Quant Interview Practice Questions

A portfolio manager is evaluating the potential returns of an investment. They believe the investment's future price, denoted by $X$, can take two possible values: 50 or 150, each with equal probability. The manager uses the natural logarithm, $ln(x)$, to represent the utility of a given return. Calculate the expected utility, $Eln(X)$, and compare it to the utility of the expected return, $ln(EX)$. What is the approximate numerical difference between $ln(EX)$ and $Eln(X)$?