Question

I need the solution by Hand since I have no idea About Excel and am not allowed to use it on the exam. TIA

1. What is the beta of firm XXX over a 6 month period ? Could you please explain very thoroughly and step-by-step. I really struggle with the topic yet

Average month market return: 1/1/1/-1/-1/-1

Average stock Price changes: 2/0/1/-1/0/-2

Answer 1

Formula for Calculating beta.

Part 1: How to Calculate Covariance. Covariance means how a stock moves relative to some other Stock or Market.

Step 1: Formula for covariance,

X & Y are the mean average.

Xi & Yi are the variables

n is the data point.

Please note the formula is for calculating covariance of a sample.

Step 2: Calculate the Average of all the Data points. Average is 0 in this case for both Market Return and Stock Price.

Step 3: Calculate the difference between Average price of Market Return and the Individual Month wise Average as shown below. Do the same exercise with Stock price also.

Step 4: Multiply the differences calculated as shown below. a x b.

Step 5: Add all the multiplied items as above which gives a value of 6.

Step 6: Divide the above sum by (n-1) which in this case is (6-1)= 5. So Covariance = 6/5 = 1.2

Serial No.	Market Return	Stock Price	Difference Market return - a	Different Stock Price - b	a x b
1	1	2	=0-1= -1	=0-2= -2	-2 x = 1 = 2
2	1	0	=0-1= -1	=0-0=0	-1 x 0 = 0
3	1	1	=0-1= -1	=0-1=-1	-1 x - 1 = 1
4	-1	-1	=0-(-1)= +1	=0-(-1)= +1	1 x 1 = 1
5	-1	0	=0-(-1)= +1	=0-0=0	1 x 0 = 0
6	-1	-2	=0-(-1)= +1	=0-(-2)= 2	1 x 2 = 2
Sum last column					6

Part 2: How to Calculate Variance. Variance means how a stock moves relative to it's own mean value.

Formula is

Step 1: calculate the stock average.

Step 2: calculate the stock difference as given below.

Step 3: Calculate the square of the Stock difference.

Step 4: Sum the square difference which comes to 10 as given below

Step 5: variance = 10/(6-1) = 10/5 = 2.

Serial No.	Stock Price	Different Stock Price - b	b square
1	2	=0-2= -2	--2 x - 2 = 4
2	0	=0-0=0	0 x0 = 0
3	1	=0-1=-1	-1 x -1 = 1
4	-1	=0-(-1)= +1	1 x 1 = 1
5	0	=0-0=0	0 x 0 = 0
6	-2	=0-(-2)= 2	2 x 2 = 4
Sum last column			10

Part 3: Beta = covariance / Variance = 1.2/2 = 0.6.

Please go through the calculations, primarily you would need to understand how to calculate covariance and variance from a simple data. Although the answer looks long once you put pen on paper you can easily calculate after practicing a few problems.