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FIN 614: Financial Management
Larry Schrenk, Instructor
1. Why Statistics?
2. Probability Measures
1.
2.
3.
4.
Mean, Median, Mode
Standard Deviation, Variance
Covariance, Correlation
Skewness, Kurtosis
3. Linear Regression
Evaluate the Data and Claims
Distinguish Good from Faulty Reasoning
Forecasting
Overcome Innate Biases
Descriptive Statistics–Describing the
Basic Features of the Data
Inferential Statistics–Trying to Reach
Conclusions that Extend Beyond the
Immediate Data
Measures of Central Tendency
Mean, Median, Mode
Measures of Dispersion
Standard Deviation, Variance
Higher Moments
Skewness, Kurtosis
Measures of Dependence
Covariance, Correlation
What is a Measure of Central Tendency?
Equal Weighted Average (m, x )
Applications
n
Calculation:
m  or x  
x
i 1
i
n
m, x = Mean of Random Variable
x i = Random Variable i
n = Number of Random Variables
Calculating the (Equally Weighted)
Average
3, 1, 4, 5, 7
3  1 4  5  7
m
4
5
(Unequally) Weighted Average
Applications
n
Calculation:
m  or x    pi xi
i 1
m, x = Mean of Random Variable
x i = Random Variable i
pi = Probability/Weight of Random Variable i
Calculating the Unequally Weighted
Average
Value
Weight
5
.30
8
.70
μ = (.3)5 + (.7)8 = 7.1
The mode is the most frequent number.
2, 3, 4, 2, 5, 7, 8, 2, 3
The mode is 2
The median is the ‘middle’ number.
2, 3, 4, 2, 5, 7, 8, 2, 3
Ordered: 2, 2, 2, 3, 3, 4, 5, 7, 8
The median is 3.
What is a Measure of Dispersion?
Variance (s2)
Applications
Calculation:
n
s 
2
(x
i 1
 x)
2
i
n 1
s 2 = Variance
x i  Random Variable i
x = Mean of Random Variable
n = Number of Random Variables
Sample versus Population
Calculating Variance
3, 1, 4, 5, 7
x=4
2
2
2
2
2
(3

4)

(1

4)

(4

4)

(5

4)

(7

4)
s2 
5
4
Standard Deviation (s)
n
s
(x
i 1
 x)
2
i
n 1
 s
2
s = Standard Deviation
s 2 = Variance
x i  Random Variable i
x = Mean of Random Variable
n = Number of Random Variables
Calculating Standard Deviation
3, 1, 4, 5, 7
(3  4)2  (1  4)2  (4  4)2  (5  4)2  (7  4)2
s
4
 5  2.24
On the exams you may use the
formulae or your calculator to calculate
these probability measures.
NOTE: There is one significant drawback to using
your calculator for these calculations: I give partial
credit if your answer demonstrates some
knowledge even if it is not correct. If you use the
calculator functions I cannot see any of your work,
so I cannot give partial credit.
What is a Higher Moment?
Normal Distribution has a skewness of 0
Normal Distribution has a kurtosis of 3
What is a Measure of Dependence?
Covariance (sX,Y)
Applications
Calculation:
s
X ,Y
n

(x
i 1
i
 x )( y i  y )
n
s X ,Y = Covariance between X and Y
x i , y i  Random Variables i
x, y = Mean of Random Variables
n = Number of Random Variables
Variance versus Covariance
Calculating Covariance
3, 1, 4, 5, 7
x=4
2, 2, 3, 7, 1 y = 3
(3  4)(2  3)  (1  4)(2  3)  (4  4)(3  3)
s X ,Y 
 (5  4)(7  3)  (7  4)(1  3)
5
Note: Unit Dependence
 0.4
Correlation (rX,Y)
Applications
s X ,Y
r X ,Y 
Calculation:
s XsY
r X ,Y = Correlation between X and Y
s X ,Y = Covariance between X and Y
s X ,s Y = Standard Deviation
Range: -1 < r <1
Calculating Correlation
r X ,Y 
0.4
 0.095
2.24  2.35
Graph of Two Series
8
7
6
5
4
3
2
1
0
1
2
3
4
5
Best Linear Fit
BLUE
‘Least Squares’ Criterion
Dependent versus Independent Variable
Minimize the sum of squared differences
from the mean
n
Min   xi  x 
i 1
2
Income
Education
Income
Education
Income
Education
Income
Rise
Run
Education
Income
Rise/Run = Slope
Rise
Run
Education
Income
Rise/Run = Slope
Rise
Slope = $3,000
Run
Education
Data: Daily Return
8-Jul-14
7-Jul-14
3-Jul-14
2-Jul-14
1-Jul-14
30-Jun-14
27-Jun-14
26-Jun-14
25-Jun-14
24-Jun-14
23-Jun-14
20-Jun-14
19-Jun-14
18-Jun-14
17-Jun-14
16-Jun-14
13-Jun-14
12-Jun-14
11-Jun-14
10-Jun-14
9-Jun-14
6-Jun-14
5-Jun-14
4-Jun-14
3-Jun-14
2-Jun-14
IBM
S&P 500
-0.44% -0.70%
-0.26% -0.39%
0.07%
0.55%
1.09%
0.07%
2.80%
0.67%
-0.24% -0.04%
0.74%
0.19%
-0.19% -0.12%
-0.09%
0.49%
-0.69% -0.64%
0.32% -0.01%
-0.69%
0.17%
-0.42%
0.13%
0.74%
0.77%
-0.05%
0.22%
-0.12%
0.08%
0.74%
0.31%
-0.57% -0.71%
-1.11% -0.35%
-1.04% -0.02%
-0.08%
0.09%
0.21%
0.46%
0.80%
0.65%
0.08%
0.19%
-0.71% -0.04%
0.72%
0.07%
S&P 500
3.00%
2.50%
2.00%
1.50%
IBM
1.00%
IBM
Predicted IBM
0.50%
-0.80%
-0.60%
-0.40%
0.00%
-0.20%
0.00%
0.20%
-0.50%
-1.00%
-1.50%
S&P 500
0.40%
0.60%
0.80%
1.00%
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.605455631
R Square
0.366576521
Adjusted R Square
0.340183876
Standard Error
0.006610242
Observations
26
ANOVA
df
SS
Regression
MS
F
1
0.000606899
0.000606899
Residual
24
0.001048687
4.36953E-05
Total
25
0.001655586
Coefficients
Intercept
S&P 500
Standard Error t Stat
Significance F
13.88934384
P-value
0.00104756
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
-0.000357995
0.001322873
-0.270619258
0.788997611
-0.003088272
0.002372282
-0.003088272
0.002372282
1.223550688
0.328307724
3.726841
0.00104756
0.545956848
1.901144528
0.545956848
1.901144528
FIN 614: Financial Management
Larry Schrenk, Instructor