However you decide to invest in the stock market, the idea of ** risk and return** is something you’ve considered. Risk and return is closely tied to volatility in the stock market. The beta equation compares the specific stock volatility to the stock market as a whole. By putting this number on a scale you can very quickly determine the risk of an investment.

A preliminary definition of investment risk is the probability that return will be less than expected.

This applies for both positive and negative returns that are lower than expected. There is no equation that tells you if a stock is worth investing in, or how long to stay in that stock, due to the random variable. In statistics, a random variable is the outcome of a chance process it has in probability distribution. You would see this as the mean or expected value, or the most likely outcome for the random variable. When you evaluate risk and return what you’re really doing is looking at the weighted average of all possible outcomes. However, variance and standard deviation are things that you need to consider. Variability relates to how far a typical observation of the variable is likely to deviate from the mean. Standard deviation gives an identification on how far the mean a typical observation is likely to fall. In financial theory, the return of a stock investment is considered a random variable. Return is influenced by the future price of the stock or expected dividends. There is an element of uncertainty in both of these variables. A risky stock has a high probability of earning a return that significantly differs from the mean of the distribution. This is due to volatility and why the beta formula can be so useful.

Market risk is crucial to the concept of investing so we need a way to identify risk for individual stocks. **The stocks beta value measures it’s risk compared to the market. Beta is developed by determining the historical relationship between a Stocks return and the return on the market index such as the S&P 500. **The stocks characteristic line reflects the average relationship between its return in the market. Beta is the slope of the characteristic line.

## Projecting Returns With Beta

Knowing a Stocks beta enables us to estimate changes in its return given changes in the market return. Beta is developed from historical data and therefore may not be accurate if a fundamental change in the business, or environment. A Beta value of 1.0 implies that the stock moves less than market. If it is greater than 1, the reverse is true. The beta value of less than zero means the stock tends to move against the market. Stocks in gold mining companies are a real world example of Negative beta stocks. **Trader tip: If the market is going down, it’s a good time to consider gold stocks. **

Beta value becomes important for individual portfolios as well as looking at Stocks. You can mitigate risk in your own investments by maintaining an average beta for your entire portfolio. This is sometimes called hedging, where are you invest a little in a high-risk high-reward stock, offset by more equity in a low-return low-risk stock. In order to effectively use beta you have to adopt the capital assessment pricing model, a.k.a. CAPM. The CAPM helps us determine how stock prices are set in the market, this was developed in the 1950s by Harry Markowitz and William Sharpe.** The CAPM attempts to explain how investors required returns are determined. **People won’t invest unless the stocks expected return is equal to the required return. Which is referred to as market aversion. Acceptable risk in the market is called the market risk premium it

**is a reflection of the investment communities’ level of risk aversion**. It is the risk premium for an investment in the market as a whole, which can change generationally.

The security market line (SML) is a portrayal of the market. The standard equation of a straight line is** y = mx + b.** The

**is the vertical axis variable;**

*y***is the horizontal;**

*x***is the slope of the line and**

*m***is the**

*b***. The slope represents risk and volatility, while the vertical intercept represents no-risk securities. If, for every stock, its expected return equals its return minimum, the SML would be a**

*y intercept**straight line*. Suppose a stocks expected return now becomes less than is required return. Investors would no longer desire the stock and the owners of the stock would sell, well potential buyers but no longer be interested.

**The stock price would drop because of supply and demand. Since the stock price is dropping its expected return is increasing driving it back towards equilibrium**. The SML represents a condition of stable equilibrium, shown by the beta value.

## Adjusting To Market Conditions

The response to a change in the risk-free rate of government securities is also shown through the SML and the beta formula. If all else remains the same a change in the risk-free rate causes a parallel shift in the SNL. The slope of the SML remains the same which means the KM variable must increase by the amount of change in the KRf variable. The response to a change in risk aversion can come from many avenues. Changes in attitude towards risk or reflected by rotations of the SML along its vertical intercept. **CAPM is an abstraction of reality designed to help make predictions. **It relates risk and return in an easy to understand concept and its simplicity has led to its popularity. *However, CAPM, SML, and beta is not universally accepted. A continuing debate exists as to its relevance and usefulness. *

Beta value can be evaluated with Google Sheets, using the googlefinance function. In the example below, the stock ticker is in cell B1.

=GOOGLEFINANCE(NASDAQ:GOOG,”Beta”)