Application of Portfolio Theory to Dairy Sire Selection

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Abstract
Data for 285 Holstein sires from eight studs were used to determine the efficient set of portfolios or the expected income versus variance frontier, that is, the com- bination of sires that gave the smallest variance of income was found for each expected income. Expected income was measured by an index combining the sire's genetic superiority (in dollars) transmitted to his offspring and semen price. Variance of income increased with increasing expected income, and fewer bulls remained in the efficient set of port- folios as expected income and variance increased. The optimum solution was computed by an estimated utility func- tion for dairymen. Because of the small negative weight for variance of income, three top-income sires were selected; if the weight for variance of income would have been larger, more bulls would have been in the optimum solution. For practical application, the expected in- come versus variance frontier can be determined with all sires available for artificial insemination, and dairymen can make their selections according to their individual weightings of expected income and variance of income.

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