- 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)

- 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**

- 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**

- 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%**

- 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 = 436.00
^{0.5}=**$20.8806**

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