# Relationship between beta and covariance

### How to Calculate Beta From Volatility & Correlation | Finance - Zacks

The solution provided can be derived using the CAPM. For asset A you have: R A − R f = α A + β A (R M − R f) + ϵ A. Similarly for asset B. To calculate the beta of a security, the covariance between the return of Covariance is used to measure the correlation in price moves of two. So the general definition of beta is how much your asset or portfolio returns vary (or how volatile they are) relative to the market. The actual formula, given asset A and market B, is the following: COV (A,B) / VAR (B). My second question is, why can't beta be expressed simply as.

It equates to the asset Beta for an ungeared firm, or is adjusted upwards to reflect the extra riskiness of shares in a geared firm. 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.

Simple explanation: Covariance vs Correlation?

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.

• CAPM Beta – Definition, Formula, Calculate Beta in Excel
• Beta - Covariance -Variance - Standard deviation - Correlation
• How to Calculate Beta From Volatility & Correlation

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.

## Beta (finance)

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.

### Beta - Covariance -Variance - Standard deviation - Correlation | AnalystForum

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.

Debt and Equity both. The beta that we calculated above is the Levered Beta. Unlevered Beta is the Beta after removing the effects of the capital structure. As seen above, once we remove the financial leverage effect, we will be able to find the Unlevered Beta. However, when we evaluate private companies not listedthen how should we find Beta? Higher amount of debt implies higher variablility in earnings Financial Leverage which in turn results in higher sensitivity to the stock prices.

As a first step, we find all the listed peers and identify their Betas levered Step 2 — Unlever the Betas We will use the formula discussed above to Unlever the Beta.

Please note that for each of the competitors, you will have to find the additional information like Debt to Equity and Tax Rates.

### Correlation, Covariance, Variance, and how they relate to Beta

While unlevering, we will be able to remove the effect of financial leverage. The calculation for the relevered beta is as follows: It is this relevered Beta that is used for calculating the Cost of Equity of the Private companies.

What Does a Negative Beta Mean? Though in the above cases we saw that Beta was greater than zero, however, there may be stocks that have negative betas. Theoretically, negative beta would mean that the stock moves in the opposite direction of the overall stock market. Though, these stocks are rate, but they do exist. Many companies that are into gold investing can have negative betas because gold and stock markets move in the opposite direction.