This post creates confidence
intervals for the mean beta of 35 growth stocks and 35 value stocks. The post discusses ways the confidence
intervals can be constructed with an Excel spreadsheet and discusses financial
implications from this analysis.
Question: The table below has the estimated stock beta for
35 growth stocks and 35 value stocks. Use Excel to calculate a
95 percent confidence interval for the mean growth stock beta and the mean
value stock beta.
Use Excel
finance to observe the skew and kurtosis of the mean growth and value stock
betas.
Discuss
the results presented here. Is it possible to create a smaller
confidence interval for mean betas?
Estimates
of Beta for Growth and Value Stocks
1

Apple

1.140

Microsoft

1.25

2

AMAZON.COM

1.720

Berkshire
Hathaway

0.88

3

Facebook Inc 
Class A

0.890

JP
Morgan Chase & Co.

1.2

4

Alphabet Inc 
Class C Capital Stock

1.300

Exxon
Mobil

0.8

5

Visa

1.020

Johnson
& Johnson

0.6

6

Home Depot Inc (the

1.070

Bank OF
America

1.67

7

Boeing Company (the

1.730

Intel

0.86

8

Mastercard

1.020

Wells
Fargo & Company

1.27

9

Abbvie

1.670

UnitedHealth
Group Incorporated (de

0.76

10

Comcast Corporation
 Class A

1.320

Chevron

1.13

11

Netflix

1.390

Pfizer

0.96

12

Walt Disney Company
(the

1.220

Cisco
Systems

1.12

13

Nvidia

1.460

Verizon
Communications

0.68

14

Mcdonalds

0.690

AT&T

0.43

15

Philip Morris
International

0.720

Procter
& Gamble Company (the

0.43

16

Adobe Systems

0.810

Citigroup

1.53

17

3M Company

1.070

Merck
& Company Inc (

1.1

18

Medtronic PLC.
Ordinary Shares

0.750

Dowdupont

1.61

19

Union Pacific

0.850

Oracle

1.12

20

Texas Instruments

1.160

Pepsico

0.64

21

Broadcom

0.560

IBM

1.04

22

Booking Holdings

0.940

Walmart

0.42

23

Accenture Plc Class
A Ordinary Shares (ireland

1.090

General
Electric Company

0.71

24

Schlumberger N.V.

1.020

Amgen

1.69

25

Paypal Holdings

1.320

Honeywell
International

1.11

26

Nike

0.640

Abbott
Laboratories

1.75

27

SALESFORCE.COM

1.180

United
Technologies

1.13

28

Costco Wholesale

1.010

Caterpillar

1.57

29

Bristolmyers
Squibb Company

1.110

Gilead
Sciences

1.45

30

Thermo Fisher
Scientific

1.340

Qualcomm

1.57

31

Cocacola Company
(the

0.530

Cocacola
Company (the

0.56

32

United Parcel
Service

0.910

Eli
Lilly And Company

0.43

33

Starbucks

0.580

Conocophillips

1.39

34

Lowes Companies

1.380

Nextera
Energy

0.17

35

Micron Technology

1.230

Goldman
Sachs Group Inc (the

1.35

Source:
Yahoo Finance
Notes on Excel Formulas:
The width
of a confidence interval is determined by the function
confidence. The function of confidence are alpha, standard
deviation and sample size. Alpha determines the size of the
confidence interval. The alpha of a 95 percent confidence interval
is 0.05.
The
result of the confidence function is added to the average to get the upper
bound of the confidence interval and subtracted from the average to get the
lower bound of the confidence interval.
The other
way to get the width of the confidence interval is from the formula
normsinv(1alpha/2) * std/ count^{0.5}
The input
for Excel formulas for skews and kurtosis is just the range of the data for the
variable.
The
formula for skew involves the third moment around the
mean. When there are very large positive outliers the date is
positively skewed. Large negative outliers result in a
negative skew.
The
formula for kurtosis involves the fourth moment around the mean. A
large positive kurtosis reveals a distribution with a sharp peak in the
middle. Low or negative kurtosis reveal a flat distribution.
It is
sometimes difficult to interpret the kurtosis coefficient when the data is also
skewed in one way.
Results:
The
results are presented below.
Statistic

Growth Stocks

Value Stocks

Average

1.081

1.039

Standard Deviation

0.318

0.430

count

35.000

35.000

confidence 95%

0.105

0.142

Lower Bound

0.976

0.897

Upper Bound

1.186

1.182

skew

0.193

0.119

Kurt

0.380

0.957

Some observations:
The
average growth and value betas are close. There is a lot of
overlap in the two confidence intervals.
The skew
for beta is positive for growth stocks and negative for value stocks.
I suspect
that a technique that adjusts for outliers perhaps a jackknife method would
give a narrower confidence interval.
Go here for more questions on confidence intervals
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