*The Business Professor*, updated September 5, 2019, last accessed August 11, 2020, https://thebusinessprofessor.com/lesson/alpha-risk-definition/.

### Alpha Risk Definition

Alpha Risk refers to the risk that a null hypothesis (one which states that there is no difference between two variables) will be discarded even when it is absolutely correct. Usually known as the Type I error, the null hypothesis, in this case, states that there is no difference in two variables that are being tested, like zero or 1. For a null hypothesis to be discarded, there must be someone who feels that there is a difference between both variables when no there actually is none. To reduce the possibility of alpha risks, one must be willing to increase the size of the test or sampling to the point that it matches the population.

### A Little More on What is an Alpha Risk

In finance, one can incur an alpha risk in analysing returns of an equity. Let us assume that an investor is looking for good investments, but he or she wants something other than 10% annual returns on equities. In the process, he or she tests samples of returns as well as analyse historical data to check if returns are higher or lower than 10%. After testing, this investor comes up with a result that is higher than 10%, thus rejecting the null hypothesis, which states that there is no significant difference between the two variables. In a case where the original return was actually 8% annually, the investor will be said to have committed a Type I error. Alpha risk can lead to unprofitable investments, as participants might feel that the return is higher than what is actually specified, whereas, it is lower than that.

### Reference for “Alpha risk”

https://www.isixsigma.com/dictionary/alpha-risk/

https://www.investopedia.com › Investing › Financial Analysis

https://www.whatissixsigma.net/alpha-beta-risk/

https://en.wikipedia.org/wiki/Alpha_(finance)

### Academics research on “Alpha risk”

The impact of services versus goods on consumers’ assessment of perceived risk and variability, Murray, K. B., & Schlacter, J. L. (1990). The impact of services versus goods on consumers’ assessment of perceived risk and variability. *Journal of the Academy of Marketing science*, *18*(1), 51-65. With the development of service marketing concepts comes the need to test theory against consumer behavior. This study examines differences in perceived risk and variability between services and goods. In a controlled experiment whereby product stimuli were objectively placed along a goods-services continuum, data from consumers was collected focusing on six types of perceived risk and product variability. The findings of the study provide evidence that services evoke heightened risk and product variability perceptions.

Risk propensity differences between entrepreneurs and managers: A meta-analytic review., Stewart Jr, W. H., & Roth, P. L. (2001). Risk propensity differences between entrepreneurs and managers: A meta-analytic review. *Journal of applied psychology*, *86*(1), 145. Research examining the relative risk-taking propensities of entrepreneurs and managers has produced conflicting findings and no consensus, posing an impediment to theory development. To overcome the limitations of narrative reviews, the authors used psychometric meta-analysis to mathematically cumulate the literature concerning risk propensity differences between entrepreneurs and managers. Results indicate that the risk propensity of entrepreneurs is greater than that of managers. Moreover, there are larger differences between entrepreneurs whose primary goal is venture growth versus those whose focus is on producing family income. Results also underscore the importance of precise construct definitions and rigorous measurement. (PsycINFO Database Record (c) 2016 APA, all rights reserved)

Optimal morphological restoration: The morphological filter mean-absolute-error theorem, Loge, R. P., & Dougherty, E. R. (1992). Optimal morphological restoration: The morphological filter mean-absolute-error theorem. *Journal of Visual Communication and Image Representation*, *3*(4), 412-432. Morphological restoration is grounded on the Matheron representation for morphological filters, in the present context these being monotonically increasing, translation-invariant image-to-image operators. As conceived in its most general form, optimal-morphological-filter design involves a search over potential bases of structuring elements that can be used to form the Matheron erosion expansion. The present paper provides expressions for the mean-absolute restoration error of general morphological filters formed from erosion bases in terms of mean-absolute errors of single-erosion filters. It does so in both the binary setting, where the expansion is a union of erosions, and in the gray-scale setting, where the expansion is a maxima of erosions. Expressing the mean-absolute-error theorem in a recursive form leads to a unified methodology for the design of optimal (suboptimal) morphological restoration filters. Applications to binary-image, gray-scale signal, and order-statistic restoration on images are provided.

Mean-absolute-error representation and optimization of computational-morphological filters, Loce, R. P., & Dougherty, E. R. (1995). Mean-absolute-error representation and optimization of computational-morphological filters. *Graphical Models and Image Processing*, *57*(1), 27-37. Computational mathematical morphology provides a framework for analysis and representation of range-preserving, finite-range operators in the context of mathematical morphology. As such, it provides a framework for statistically optimal design in the framework of a Matheron-type representation; that is, each increasing, translation-invariant filter can be expressed via the erosions generated by structuring elements in a basis. The present paper develops the corresponding mean-absolute-error representation, This representation expresses the error of estimation of a filter composed of some number of erosions in terms of single-erosion filter errors. There is a recursive form of the representation that permits calculation of filter errors from errors for filters composed of fewer structuring elements, Finally, the error representation is employed in designing an optimal filter to solve an image enhancement problem in electronic printing, the transformation of a 1-bit per pixel image into a 2-bit per pixel image.

Effects of cow families on type traits in dairy cattle, Roughsedge, T., Brotherstone, S., & Visscher, P. M. (2000). Effects of cow families on type traits in dairy cattle. *Animal Science*, *70*(3), 391-398. The component of variance attributable to maternal lineage for type traits in the UK Holstein Friesian dairy population was estimated. First lactation type classification records of 33 325 contemporary cows, classified between 1996 and 1998 were used in the analysis. Maternal pedigree records were traced back to 1960 to establish maternal lineages. The tracing resulted in cows being assigned to 10 332 cow families with more than one cow per family. Sixty-six percent of the cows were in families of less than five. The traits comprised 16 linear type traits, a total score trait, four composite scores and measures of temperament and ease of milking. Univariate analysis of each trait was performed using residual maximum likelihood, with and without a maternal lineage component. A principal component analysis used a scree test to determine the number of independent traits being considered in-order to establish a level of significance for the test statistic. It was found that eight principal components were responsible for the variation in type. The composite body score trait was found to have a 1·5% component of maternal lineage variance, significant at the 5% level. No other traits showed a significant maternal lineage variance component.