## Solutions to More Risk and Return Practice Problems

1. Consider the following investments. Which investment would a risk averse investor prefer?:
• Investment A: Expected return = 11%, Standard deviation = 12%
• Investment B: Expected return = 10%, Standard deviation = 10%
• Investment C: Expected return = 11%, Standard deviation = 10%
• Investment D: Expected return = 11%, Standard deviation = 11%

• Investment C since it provides the greater return for the lowest risk (in comparison with the other three investments)

2. Joe Investor has invested in three securities: A, B, and C. What is the beta of his portfolio, considering the amount invested in each security and the individual security betas?
• Security A: Invested \$30,000, beta of 1.50
• Security B: Invested \$20,000, beta of 2.00
• Security C: Invested \$20,000, beta of 0.50

• Total investment in the portfolio is \$70,000.
• Proportion invested in Security A = \$30,000/\$70,000 = 0.4286
• Portfolio beta = (0.4286)(1.5) + (0.2857)(2.0) + (0.2857)(0.5)
• Portfolio beta = 0.6429 + 0.5714 + 0.1429
• Portfolio beta = 1.3572

3. Consider Joe Investor once again (the previous problem). If he had invested \$100,000 in Security C (instead of \$20,000), with all other investments the same, what is Joe's portfolio beta?
• Total investment in the portfolio = \$150,000
• Proportion invested in Security A = \$30,000/\$150,000 = 0.2000
• Portfolio beta = 0.8997

4. An analyst has provided information on possible returns (and their likelihood of occurring) for the Icahn Trust Corporation stock. What is the standard deviation of the expected returns for this stock, given the following distribution?
• Scenario 1: probability = 20%, return = -40%
• Scenario 2: probability = 50%, return = 0%
• Scenario 3: probability = 30%, return = 30%

Calculations:
 p x return p x (return - Expected return)2 -0.08 0.03360 0.00 0.00005 0.09 0.02520 0.01 0.0589

• Expected return = .01 or 1%
• Standard deviation = square root (0.0589) = 0.2426 or 24.26%

5. Calculate the expected dollar return and the standard deviation of these possible returns for the Pizza Palace, given the following possible returns:
 Scenario Probability Possible dollar return Success 20% +\$50 Normal 50% +\$10 Bomb 30% -\$10

• Expected dollar return = (0.2)(\$50) + (0.5)(\$10) + (0.3)(-\$10) = \$12

• Variance = 288.80 + 2.00 + 145.20 = 436.00
• Standard deviation = 436.000.5 = \$20.8806