Beta (ß) is the measure of the systematic risk of an asset. It does not measure all of the company’s risk, but only the part of the risk that cannot be eliminated through diversification (the company’s sensitivity to general macroeconomic conditions).
Here’s how it’s calculated and the factors that determine its value:

1. Mathematical and econometric calculation

The theoretical formula The Beta of a security “i” corresponds to the correlation coefficient between the return generated by this security and the return generated by the market. It is calculated by the ratio between the covariance of returns and the variance of market profitability, :

${\mathbf{ß}}_{\mathbf{i}}=\frac{\mathbf{Cov}(\mathbf{Ri} ; \mathbf{Rm})}{\mathbf{Var}\left(\mathbf{Rm}\right)}$

Where Ri is the return of the security and Rm is the return of the market.
Practice (econometric approach): in practice, it is not calculated “by hand” but is estimated by observing the history of stock prices. A linear regression of the stock’s returns against a benchmark index (e.g. S&P 500, CAC 40) is performed.
Duration of observation: It is recommended to use a period of 36 months. A period that is too short (12 months) makes the Beta too volatile and “chaotic”, while a period that is too long (60 months) incorporates outdated data that no longer reflects the company’s current risk.
Frequency: The calculation is usually based on monthly returns.

2. Factors that influence the value of Beta

The value of the Beta is not stable; It evolves according to the life of the company and its financial and strategic decisions.

A. Economic risk (Sector and competitive position) This is the ${\mathrm{ß}}_{\mathrm{U}}$ (Unlevered Beta). It depends on the sensitivity of the activity to economic cycles:

• Cyclical sectors: Companies operating in commodities or the mining industry often have high and highly variable Beas.
• Monopoly situation: A company in a dominant position is less sensitive to macroeconomic fluctuations because it can impose its conditions on its customers and suppliers. For example, Facebook’s (Meta) Beta converged to 0.5 (very low) when it consolidated its monopoly via the acquisitions of Instagram and WhatsApp.
• Nature of revenues: A company like American Tower saw its Beta drop to 0.2 (the level of a bond) when it secured its revenues with very long-term contracts, before rising back to 0.5 when market conditions changed.

B. Financial risk (debt): this is the impact of the financial structure that transforms the ${\mathbf{ß}}_{\mathbf{U}}$ into ${\mathbf{ß}}_{\mathbf{L}}$(Levered Beta). Debt increases the volatility of shareholder earnings (leverage). The more indebted the company, the higher its observed Beta (ßL) relative to its intrinsic economic risk. This relationship is modelled by Hamada’s formula :

${\mathrm{ß}}_{\mathrm{L}}={\mathrm{ß}}_{\mathrm{U}}\times [1+(1–\mathrm{T})\times \mathrm{D}/\mathrm{CP}]$

C. The life cycle of the company

• Initial Public Offering (IPO): At the time of its IPO, a company’s Beta is often “chaotic” and has no immediate economic significance.
• Specific trajectories: Some technology companies such as Zoom may temporarily have a negative Beta (they rise when the market falls), reflecting a specific trajectory uncorrelated from the economy, before joining a classic positive correlation.

3. How to calculate the Beta of an unlisted company?

Since there are no stock market prices to make the regression, we use the method of comparables:

1. Identify comparable listed companies (same sector, same risk).
2. Calculate their observed Beta (${\mathrm{ß}}_{\mathrm{L}}$).
3. “Deleverage” these Betas with Hamada’s formula to find their ${\mathrm{ß}}_{\mathrm{U}}$(pure economic risk).
4. Average these ${\mathrm{ß}}_{\mathrm{U}}$to estimate the economic risk of the project or target company.
5. “Re-leverage” this Beta with the target financial structure (Debt/Equity) of the unlisted company to obtain its estimated ${\mathrm{ß}}_{\mathrm{L}}$ 

Limitations

It should be noted that the calculated Beta is focused on the past (historical data), whereas the assessment requires an estimate of future risk. In addition, the statistical quality of the Beta is often low (the model explains only a small part of the true variance of yields), which calls for caution and additional qualitative analysis.