# Squared and beta relationship

### Morningstar FundInvestor Glossary There are statistical tools, which can give you an idea of how a fund will move in relation to the market. Beta is a statistical measure that shows. In this article we will cover significance of Beta and Standard Deviation. Beta Variance = (Sum of squared difference between each monthly return and its. Learn about beta, how to calculate it, and how it's used as a risk measure the volatility of an asset or portfolio in relation to the overall market.

The beta of the market is 1.

### Use R-Squared To Measure How Accurate Beta Is | ShareInvestor Educational Series

Morningstar calculates beta by comparing a fund's excess return over Treasury bills to the market's excess return over Treasury bills, so a beta of 1.

Conversely, a beta of 0. Beta can be a useful tool when at least some of a fund's performance history can be explained by the market as a whole. Beta is particularly appropriate when used to measure the risk of a combined portfolio of mutual funds. It is important to note that a low beta for a fund does not necessarily imply that the fund has a low level of volatility.

A low beta signifies only that the fund's market-related risk is low. Standard deviation is a measure of a fund's absolute volatility. A specialty fund that invests primarily in gold, for example, will usually have a low beta, as its performance is tied more closely to the price of gold and gold-mining stocks than to the overall stock market.

Thus, the specialty fund might fluctuate wildly because of rapid changes in gold prices, but its beta will remain low. R-squared is a necessary statistic to factor into the equation, because it reflects the percentage of a fund's movements that are explained by movements in its benchmark index.

The beta of 0. See also Alpha, R-Squared Category: This is a proprietary Morningstar data point. While the investment objective stated in a fund's prospectus may or may not reflect how the fund actually invests, the Morningstar category is assigned based on the underlying securities in each portfolio.

Morningstar categories help investors and investment professionals make meaningful comparisons between funds. The categories make it easier to build well-diversified portfolios, assess potential risk, and identify top-performing funds.

Morningstar places funds in a given category based on their portfolio statistics and compositions over the past three years. If the fund is new and has no portfolio history, Morningstar estimates where it will fall before giving it a more permanent category assignment. When necessary, Morningstar may change a category assignment based on recent changes to the portfolio. Duration is a time measure of a bond's interest-rate sensitivity, based on the weighted average of the time periods over which a bond's cash flows accrue to the bondholder.

Time periods are weighted by multiplying by the present value of its cash flow divided by the bond's price. A bond's cash flows consist of coupon payments and repayment of capital. A bond's duration will almost always be shorter than its maturity, with the exception of zero-coupon bonds, for which maturity and duration are equal.

An assessment of the variations in a fund's monthly returns, with an emphasis on downside variations, in comparison to similar funds.

Morningstar Risk is measured for up to three time periods three, five, and 10 years. These separate measures are then weighted and averaged to produce an overall measure for the fund. Funds with less than three years of performance history are not rated. This figure is recorded in millions of dollars and represents the fund's total asset base, net of fees and expenses.

R-Squared is the measure of correlation between a fund and the market benchmark. It is calculated by regressing the fund against an appropriate index over time.

## Beta (finance)

Values range between 0 and 1. The higher the value of R-Square, the greater the correlation between the two. R-Squared is calculated over the last 36 months.

An R-squared of 1 means that all movements of a fund are completely explained by movements in the index. Conversely, a low R-squared indicates that very few of the fund's movements are explained by movements in its benchmark index. An R-squared measure of 0. Therefore, R-squared can be used to ascertain the significance of a particular beta or alpha.

Generally, a higher R-squared will indicate a more useful beta figure. If the R-squared is lower, then the beta is less relevant to the fund's performance. This statistical measurement of dispersion about an average, depicts how widely a mutual fund's returns varied over a certain period of time. Investors use the standard deviation of historical performance to try to predict the range of returns that are most likely for a given fund.

### volatility - Relationship between Beta and Standard Deviation - Quantitative Finance Stack Exchange

Each risk factor has a corresponding beta indicating the responsiveness of the asset being priced to that risk factor. Multiple-factor models contradict CAPM by claiming that some other factors can influence return, therefore one may find two stocks or funds with equal beta, but one may be a better investment. Estimation[ edit ] To estimate beta, one needs a list of returns for the asset and returns for the index; these returns can be daily, weekly or any period.

Then one uses standard formulas from linear regression. The slope of the fitted line from the linear least-squares calculation is the estimated Beta. The y-intercept is the alpha. Myron Scholes and Joseph Williams provided a model for estimating betas from nonsynchronous data.

To take an extreme example, something may have a beta of zero even though it is highly volatile, provided it is uncorrelated with the market. The relative volatility ratio described above is actually known as Total Beta at least by appraisers who practice business valuation.

Total beta is equal to the identity: Total beta captures the security's risk as a stand-alone asset because the correlation coefficient, R, has been removed from betarather than part of a well-diversified portfolio.

Because appraisers frequently value closely held companies as stand-alone assets, total beta is gaining acceptance in the business valuation industry. Appraisers can now use total beta in the following equation: Some interpretations of beta are explained in the following table: Moves in the same direction as the market at large, but less susceptible to day-to-day fluctuation.

It measures the part of the asset's statistical variance that cannot be removed by the diversification provided by the portfolio of many risky assets, because of the correlation of its returns with the returns of the other assets that are in the portfolio. Beta can be estimated for individual companies using regression analysis against a stock market index. An alternative to standard beta is downside beta. Beta is always measured in respect to some benchmark. Therefore, an asset may have different betas depending on which benchmark is used. Just a number is useless if the benchmark is not known.

Extreme and interesting cases[ edit ] Beta has no upper or lower bound, and betas as large as 3 or 4 will occur with highly volatile stocks. Beta can be zero. Some zero-beta assets are risk-free, such as treasury bonds and cash. However, simply because a beta is zero does not mean that it is risk-free. A beta can be zero simply because the correlation between that item's returns and the market's returns is zero. An example would be betting on horse racing. The correlation with the market will be zero, but it is certainly not a risk-free endeavor.

On the other hand, if a stock has a moderately low but positive correlation with the market, but a high volatility, then its beta may still be high. A negative beta simply means that the stock is inversely correlated with the market.