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# Beta Risk

## What Is Beta Risk?

Beta risk is the probability that a false null hypothesis will be accepted by a statistical test. This is also known as a Type II error or consumer risk. In this context, the term "risk" refers to the chance or likelihood of making an incorrect decision. The primary determinant of the amount of beta risk is the sample size used for the test. Specifically, the larger the sample tested, the lower the beta risk becomes.

### Key Takeaways

• Beta risk represents the probability that a false hypothesis in a statistical test is accepted as true.
• Beta risk contrasts with alpha risk, which measures the probability that a null hypothesis is rejected when it is actually true.
• Increasing the sample size used in a statistical test can reduce beta risk.
• An acceptable level of beta risk is 10%; beyond that, the sample size should be increased.
• Beta, which is part of the capital asset pricing model and measures the relative volatility of a security, is only remotely related to beta risk in decision-making.

## Understanding Beta Risk

Beta risk may be defined as the risk found in incorrectly accepting the null hypothesis when an alternative hypothesis is true. Put simply, it is taking the position that there is no difference when, in fact, there is one. A statistical test should be employed to detect differences and the beta risk is the probability that a statistical test will be unable to do so. For example, if beta risk is 0.05, there is a 5% likelihood of inaccuracy.

Beta risk is sometimes called "beta error" and is often paired with "alpha risk," also known as a Type I error. Alpha risk is an error occurring when a null hypothesis is rejected when it is actually true. It is also known as "producer risk." The best way to decrease alpha risk is to increase the size of the sample being tested with the hope that the larger sample will be more representative of the population.

Beta risk is based on the characteristics and nature of a decision that is being taken and may be determined by a company or individual. It depends on the magnitude of the variance between sample means. The way to manage beta risk is by boosting the test sample size. An acceptable level of beta risk in decision-making is about 10%. Any number higher should trigger increasing the sample size.

## Examples of Beta Risk

An interesting application of hypothesis testing in finance can be made using the Altman Z-score. The Z-score is a statistical model meant to predict the future bankruptcy of firms based on certain financial indicators.

Statistical tests of the accuracy of the Z-score have indicated relatively high accuracy, predicting bankruptcy within one year. These tests show a beta risk (firms predicted to go bankrupt but did not) ranging from approximately 15% to 20%, depending on the sample being tested.

In 2007, Altman Z-score indicated that the companies' risks were increasing significantly as the credit ratings of specific asset-related securities had been rated higher than they should have been. The median Altman Z-score of companies in 2007 was 1.81, which is very close to the threshold that would indicate a high probability of becoming bankrupt; Altman's calculations led him to believe a crisis would occur.

The Z-score should be calculated and interpreted with care. For example, the Z-score is not immune to false accounting practices. Since companies in trouble may sometimes misrepresent or cover up their financials, the Z-score is only as accurate as the data that goes into it.

## Beta Risk vs. Beta

Beta, in the context of investing, is also known as beta coefficient and is a measure of the volatility, or systematic risk, of a security or a portfolio in comparison to the market as a whole. In short, the beta of an investment indicated whether it is more or less volatile compared to the market.

It is a component of the capital asset pricing model (CAPM), which calculates the expected return of an asset based on its beta and expected market returns. As such, beta is only tangentially related to beta risk in the context of decision-making.

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