Consider returns R on a stock XYZ in the follwoing 4 states of he economy. each with probability p Boom state: p=0.15, R=35% Normal state: p=x?, R=8% Slowdown state: p=0.1, R=1% Recession state: p=0.2, R = -33% What is the expected return for stock XYZ? Quote your answer to 1 decimal place, but do not type the "%" Do not round intermediate results.

The return on stock XYZ is 3.2

Explanation:

The expected return on a stock whose returns differ based on different scenarios can be calculated by multiplying the return in a scenario by the probability of that scenario and taking a sum of all such scenario returns after they have been multiplied by their respective probabilities.

The formula can be written as,

Return on a stock = rA * pA + rB * pB + ... + rN * pN

Where,

Probability of normal state (x) = 1 - (0.15 + 0.1 + 0.2)    =  0.55

Return on stock XYZ =  0.35 * 0.15  +  0.08 * 0.55  +  0.01 * 0.1  + (-0.33) * 0.2

Return on stock XYZ = 0.0315 or 3.15% rounded off to 3.2%

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