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 ___?

To calculate the expected return for each fund, you need to multiply the possible returns in each state of the economy by their respective probabilities and sum them up.

For Fund A:
Expected return = (20% * 0.2) + (10% * 0.5) + (-10% * 0.3)
= 4% + 5% - 3%
= 6%

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

Now, to calculate the standard deviation of Fund A return, you need to find the variance first. Variance measures the dispersion of the returns around the expected return. Once you have the variance, you can calculate the standard deviation by taking the square root of the variance.

For Fund A:
Variance = [(20% - 6%)^2 * 0.2] + [(10% - 6%)^2 * 0.5] + [(-10% - 6%)^2 * 0.3]
= 0.196 + 0.04 + 0.4224
= 0.6584

Standard deviation = √(Variance)
= √(0.6584)
≈ 0.8123 (rounded to four decimal places)

Therefore, the standard deviation of Fund A return is approximately 0.8123.

Now let's calculate the expected return and standard deviation for Fund B.

For Fund B:
Expected return = (40% * 0.2) + (20% * 0.5) + (-40% * 0.3)
= 8% + 10% - 12%
= 6%

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

For the standard deviation, we'll follow the same process as for Fund A.

Variance = [(40% - 6%)^2 * 0.2] + [(20% - 6%)^2 * 0.5] + [(-40% - 6%)^2 * 0.3]
= 1.44 + 0.196 + 1.1568
= 2.7928

Standard deviation = √(Variance)
= √(2.7928)
≈ 1.6703 (rounded to four decimal places)

Therefore, the standard deviation of Fund B return is approximately 1.6703.

To calculate 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)

Expected Return for Fund A = (20% * 20%) + (10% * 50%) + (-10% * 30%)
Expected Return for Fund A = 4% + 5% - 3%
Expected Return for Fund A = 6%

The expected return for Fund A is 6%.

To calculate the standard deviation of Fund A return, we need to use the formula:

Standard Deviation for Fund A = Square Root of [(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]

Standard Deviation for Fund A = √[(20% - 6%)^2 * 20% + (10% - 6%)^2 * 50% + (-10% - 6%)^2 * 30%]
Standard Deviation for Fund A = √[(0.14^2 * 0.2) + (0.04^2 * 0.5) + (-0.16^2 * 0.3)]
Standard Deviation for Fund A = √[(0.0196 * 0.2) + (0.0016 * 0.5) + (0.0256 * 0.3)]
Standard Deviation for Fund A = √[0.00392 + 0.0008 + 0.00768]
Standard Deviation for Fund A = √0.0124
Standard Deviation for Fund A = 0.111

The standard deviation of Fund A return is approximately 0.111.

Similarly, to 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)

Expected Return for Fund B = (40% * 20%) + (20% * 50%) + (-40% * 30%)
Expected Return for Fund B = 8% + 10% - 12%
Expected Return for Fund B = 6%

The expected return for Fund B is 6%.

To calculate the standard deviation of Fund B return, we need to use the formula:

Standard Deviation for Fund B = Square Root of [(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]

Standard Deviation for Fund B = √[(40% - 6%)^2 * 20% + (20% - 6%)^2 * 50% + (-40% - 6%)^2 * 30%]
Standard Deviation for Fund B = √[(0.34^2 * 0.2) + (0.14^2 * 0.5) + (-0.46^2 * 0.3)]
Standard Deviation for Fund B = √[(0.1156 * 0.2) + (0.0196 * 0.5) + (0.2116 * 0.3)]
Standard Deviation for Fund B = √[0.02312 + 0.0098 + 0.06348]
Standard Deviation for Fund B = √0.0964
Standard Deviation for Fund B = 0.311

The standard deviation of Fund B return is approximately 0.311.