.xlsx’ on tab ‘Discrete’. We can also graph as above. You may
chance the probabilities and possible returns to view impact.
5b.3
Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Remember?
Distribution Discussions
• So how do we create graphs
that represent something
akin to a normal distribution
that is continuous?
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-15%
-3%
9%
21%
33%
0.035
0.03
0.025
0.02
0.015
0.01
0.005
5b.4
67%
58%
49%
40%
31%
22%
4%
13%
-5%
-14%
-23%
-32%
-41%
-50%
0
• In file ‘VW13E-05b.xlsx’ on
tab ‘Standard Normal’ we can
create our own distributions
with our own defined means
and standard deviations!
Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Discrete Distribution: Expected
Return and Variance Calculation
•
We can recreate our own distributions using Excel. While the process can be
used for many different simulations and analysis techniques, we will focus
on the creation of the distribution graph for an individual firm.
•
Assume a stock has an expected mean return of 10% and a standard
deviation of 30%. Together, we can create a standard normal distribution as
above.
•
Note that we f(x) creates the data for a normal distribution graph and F(x)
creates the data for the cumulative probability (F(x): probability totals 100%)
•
Refer to ‘VW13E-05b.xlsx’ on tab ‘Standard Normal’
5b.5
Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Discrete Distribution: Expected
Return and Variance Calculation
f(x)
1.4
•
The f(x) graph to the left is created
from the data described earlier.
Refer to ‘VW13E-05b.xlsx’ on tab
‘Standard Normal’
•
Note that the x-axis indicates the
range of returns for this stock with
the height representing the
likelihood of the return occurring.
•
The F(x) graph to the left is created
from the data described earlier.
Also refer to ‘VW13E-05b.xlsx’ on
tab ‘Standard Normal’
•
Note that the x-axis indicates the
probability of a return being that
rate or lower. For example, the
probability of earning a return that
is 0% or less (negative) is 36.9%.
1.2
1
0.8
0.6
f(x)
0.4
0.2
0
-250.0%
-150.0%
-50.0%
50.0%
150.0%
250.0%
1.2 F(x)
1
0.8
0.6
0.4
F(x)
0.2
0
-250.0%
5b.6
-150.0%
-50.0%
50.0%
150.0%
250.0%
Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Remember?
Characteristic Line
EXCESS RETURN
ON STOCK
Narrower spread
is higher correlation
Rise
Beta = Run
EXCESS RETURN
ON MARKET PORTFOLIO
Characteristic Line
5b.7
Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
How do you create a Characteristic
Line in Excel?
5b.8
•
Step 1: Collect the data. We generated
monthly data using Finance.Yahoo.com.
•
We chose to use the S&P 500 to represent
the “market” portfolio, GE to represent our
individual stock asset, and the US Treasury
30-year bond yield to represent our risk-free
asset.
•
We started by downloading the prices on a
monthly basis for GE and the S&P 500 and
yields on the Treasury for the period
September 2005 through March 2008.
•
Refer to ‘VW13E-05b.xlsx’ on tab ‘Excess
Returns’
Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
How do you create a Characteristic
Line in Excel?
•
Step 2: Calculation of monthly excess returns.
•
We used the price data and calculated a monthly
return. For example, for March 2008 GE’s return
was $37.01/$33.14 - 1 = .11678 or 11.678%. We did
this for both the S&P and GE.
•
The yield on the 30-year is an annual yield, so we
divided the annual rate by 12 to generate a
monthly rate and adjusted it to the same format as
the other returns (%). For March it is .00359.
•
We then subtracted the monthly risk-free rate
from the monthly return to generate 30 excess
return data points for each GE and the S&P. This
gives us the .1132 or 11.32% return in March 2008.
•
Refer to ‘VW13E-05b.xlsx’ on tab ‘Excess Returns’
5b.9
Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
How do you create a Characteristic
Line in Excel?
•
Step 3: Plot the excess returns
for the S&P (on the x-axis) and
for GE (on the y-axis) for each
monthly data point.
•
Click on the “Insert” tab in
Excel and then choose the
“Scatter” graph option.
•
Upon generating the graph,
right-click on any one of the
data points. Choose “Add
trendline …” from the options
available.
Choose “linear” and click “Close”.
•
•
You may choose to change some formatting, but you have created a characteristic
line. The slope of that line is an estimate of beta.
•
Beta is estimated to be 0.756 for GE
•
Refer to ‘VW13E-05b.xlsx’ on tab ‘Excess Returns’
5b.10
Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
How do you find beta?
•
Trendline (as shown on the
previous slide) calculates the
beta estimate to be 0.756 for GE.
•
Use the formula approach as
Beta = [Covariance S&P, GE ] /
[Variance S&P]
•
•
0.000487/0.000644 = 0.756
beta estimate for GE
•
The same as the trendline
approach!
A third alternative is to us the
“slope” function in Excel.
•
Use ‘=slope(excess return
array for GE, excess return
array for S&P) = 0.756 beta
estimate for GE.
•
Again, same as others!!
5b.11
Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Remember? Determining
Portfolio Standard Deviation
sP =
m
m
S
S
W
W
s
j
k
jk
j=1 k=1
Wj is the weight (investment proportion)
for the jth asset in the portfolio,
Wk is the weight (investment proportion)
for the kth asset in the portfolio,
sjk is the covariance between returns for
the jth and kth assets in the portfolio.
5b.12
Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Remember? Determining
Portfolio Standard Deviation
B
C
D
2
Period
Stock 1
Stock 2
3
1
-0.60%
11.68%
4
2
-3.48%
-5.42%
5
3
-6.12%
-4.63%
6
4
-0.86%
-2.34%
7
5
-4.40%
-6.97%
8
6
1.48%
-0.59%
9
7
3.58%
7.22%
10
8
1.29%
0.29%
11
9
-3.20%
1.26%
12
10
-1.78%
2.61%
13
11
3.25%
1.93%
14
12
4.33%
4.26%
15
13
1.00%
1.27%
16
14
-2.18%
-2.39%
17
15
1.41%
-3.13%
18
16
1.26%
6.27%
19
17
1.65%
0.48%
20
18
3.15%
-0.53%
21
19
2.46%
4.40%
22
20
2.13%
4.16%
23
21
0.51%
-0.80%
24
22
0.01%
-3.07%
25
23
-3.09%
-0.95%
26
24
1.22%
-0.55%
27
25
1.11%
5.79%
28
26
0.05%
1.14%
29
27
2.55%
-6.57%
30
28
-0.10%
-1.18%
31
29
3.52%
5.35%
32
30
-1.77%
0.70%
5b.13
•
Why don’t we go through an example.
•
Assume we take the raw S&P 500 and GE returns that
we used in the previous example and assume they are
‘Stock 1’ and ‘Stock 2’ respectively (returns are to the
left).
•
Let us determine a portfolio standard deviation based
on weights of 40% in ‘Stock 1’ and 60% ‘Stock 2’
respectively.
•
Our first step will be to calculate a variance-covariance
matrix for our two assets. This is shown above.
•
Refer to ‘VW13E-05b.xlsx’ on tab ‘Diversification’
Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Remember? Determining
Portfolio Standard Deviation
•
We take the weights and appropriately multiply through with the
associated variances and covariances to generate a portfolio variance of
0.000968. Refer to ‘VW13E-05b.xlsx’ on tab ‘Diversification’
•
This equates to a standard deviation (SD) of 3.11% (note we assumed the
individual stocks were a population).
•
If we multiple 0.4(2.59% SD for Stock 1) + 0.6(4.25% SD for Stock 2) we
would get 3.59%. As such, diversification has reduced the SD by 0.48%
which is a significant reduction for adding just a single additional stock.
5b.14
Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Summary of the Portfolio
Return and Risk Calculation
Stock 1
Stock 2
Portfolio
Monthly Return
0.278%
0.656%
0.505%
Stand. Dev
Coefficient of
Variation
2.587%
4.253%
3.111%
6.48
6.16
9.30
The portfolio has the LOWEST coefficient of
variation due to diversification!
As such, we have reduced risk per unit of return.
5b.15
Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
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