Based on an investor's attitude to risk, we can distinguish among 3 types of investors.
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Let's try and determine the utility of an investment with the same expected return of 20% and the same standard deviation of 30%. This time, however, we assume that the investor's risk aversion is 2.
Note: When an investor is characterized by lower risk aversion, he achieves greater utility for a given expected return and standard deviation. Also, what follows from the utility function is that all else equal the higher the expected return, the higher the utility for all 3 types of investors.
A risk-neutral investor is not sensitive to risk. The higher the risk, the higher the utility of risk-seeking investor, and the lower the utility of risk-averse investor.
Utility alone does not tell us much. What can we tell about an investor if we know that his utility of investment is 0.02 or 0.11? The number alone does not tell us much, but utility allows us to rank investments from the most to the least beneficial for the investor.
Note: The lower the risk aversion, the higher the risk tolerance. And conversely, the higher the risk aversion, the lower the risk tolerance.
