In general, standard deviation measures how spread out the data points are from their average value.

In the context of investing, the standard deviation of an asset's returns measures how volatile the returns are. The larger the standard deviation, the higher the total risk, and the broader the distribution curve.

A diversified investor spreads their investments out across many different assets, as opposed to a concentrated investor who invests in just one or a handful of securities.

Idiosyncratic risk is unique to a specific company or industry. For instance, it could result from factors like management decisions. Because these risks are specific to a single company and do not affect the broader market, they can be mitigated by building a portfolio of many different investments. 

Only the market-wide risk that cannot be diversified away. For instance, a wide-scale economic downturn would affect all stocks.

Beta (β) measures a stock's market risk.

It is found through a regression analysis of the stock's returns against the market's returns. The gradient/slope of the regression line is the beta.

For instance, if a stock has a beta of 1.50, it means that when the market is up by 1%, the stock has tended to be up by 1.50%, and vice versa.

The capital asset pricing model (CAPM) assumes that an investor is diversified. Therefore, the only risk they face is market risk. The market risk that any stock adds to their portfolio can be measured by beta (β). 

Therefore, the higher the beta, the higher the risk of that stock, and the higher the required return an investor should demand. 

• Using the risk-free rate (RF), typically short-term government bonds, as the 'base'...

• We can scale the required return according to the market risk premium (RM - RF)...

Hence finding the required return that adequately compensates an investor for the risk of any given stock.

Thus, the CAPM equation is: Required return = RF + (RM - RF)β 

CAPM can be used to determine the return that an investor should require/demand to get, in order to justify taking on the risk of investing in that particular stock.

Therefore, an investor would only invest in a stock if their expected return on the stock was greater or equal to the required return.

CAPM is also used to calculate the cost of equity for various forms of financial analysis.