# Southeaster Specialty Case Study

**Topics:**Standard deviation, Investment, Probability theory

**Pages:**6 (1578 words)

**Published:**October 11, 2014

Financial Risk (1, 2, 3, 4, & 6)

1. Is the return on the one-year T-bill risk free?

No, the return on the one-year T-bill is not risk free. Financial risk is related to the probability of earning a return less than expected and the larger the chance of earning a return far below that expected, the greater the amount of financial risk. Risk free assumes 100% probability that the investment will earn the total percent of return that is expected. 2. Calculate the expected rate of return on each of the five investment alternatives listed in Exhibit 13.1. Based solely on expected returns, which of the potential investments appear best? Based on the expected returns, the potential investment that appears the best is 15% with S & P 500 Fund. (Probability of Return 1 x Return 1) + (Probability of Return 2 x Rate 2) = Expected Rate of Return 1-Year T-Bill

(0.10 x .07) + (0.20 x .07) + (0.40 x .07) + (0.20 x .07) + (0.10 x .07) = .07 = 7% Project A

(0.10 x [-.08]) + (0.20 x .02) + (0.40 x .14) + (0.20 x .25) + (0.10 x .33) = .135 = 13.5% Project B

(0.10 x .18) + (0.20 x .23) + (0.40 x .07) + (0.20 x [-.03]) + (0.10 x .02) = .088 = 8.8% S & P 500 Fund

(0.10 x [-.15]) + (0.20 x 0) + (0.40 x .15) + (0.20 x .30) + (0.10 x .45) = .15 = 15% Equity in SSI

(0.10 x 0) + (0.20 x .05) + (0.40 x .10) + (0.20 x .15) + (0.10 x .20) = .10 = 10% 3. Now calculate the standard deviations and coefficients of variation of returns for the five alternatives. (Hint: Coefficient of variation of return is defined as the standard deviation divided by the expected rate of return. It is a standardized measure of risk that assesses risk per unit of return). 1-Year T-Bill

Variance = (0.10 x [.07-.07]2)+ (0.20 x [.07-.07]2) + (0.40 x [.07-.07]2) + (0.20 x [.07-.07]2) + (0.10 x [.07-.07]2) = 0 Standard Deviation = 0 = 0%

Coefficient of variation = 0%/7% = 0

Project A

Variance = (0.10 x [-.08-.135]2) + (0.20 x [.02-.135]2) + (0.40 x [.14-.135]2) + (0.20 x [.25-.135]2) + (0.10 x [.33-.135]2) = 137.25 Standard Deviation = 137.5 = 11.71% = 12%

Coefficient of variation = 11.71%/13.5% = 0.87

Project B

Variance = (0.10 x [.18-.088]2) + (0.20 x [.23-.088]2) + (0.40 x [.07-.088]2) + (0.20 x [-.03-.088]2) + (0.10 x [.02-.088]2) = 82.56 Standard Deviation = 82.56 = 9.09% = 9%

Coefficient of variation = 9.09/8.8% = 1.03

S & P 500 Fund

Variance = (0.10 x [-.15-.15]2) + (0.20 x [0-.15]2) + (0.40 x [.15-.15]2) + (0.20 x [.30-.15]2) + (0.10 x [.45-.15]2) = 270 Standard Deviation = 270 = 16.43% = 16%

Coefficient of variation = 16.43%/15% = 1.10

Equity in SSI

Variance = (0.10 x [0-.10]2) + (0.20 x [.05-.10]2) + (0.40 x [.10-.10]2) + (0.20 x [.15-.10]2) + (0.10 x [.20-.10]2) = 30 Standard Deviation = 30 = 5.48% = 5%

Coefficient of variation = 5.48%/10% = 0.55

4. Suppose SSI forms a two-asset portfolio by investing in both Projects A and B. a. To begin, assume that required investment is the same for both projects—say, $5 million each. 1. What will be the portfolio’s expected rate of return, standard deviation, and coefficient variation? Portfolio’s Expected ROR: Project A = E[R] = 13.5%; Project B = E[R2] = 8.8% E(Rp) = (w1 x E[R1]) + (w2 x E[R2]) +… (0.5 x 13.5%) + (0.5 x 8.8%) = 11.15% WeightedAverage SD: SDA = 11.71; SDB = 9.09

SDAB = (0.5 x 11.71) + (0.50 x 9.09) = 10.4%

Coefficient of variation for AB = σ / E(R) = 10.4% / 11.15% = 0.93 Rate of Return if State Occurs

Poor: (18-8)/2 = 5%

Below average: (23+2)/2 = 12.5%

Average: (7+14)/2 = 10.5%

Above average: (25-3)/2 =11%

Excellent: (33+2) = 35/2 = 17.5%

Expected ROR: (5+12.5+10.5+11+56.5)/5 = 11.3%

Variance = (0.10 x [5%-11.3%]2)+ (0.20 x [12.5%-11.3%]2) + (0.40 x [10.5%-11.3%]2) + (0.20 x [11%-11.3%]2) + (0.10 x [17.5%-11.3%]2) = 8.375 Standard Deviation = 8.375 = 2.89 = 2.9%

Coefficient of variation for AB = σ / E(R = 2.89% / 11.3% = 0.26 2. How do these values compare with the corresponding values for the individual projects? These values compare with...

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