Questions:
What is the beta of a stock? How should you interpret a beta value?

Blake is considering three companies to suggest his client, William who is trying to invest his money for retirement. Blake wants to select the stock which has the lowest volatility compared to the market.

The first company is Amazon which has an expected return of 13% with an expected deviation in the return of 25%. Moreover, its correlation with the U.S. stock market is 0.6. The second company is Microsoft with an expected annual return of 16% with an expected deviation in the return of 20%. And its correlation with the market is 0.9. The third company is Meta which has an expected annual return of 12% with an expected standard deviation of 21% and a correlation with the market of 0.7. The standard deviation of the market returns is 15%.

Which company should Blake suggest to William?

Reference answers:
# Formula

Beta is the risk measure that measures the volatility of a stock compared to the market. Beta is measured as follows:

Beta = Correlation(Ri, Rm) * σi  / σm

Here: 

- Correlation (Ri, Rm) is the correlation between the return of a stock and the market return.
- σi is the standard deviation of the return of the stock.
- σm is the standard deviation of the market returns.

# Interpretation

If a stock has a beta of 1, it moves with the market
If a stock has a beta of less than 0, it moves in the opposite direction to the market.
If a stock has a beta of >1, it is more volatile than the market.
If a stock has a beta of <1, it is less volatile than the market.

.

# Calculation

Beta = Correlation(Ri, Rm) * σi  / σm

## Amazon

Beta = Correlation(Ri, Rm) * σi  / σm
Beta = 0.6 * 0.25 / 0.15
Beta = 1.0

## Microsoft

Beta = Correlation(Ri, Rm) * σi  / σm
Beta = 0.9 * 0.20 / 0.15
Beta = 1.2


## Meta

Beta = Correlation(Ri, Rm) * σi  / σm
Beta = 0.7 * 0.21 / 0.15 
Beta = 0.98

# Result

Based on the calculations, Meta has the lowest beta value which means that it is less volatile than the market. Therefore, based on Blake’s criteria, Meta should be suggested to William