This post uses data on stock betas for growth and value stocks to create and understand confidence intervals.
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 he 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
http://www.dailymathproblem.com/p/confidenceintervalquizquestionbelow.html
Go here for more questions on confidence intervals
http://www.dailymathproblem.com/p/confidenceintervalquizquestionbelow.html
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