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8-1. Two recent graduates from business school (Mark Van and Sheila Epps) decid...
May 11, 2024
Solution by Steps
step 1
Calculate the expected rate of return by multiplying each fund return by its probability and summing the results
step 2
Expected rate of return = (0.05×1.00)+(0.30×0.35)+(0.55×0.05)+(0.10×−1.00)(0.05 \times 1.00) + (0.30 \times 0.35) + (0.55 \times 0.05) + (0.10 \times -1.00)
step 3
Simplify the calculation: Expected rate of return = (0.05)+(0.105)+(0.0275)−(0.10)(0.05) + (0.105) + (0.0275) - (0.10)
step 4
Sum the products: Expected rate of return = 0.05+0.105+0.0275−0.10=0.08250.05 + 0.105 + 0.0275 - 0.10 = 0.0825 or 8.25%8.25\%
[question 1] Answer
The expected rate of return from this investment opportunity is 8.25%8.25\%.
Key Concept
Expected Rate of Return
Explanation
The expected rate of return is calculated by summing the products of each possible return and its probability.
step 5
To calculate the standard deviation, first find the variance by computing the squared deviations of each return from the expected return, weighted by their probabilities
step 6
Variance = ∑(pi×(ri−E[r])2)\sum (p_i \times (r_i - E[r])^2) where pip_i is the probability, rir_i is the return, and E[r]E[r] is the expected return
step 7
Calculate each term: (0.05×(1.00−0.0825)2)+(0.30×(0.35−0.0825)2)+(0.55×(0.05−0.0825)2)+(0.10×(−1.00−0.0825)2)(0.05 \times (1.00 - 0.0825)^2) + (0.30 \times (0.35 - 0.0825)^2) + (0.55 \times (0.05 - 0.0825)^2) + (0.10 \times (-1.00 - 0.0825)^2)
step 8
Simplify the calculation: Variance = (0.05×0.84150625)+(0.30×0.07150625)+(0.55×0.00105625)+(0.10×1.17150625)(0.05 \times 0.84150625) + (0.30 \times 0.07150625) + (0.55 \times 0.00105625) + (0.10 \times 1.17150625)
step 9
Sum the terms: Variance = 0.0420753125+0.021451875+0.0005809375+0.117150625=0.181258750.0420753125 + 0.021451875 + 0.0005809375 + 0.117150625 = 0.18125875
step 10
The standard deviation is the square root of the variance: Standard deviation = 0.18125875\sqrt{0.18125875}
step 11
Calculate the square root: Standard deviation = 0.18125875≈0.425744\sqrt{0.18125875} \approx 0.425744 or 42.57%42.57\%
[question 2] Answer
The standard deviation in the anticipated returns is approximately 42.57%42.57\%.
Key Concept
Standard Deviation
Explanation
The standard deviation measures the dispersion of a set of values and is calculated as the square root of the variance.
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