Compute the expected return given these three economic states, their likelihoods, and the potential returns: (Round your answer to 2 decimal places.) Economic State Probability Return Fast growth 0.31 32 % Slow growth 0.43 20
26 -4 %
Expected return is an important measure to determine the expected rate of return on an investment. It is calculated by weighting each potential outcome (or economic state) by its respective probability, and then summing up these weighted values. In this case, we are given three economic states (fast growth, slow growth, and recession), their likelihoods (probabilities), and the potential returns in the form of percentages. Thus, the equation for determining expected return can be written as:
Expected Return = (P1 x R1) + (P2 x R2) + … + (PN x RN)
Where Pn represents the probability of a certain economic state occurring, and RN represents its corresponding return if it occurs. In our example above this becomes:
Expected Return = (0.31 x 32%) + (0.43 x 20%) + (0.26 x (-4%)) = 11.88%
This means that given these three possible economic states with their respective probability and returns associated with them, one can expect a 11.88% annualized rate of return over time from investing in this particular asset or portfolio.
It is important to note that while expected returns provide a useful metric for calculating average future performance, they do not take into account any risks associated with such an investment nor do they guarantee any specific level of gains or losses from such investments since all outcomes are not equally likely or desirable.
Therefore when evaluating investments for long-term performance it is important to consider other factors such as volatility levels and potential downside risk before making any final decisions about which assets to invest in for optimal returns over time