You are considering two mutual funds for your investment. The possible returns for the funds are dependent on the state of the economy and are given in the accompanying table.

State of the Economy
Fund A Fund B
Good 20% 40%
Fair 10% 20%
Poor -10% -40%

You believe that the likelihood is 20% that the economy will be good, 50% that it will be fair, and 30% that it will be poor.

The expected return for Fund A is ; the standard deviation of Fund A return is ;

The expected return for Fund B is ; the standard deviation of Fund B return is

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To calculate the expected return and standard deviation for each mutual fund, we need to multiply the possible returns by their respective probabilities and then perform the necessary calculations.

Let's start by calculating the expected return for Fund A:

Expected Return for Fund A = (Return in Good Economy * Probability of Good Economy) + (Return in Fair Economy * Probability of Fair Economy) + (Return in Poor Economy * Probability of Poor Economy)

= (20% * 0.20) + (10% * 0.50) + (-10% * 0.30)

= 4% + 5% - 3% = 6%

Therefore, the expected return for Fund A is 6%.

Next, let's calculate the expected return for Fund B:

Expected Return for Fund B = (Return in Good Economy * Probability of Good Economy) + (Return in Fair Economy * Probability of Fair Economy) + (Return in Poor Economy * Probability of Poor Economy)

= (40% * 0.20) + (20% * 0.50) + (-40% * 0.30)

= 8% + 10% - 12% = 6%

Therefore, the expected return for Fund B is 6%.

Now, let's calculate the standard deviation for Fund A:

Standard Deviation for Fund A = √[(Return in Good Economy - Expected Return for Fund A)^2 * Probability of Good Economy + (Return in Fair Economy - Expected Return for Fund A)^2 * Probability of Fair Economy + (Return in Poor Economy - Expected Return for Fund A)^2 * Probability of Poor Economy]

= √[(20% - 6%)^2 * 0.20 + (10% - 6%)^2 * 0.50 + (-10% - 6%)^2 * 0.30]

= √[(0.14)^2 * 0.20 + (0.04)^2 * 0.50 + (-0.16)^2 * 0.30]

= √[0.0196 * 0.20 + 0.0016 * 0.50 + 0.0256 * 0.30] = √[0.00392 + 0.0008 + 0.00768]

= √0.0124 = 0.11 or 11%

Therefore, the standard deviation for Fund A is 11%.

Finally, let's calculate the standard deviation for Fund B:

Standard Deviation for Fund B = √[(Return in Good Economy - Expected Return for Fund B)^2 * Probability of Good Economy + (Return in Fair Economy - Expected Return for Fund B)^2 * Probability of Fair Economy + (Return in Poor Economy - Expected Return for Fund B)^2 * Probability of Poor Economy]

= √[(40% - 6%)^2 * 0.20 + (20% - 6%)^2 * 0.50 + (-40% - 6%)^2 * 0.30]

= √[(0.34)^2 * 0.20 + (0.14)^2 * 0.50 + (-0.46)^2 * 0.30]

= √[0.1156 * 0.20 + 0.0196 * 0.50 + 0.2116 * 0.30] = √[0.02312 + 0.0098 + 0.06348]

= √0.0964 = 0.31 or 31%

Therefore, the standard deviation for Fund B is 31%.

To summarize:

Expected Return for Fund A: 6%
Standard Deviation for Fund A: 11%

Expected Return for Fund B: 6%
Standard Deviation for Fund B: 31%