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We know the following expected returns for stocks A and B, given different states of the economy:
State (s) Probability E(rA,s) E(rB,s)
Recession 0.2 -0.03 0.04
Normal 0.5 0.12 0.07
Expansion 0.3 0.2 0.11
Note: If you can, it is much faster to solve these problems in a spreadsheet. However, the answer cannot be had simply by using the built-in AVERAGE() or STDEV() functions. If you are somewhat familiar with Excel, you might look into the SUMPRODUCT() function which is widely used to calculate weighted sums.
Problem 1: What is the expected return for stock A?
Problem 2: What is the expected return for stock B?
Problem 3: What is the standard deviation of returns for stock A?
Problem 4: What is the standard deviation of returns for stock B?
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