Beta (β) which is also known as systematic risk or Market risk of a stock and can also be referred as a measure of the sensitivity of the stock’s return to the market return.
There are various methods and formulae of calculating beta of a stock within a portfolio but here equation which is used for calculating the beta(β) of a stock is:
β(Beta) = n ∑XY - ∑X ∑Y
n ∑X2 – (∑X)2
n ∑X2 – (∑X)2
Where X is the value of Sensex or stock market, Y is the closing price of stock
Date | Sensex (X) | Stock Price (Y) | X (Return %) | Y (Return%) | XY | X2 |
24/02/2012 | 5429.30 | 160.20 | (0.98) | (1.08) | 1.06 | 0.97 |
23/02/2012 | 5483.30 | 161.95 | (0.40) | (2.12) | 0.85 | 0.16 |
22/02/2012 | 5505.35 | 165.45 | (1.82) | (3.70) | 6.71 | 3.30 |
21/02/2012 | 5607.15 | 171.80 | 0.77 | (0.72) | (0.56) | 0.59 |
17/02/2012 | 5564.30 | 173.05 | 0.77 | 1.64 | 1.26 | 0.59 |
16/02/2012 | 5521.95 | 170.25 | (0.18) | (0.70) | 0.13 | 0.03 |
15/02/2012 | 5531.95 | 171.45 | 2.14 | 0.50 | 1.07 | 4.58 |
14/02/2012 | 5416.05 | 170.60 | 0.48 | 0.44 | 0.21 | 0.23 |
13/02/2012 | 5390.20 | 169.85 | 0.16 | (1.25) | (0.20) | 0.03 |
10/2/2012 | 5381.60 | 172.00 | (0.57) | (3.34) | 1.90 | 0.32 |
9/2/2012 | 5412.35 | 177.95 | 0.82 | 0.39 | 0.33 | 0.68 |
8/2/2012 | 5368.15 | 177.25 | 0.62 | (0.23) | (0.14) | 0.38 |
7/2/2012 | 5335.15 | 177.65 | (0.49) | (1.25) | 0.62 | 0.24 |
6/2/2012 | 5361.65 | 179.90 | 0.67 | 4.26 | 2.86 | 0.45 |
3/2/2012 | 5325.85 | 172.55 | 1.06 | 1.68 | 1.78 | 1.13 |
2/2/2012 | 5269.90 | 169.70 | 0.65 | 3.32 | 2.17 | 0.43 |
1/2/2012 | 5235.70 | 164.25 | 0.70 | 2.21 | 1.55 | 0.49 |
31/01/2012 | 5199.25 | 160.70 | 2.20 | 0.16 | 0.34 | 4.84 |
30/01/2012 | 5087.30 | 160.45 | (2.26) | (0.74) | 1.67 | 5.09 |
27/01/2012 | 5204.70 | 161.65 | 0.90 | 0.40 | 0.36 | 0.81 |
25/01/2012 | 5158.30 | 161.00 | 0.60 | 0.81 | 0.49 | 0.36 |
24/01/2012 | 5127.35 | 159.70 | ||||
Sum (Σ) | 5.85 | 0.69 | 24.47 | 25.70 |
Now, From the above table:
ΣX = 5.85, ΣXY = 24.47
ΣY = 0.69, ΣX2 = 25.70
Formula used for calculating the return % = (P2 – P1)/P1 × 100 Where, P1 = Old Value and, P2 = New Value according to the dates given in the table.
Formula used for calculating the return % = (P2 – P1)/P1 × 100 Where, P1 = Old Value and, P2 = New Value according to the dates given in the table.
Now From the data we can calculate the beta (β)
β(Beta) = n ∑XY - ∑X ∑Y
n ∑X2 – (∑X)2
n ∑X2 – (∑X)2
= 21(24.47) – (5.85)(0.69) [ n = 21]
21(25.70) – (5.85)2
21(25.70) – (5.85)2
= 1.008
so, from the calculation β= 1.008
so, from the calculation β= 1.008
Value of beta should be approximately around 1.
