Suppose you could make an investment. With Investment 1, there is a 20% chance o
ID: 2715576 • Letter: S
Question
Suppose you could make an investment. With Investment 1, there is a 20% chance of making $10, a 15% chance of making $20, a 20% chance of making $25, a 20% chance of making $30, a 20% chance of making $40, and a 5% chance of making $100. For Investment 2, there is a 25% chance of making $1,000, a 50% chance of making $2,000, and a 25% chance of making $7,500. Use the coefficient of variation to evaluate the risk involved in these two investments. How does this result differ from using the range? How does it differ from comparing the two using only the standard deviation? Why is this important?
Explanation / Answer
Investment 1
20% chance of making $10 2
15% chance of making $20 3
20% chance of making $25 5
20% chance of making $30 6
20% chance of making $40 8
5% chance of making $100 5
Expected Return = $29 | Average of all = $4.83
Investment 2
25% chance of making $1,000 $250
50% chance of making $2,000 $1000
25% chance of making $7,500 $1875
Expected Return = $3125 | Average of all = $1041.67
Calculating Standard Deviation for Investment 1
Standard Deviation= Square root of (22.84/(6-1)) = 2.14
Calculating Coefficient of Variation for Investment 1
CV= Std Dev / Expected return
CV1 = 2.14/29 = 0.074
Calculating Standard Deviation for Investment 2
Standard Deviation= Square root of (1322915/(3-1)) = 813.3
Calculating Coefficient of Variation for Investment 2
CV= Std Dev / Expected return
CV2 = 813.3/3125 = 0.26
The coefficient of variation allows you to determine how much volatility (risk) you are assuming in comparison to the amount of return you can expect from your investment.
The lower the ratio of standard deviation to mean return, the better your risk-return tradeoff.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.