Enter the company and market return to get beta of the company through this tool.
In finance:
“Beta is seemed because the contrast among the market index and the historical volatility of a employer”
Basically, calculating the beta of a inventory allows finance specialists to estimate the go back for a positive risk they may take.
A organization has invested certain shares in a enterprise for which the stats for both the organisation and the market are as follows:
Company’s Return = 2, 1, 4, 25, 4, 4
Market’s Return = 2, 7, 6, 8, 2, 7
Calculate beta to estimate whether or not the inventory’s rate is going higher or lower than the market.
As we have the within the following desk:
| Obs. | rM">rM | rS">rS |
| 1 | 2 | 2 |
| 2 | 7 | 1 |
| 3 | 6 | 4 |
| 4 | 8 | 25 |
| 5 | 2 | 4 |
| 6 | 7 | 4 |
Now we can calculate the regression coefficient.
| Obs. | rM">rM | rS">rS | Xᵢ² | Yᵢ² | Xᵢ · Yᵢ |
| 1 | 2 | 2 | 4 | 4 | 4 |
| 2 | 7 | 1 | 49 | 1 | 7 |
| 3 | 6 | 4 | 36 | 16 | 24 |
| 4 | 8 | 25 | 64 | 625 | 200 |
| 5 | 2 | 4 | 4 | 16 | 8 |
| 6 | 7 | 4 | 49 | 16 | 28 |
| Sum = | 32 | 40 | 206 | 678 | 271 |
\(SS_{XX} = \sum^n_{i=1}X_i^2 - \dfrac{1}{n} \left(\sum^n_{i=1}X_i \right)^2\)
\(= 206 - \dfrac{1}{6} (32)^2\)
\(= 35.333\) \(SS_{YY} = \sum^n_{i=1}Y_i^2 - \dfrac{1}{n}
\left(\sum^n_{i=1}Y_i \right)^2\) \(= 678 - \dfrac{1}{6} (40)^2\)
\(= 411.33\) \(SS_{XY} = \sum^n_{i=1}X_iY_i - \dfrac{1}{n}
\left(\sum^n_{i=1}X_i \right)
\left(\sum^n_{i=1}Y_i \right)\)
\(= 271 - \dfrac{1}{6} (32) (40)\) \(= 57.667\)
\(\hat{\beta}_1 = \dfrac{SS_{XY}}{SS_{XX}}\)
\(= \dfrac{57.667}{35.333}\)
\(= 1.632\)
because the beta cost is extra than 1.0, it manner that the inventory cost is higher than the marketplace index.
A terrible beta cost suggests a clear difference with recognize to the market fee of an index. but it not often takes place.
From the source Wikipedia: Beta (finance), Interpretation of values, significance as hazard measure, Technical aspects, choice of marketplace portfolio and danger-free rate, Empirical estimation, Equilibrium use: fair praise for threat?
