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. The primary determinant of the amount of beta risk is the sample size used for the test. The larger the sample tested, the lower the beta risk becomes. Beta risk is sometimes called "beta error" and is often paired with "alpha risk," also known as a Type I error.

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. To detect differences a statistical test should be employed; beta risk is the probability that a statistical test will be unable to do so (for example if a beta risk was found to be 0.5. that would mean a 5% likelihood of inaccuracy).

Alpha risk is an error occurring when a null hypothesis is rejected when it is actually true. It is also known as "producer's 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. More information on how to calculate alpha risk and beta risk may be found here.

Beta risk is based on the characteristic 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.

An interesting application of hypothesis testing in finance can be done 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 showed a beta risk (firms predicted to go bankrupt but did not) ranging from approximately 15% to 20%, depending on the sample being tested.

Beta, in the context of investing, is a measure of the volatility, or systematic risk, of a security or a portfolio in comparison to the market as a whole. The beta of an investment indicated whether it is more less volatile compared to the market. Beta, is also known as the beta coefficient, is used in the capital asset pricing model (CAPM), which calculates the expected return of an asset based on its beta and expected market returns. As such, it is only tangentially related to beta risk in the context of decision making.