Beta is a measure of a stock's volatility in relation to the overall market. High-beta stocks are supposed to be riskier but provide higher return potential; low-beta stocks pose less risk but also lower returns.
In investing, standard deviation is used as an indicator of market volatility and, therefore, of risk. The more unpredictable the price action and the wider the range, the greater the risk. Range-bound securities, or those that do not stray far from their means, are not considered a great risk.
By and large, beta is a measure of a stock's volatility in relation to the market. If a stock moves less than the market, the stock's beta is less than 1.0. High-beta stocks are supposed to be riskier but provide a potential for higher returns; low-beta stocks pose less risk but also lower returns.
Volatility is the most widespread measure of risk. And this is pretty much the basis for Modern Portfolio Theory, where portfolios are optimized in a mean-- variance (volatility) framework, meaning that they are constructed taking into account the risk (viewed as volatility) and the expected return.
Volatility ExplainedVolatility often refers to the amount of uncertainty or risk related to the size of changes in a security's value. A higher volatility means that a security's value can potentially be spread out over a larger range of values.
Standard deviation is a measure of the risk that an investment will fluctuate from its expected return. The smaller an investment's standard deviation, the less volatile it is. The larger the standard deviation, the more dispersed those returns are and thus the riskier the investment is.
Systematic risk refers to the risk inherent to the entire market or market segment. Systematic risk, also known as “undiversifiable risk,” “volatility” or “market risk,” affects the overall market, not just a particular stock or industry. This type of risk is both unpredictable and impossible to completely avoid.
Because the stock market is unpredictable, systematic risk always exists. Systematic risk is largely due to changes in macroeconomics. The portfolio's risk (systematic + unsystematic) is measured by standard deviation, variation of the mean (average, not annualized) return of a portfolio's returns.
A beta of less than 1 means it tends to be less volatile than the market. If a stock had a beta of 0.5, we would expect it to be half as volatile as the market: A market return of 10% would mean a 5% gain for the company.
– 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. Higher standard deviations are generally associated with more risk.
The difference between beta and standard deviation is best described as: Beta measures the risk of the market as a whole, while standard deviation measures the risk of individual stocks. b. Beta measures total volatility, while standard deviation measures total risk.
The formula for calculating beta is the covariance of the return of an asset with the return of the benchmark, divided by the variance of the return of the benchmark over a certain period.
Usually, any Sharpe ratio greater than 1.0 is considered acceptable to good by investors. A ratio higher than 2.0 is rated as very good. A ratio of 3.0 or higher is considered excellent. A ratio under 1.0 is considered sub-optimal.
The risk-return tradeoff states the higher the risk, the higher the reward—and vice versa. Using this principle, low levels of uncertainty (risk) are associated with low potential returns and high levels of uncertainty with high potential returns.
A beta that is greater than 1.0 indicates that the security's price is theoretically more volatile than the market. For example, if a stock's beta is 1.2, it is assumed to be 20% more volatile than the market. Technology stocks and small cap stocks tend to have higher betas than the market benchmark.
FORMULA FOR UNLEVERED BETAUnlevered beta or asset beta can be found by removing the debt effect from the levered beta. The debt effect can be calculated by multiplying debt to equity ratio with (1-tax) and adding 1 to that value. Dividing levered beta with this debt effect will give you unlevered beta.
Alpha= R – Rf – beta (Rm-Rf)R represents the portfolio return. Rf represents the risk-free rate of return. Beta represents the systematic risk of a portfolio. Rm represents the market return, per a benchmark.
If we have 30-day volatility of 5% (the current figure for Bitcoin), then on 20 of those days (i.e. 68%) the next day's price should differ by less than 5% (one standard deviation). On about 28 of the days (i.e. 95%), the daily price difference should be less than 10% (two standard deviations).
To calculate the standard deviation of those numbers:
- Work out the Mean (the simple average of the numbers)
- Then for each number: subtract the Mean and square the result.
- Then work out the mean of those squared differences.
- Take the square root of that and we are done!
You can determine the beta of your portfolio by multiplying the percentage of the portfolio of each individual stock by the stock's beta and then adding the sum of the stocks' betas. For example, imagine that you own four stocks.
Multiply the stock beta by the market standard deviation, which you calculated in Step 1. Divide the result of the calculation in Step 3 by the correlation between the stock and the market. This gives you the stock standard deviation. Find the square root of the stock standard deviation to get the variance.
Volatility is a formal measure of a stock's risks. The higher the volatility of a stock, the greater its up and down swings. The volatility of a portfolio of stocks, on the other hand, is a measure of how wildly the total value of all the stocks in that portfolio appreciates or declines.
Standard deviation tells you how spread out the data is. It is a measure of how far each observed value is from the mean. In any distribution, about 95% of values will be within 2 standard deviations of the mean.
Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out. A standard deviation close to zero indicates that data points are close to the mean, whereas a high or low standard deviation indicates data points are respectively above or below the mean.
A low standard deviation indicates that the data points tend to be very close to the mean; a high standard deviation indicates that the data points are spread out over a large range of values. A useful property of standard deviation is that, unlike variance, it is expressed in the same units as the data.
Therefore, the portfolio's total risk is simply a weighted average of the total risk (as measured by the standard deviation) of the individual investments of the portfolio. Portfolio 1 is the most efficient portfolio as it gives us the highest return for the lowest level of risk.
The standard deviation of a stock determines the dispersion of a dataset in relation to its mean. A high standard deviation represents volatile stocks, while a low standard deviation usually points to consistent blue-chip stocks. The greater the standard deviation, the riskier the stock.
The standard deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance. If the data points are further from the mean, there is a higher deviation within the data set; thus, the more spread out the data, the higher the standard deviation.
This risk is also known as diversifiable risk, since it can be eliminated by sufficiently diversifying a portfolio. There isn't a formula for calculating unsystematic risk; instead, it must be extrapolated by subtracting the systematic risk from the total risk.
Capital Asset Pricing Model
Comparison of variances: if you want to compare two known variances, first calculate the standard deviations, by taking the square root, and next you can compare the two standard deviations. In the dialog box, enter the two standard deviations that you want to compare, and the corresponding number of cases.
