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A fair multiple is that multiple paid which results in the investment having a net present value of zero.
We assume a cost of equity based on the U.S. 10-year bond yield plus a 6% equity risk premium and discount back today's price, and divide the result by EPS (or revenue), corresponding to a specific period in the past.
So, we get fair P/E (or P/S) value based on the current share price at a point of time in the past, taking into account the acceptable cost of capital.
Generally, Beta is a measure of the volatility of a security in comparison to the market as a whole.
In other words, Beta evaluates how much the share price is prone to change in one direction with the market.
In my opinion, Beta allows you to define the periods when the stock is overheated because of the high speculative interest.
Let's assume there is a company the shareholders of which are mostly long-term investors not prone to actively buying and selling stocks under the influence of the external market background.
This stock will have a low beta and it will show a stable growth with a low volatility.
And the opposite case - let's suppose the stock generates a high speculative interest of investors who tend to actively buy stock in a positive market and quickly sell it even if the market slightly falls. This stock will have high beta and high volatility.
Bearish Beta - a measure of how a stock price tends to drop when the market is only down.
Bullish Beta - a measure of how a stock price tends to rise when the market is only on the rise.