Compute The Expected Return Given These Three Economic State

Compute The Expected Return Given These Three Economic States Their L

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. % Slow growth 0. Recession 0.26 –33 Expected return %

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The task involves calculating the expected return based on different economic states, their probabilities, and the corresponding returns. The expected return is a key concept in investment analysis, offering an average anticipated return on an investment considering various possible economic scenarios and their likelihoods. To accurately compute this, it is essential to understand the formula for expected return, which involves multiplying each potential return by its associated probability and summing these products across all states.

The formula for expected return (E[R]) is as follows:

E[R] = (P1 × R1) + (P2 × R2) + (P3 × R3) + ... + (Pn × Rn)

where P represents the probability of each economic state, and R represents the return associated with that state. In this case, we are provided with three economic states: fast growth, slow growth, and recession. It is essential to identify the probabilities and returns associated with each state. The data given appears incomplete, with probabilities and returns not fully specified, which needs to be clarified or assumed for the calculations.

Suppose the probabilities are as follows: fast growth (P1), slow growth (P2), and recession (P3 = 0.26). The returns are also linked to these states, with recession providing a return of -33%. To complete the calculation, assume or identify the probabilities and returns for fast growth and slow growth states. Typical reasonable assumptions might be that the remaining probability is divided equally among the fast and slow growth states, or as specified in the provided data.

Assuming equal likelihoods for fast and slow growth states, and given the recession probability, the sum of probabilities should equal 1. If P3 = 0.26, then P1 + P2 = 0.74. Assuming equal probabilities for simplicity, P1 = P2 = 0.37. The returns for the fast and slow growth states are needed; for illustration, suppose they are 15% and 5%, respectively.

Applying the expected return formula:

E[R] = (0.37 × 15%) + (0.37 × 5%) + (0.26 × –33%)

Calculating each term:

E[R] = (0.37 × 0.15) + (0.37 × 0.05) + (0.26 × –0.33)

E[R] = 0.0555 + 0.0185 – 0.0858

E[R] = 0.088 – 0.0858 = 0.0022

Expressed as a percentage, this is approximately 0.22%. Rounded to two decimal places, the expected return is 0.22%.

This calculation illustrates how the expected return accounts for different economic states and their likelihoods, providing a weighted average return that helps investors make informed decisions under uncertainty.

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