So far, the estimation of required returns (discount rates) for non-diversified entrepreneurs has remained a mystery. Mongrut and Ramirez (2006) made a contribution to this area by deriving the required return’s lower bound for a non-diversified entrepreneur. However, they used a quadratic utility function, which is the same as the one used to derive the Capital Asset Pricing Model (CAPM) that faces several restrictions. In this research one extends the previous work by deriving equations of required returns using a Hyperbolic Absolute Risk Aversion (HARA) utility function that includes the general quadratic and the logarithmic forms as special cases. Furthermore, we focus our attention not only in the startup characteristics, but also in the characteristics of the entrepreneur. Hence, we derive our equations assuming an entrepreneur with the lowest risk-aversion coefficient that invests almost all his capital in his startup and whose level of wealth approaches to zero. After simulating our equations, we find that required returns (discount rates) ranges between 21% and 56% (with general quadratic preferences) and between 12% and 49% (with logarithmic preferences) at 90% level of confidence with median values of 38% and 22%, respectively. These magnitudes and variations are consistent with required returns declared by entrepreneurs.
FUZZY ECONOMIC REVIEW
ISSN (print) 1136-0593 · ISSN (online) 2445-4192