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Medium · Probability & Statistics · Quant Trader interview question · probability, expected-value, mental-math, jensen's-inequality
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) $?