Thursday, August 9, 2018

Confidence Interval and Other Statistics for Growth & Value Stock Betas.



Confidence Interval and Other Statistics for Growth & Value Stock Betas.


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
Bristol-myers Squibb Company
1.110
Gilead Sciences
1.45
30
Thermo Fisher Scientific
1.340
Qualcomm
1.57
31
Coca-cola Company (the
0.530
Coca-cola 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(1-alpha/2) * std/ count0.5

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/confidence-interval-quiz-question-below.html

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