# Difference Between Beta and Standard Deviation

The two most important factors influencing share/security pricing are expected risk and projected return. In general, the projected average return is higher for riskier investments. Practically speaking, risk is the likelihood and magnitude of financial loss. The volatility of a fund's price over time is a good statistical proxy for this. Beta and standard deviation are two ways to describe market volatility.

Beta measures the fund's volatility in comparison to other funds, whereas standard deviation measures the fluctuation in the fund's share price over time. Standard deviation, on the other hand, solely characterises the fund in question and not how it compares to the index or other funds. Yet, volatility is simply one sort of risk.

Bankruptcy, a lack of liquidity, and persistently bad performance are examples of risks that cannot be quantified using beta and standard deviation. Sadly, there is no method to quantify these dangers. Let's examine the two commonly used volatility metrics in further detail.

## What is Beta?

Beta is a measure of the volatility or systematic risk of an investment relative to the market as a whole. In other words, it measures how much an investment’s price moves in response to movements in the overall market.

A beta of 1 indicates that the investment moves in tandem with the market, a beta greater than 1 indicates that the investment is more volatile than the market, and a beta less than 1 indicates that the investment is less volatile than the market. A negative beta indicates that the investment moves in the opposite direction of the market.

Beta is calculated by comparing the return of the investment to the return of the market over a specified period of time. The formula for beta is as follows −

$$\mathrm{Beta=\frac{Covariance (Ri, Rm)}{Variance (Rm)}}$$

Where Ri is the return of the investment and $R_{m}$ is the return of the market.

## What is Standard Deviation?

Standard deviation, on the other hand, is a measure of the total risk associated with an investment. It measures the degree to which an investment’s returns deviate from its average return. The higher the standard deviation, the greater the volatility of the investment.

Standard deviation is calculated by finding the square root of the variance of the investment’s returns. Higher standard deviations are generally associated with more risk. If you scale the standard deviation of one market against another, you obtain a measure of relative risk. The funds with standard deviations of their annual returns greater than 16.5 are more volatile than average.

## Differences: Beta and Standard Deviation

Standard deviation is a more general measure of risk than beta because it takes into account all types of risk, including both systematic (market-wide) risk and unsystematic (company-specific) risk. Beta only measures systematic risk.

Characteristics

Beta Deviation

Standard Deviation

Definition

Both Beta and Standard deviation are two of the most common measures of fund’s volatility.

However, beta measures a stock’s volatility relative to the market as a whole, while standard deviation measures the risk of individual stocks.

Standard deviation is a measure that indicates the degree of uncertainty or dispersion of cash flow and is one precise measure of risk. Higher standard deviations are generally associated with more risk.

Beta, on the other hand, measures the risk (volatility) of an individual asset relative to the market portfolio.

Calculation

Beta is the average change in percentage in the value of the fund accompanying a 1% increase or decrease in the value of the S&P 500 index. An S&P index fund, by definition, has a beta of 1.0.

A beta greater than 1.0 means greater volatility than the overall market, while a beta below 1.0 accounts for less volatility.

Standard deviation is defined as the square root of the mean of the squared deviation, where deviation is the difference between an outcome and the expected mean value of all outcomes.

Example

A stock with a 1.50 beta is significantly more volatile than its benchmark. It is expected to go up about 50% more than the index when the market goes down.

Similarly, a stock with a beta of 2.00 experiences price swings double than those of the broader market.

Standard deviation can be used as a measure of the average daily deviation of share price from the annual mean, or the year-to-year variation in total return.

Higher standard deviations are generally associated with more risk and lower standard deviations mean more return for the amount of risk acquired.

## Conclusion

In summary, beta is a measure of the volatility of an investment relative to the market, while standard deviation is a measure of the total risk associated with an investment.

Beta is useful for investors who want to know how an investment will perform in relation to the market, while standard deviation is useful for investors who want to know the overall risk associated with an investment.

Both measures are important for assessing risk, and investors should consider both when making investment decisions.

Updated on: 17-Apr-2023

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