Quantitative Analysis

Question 1

Sample covariance (cov)

Answer 1

∑(x-xbar)(y-ybar) / n-1

Question 2

Sample correlation coefficient (r)

Answer 2

Cov(x,y) / (Sx)(Sy)

S = Standard Deviation

Question 3

Limitations of Correlation Analysis

Answer 3

1. Linear relationships (not quadratic)
2. Outliers (news vs. noise)
3. Not causation
4. Spurious (Chance, mixed third variables)

Question 4

Two-tailed “t-test” with n-2 degrees of freedom to tell if population correlation is 0 or not 0

Answer 4

t = r√n-2 / √1-r^2

Question 5

Decision rule for two-tailed test

Answer 5

Reject H0 if

1. t-stat > +ve tc (Positive critical value)
2. t-stat < -ve tc (Negative critical value)
3. t-stat > |Tc|

|Tc| = T critical value

Question 6

Dependent Variable (which axis and description)

Answer 6

1. Y-axis

2. Seeking to explain or predict the Y variable

Question 7

Independent Variable (which axis and description)

Answer 7

1. X-axis

2. Used to explain or predict the Y or dependent variable

Question 8

Regression Model Equation

Answer 8

Yi = b0 + b1Xi+Ei

1. i = 1,…,n
2. This uses the estimates of Y (includes a carot above the Y and b)

Question 9

Some of Squared Errors (SSE)

Answer 9

∑(Yi - Yi~ or (b0+b1Xi))^2

Question 10

Calculation for b1

Answer 10

b1 = Cov(X,Y) / Var (X)

Question 11

Calculation for b0

Answer 11

b0 = Yaverage - b1(Xaverage)

Question 12

The midpoint of a regression series

Answer 12

= (Xbar, Ybar)

1. will be plotted on the regression line

Question 13

Standard Deviation

Answer 13

= ∑√(xi - xbar)^2 / n-1

Question 14

Steps for calculating correlation coefficient

Answer 14

1. calculate sum and mean of each variable
2. Calculate cross product of (xi-xbar)(yi-ybar) for each variable (by row)
3. Calculate squared deviation for each variable (by row)

Question 15

Regression Line Equation

Answer 15

Yi~ = b0~+b1~Xi

~ = ‘hat’ or estimate of these variables

Question 16

Find correlation of two stocks using market model

Answer 16

Calcuate total risk (standard deviation) for both securities being compared. V’ is the common macro factor variance:

Security 1 σ² = (β² x V’) + unsystematic risk²

Calculate covariance:

Beta(a) X Beta(b) X common macro factor variance

Calculate correlation:

cov/totalriskA X total risk Y