Consider an investment that pays off $900 or $1,300 per $1,000 invested with equ
ID: 2815720 • Letter: C
Question
Consider an investment that pays off $900 or $1,300 per $1,000 invested with equal probability Suppose you have $1,000 but are willing to borrow to increase your expected return. What would happen to the expected value and standard deviation of the investment if you borrowed an additional $1,000 and invested a total of $2.000? What if you borrowed $2,000 to invest a total of $3,000? Instructions: Complete the table below to answer the questions above. Enter your responses as whole numbers and enter percenta values as percentages not decimals (Le.. 23% nof 023) Enter a negative sign (-) to indicate a negative number if necessary Expected Value Percentage Standard Deviation N/A Invest $1,000 Invest $2,000 Click to select) (Click to select) Invest $5,000 1 % 1 pray 6 of 8 Next >Explanation / Answer
1. Invest $1000
Expected Value = Probability * Income
Expected Value = 0.50 * $900 + 0.50 * $1300
Expected Value = $1100
Percentage = $100 / $1000 = 10%
Standard Deviation = Square Root (Probability * (Income - Expected Value)^2)
Standard Deviation = Square Root (0.50 * ($900 - $1100)^2 + 0.50 * ($1300 - $1100)^2)
Standard Deviation = Square Root (20000 + 20000)
Standard Deviation = 200
2. Invest $2000
Expected Value = Probability * (Income - Borrowed amount)
Expected Value = 0.50 * ($900 + $900 - $1000) + 0.50 * ($1300 + $1300 - $1000)
Expected Value = $1200
Percentage = $200 / $1000 = 20%
Standard Deviation = Square Root (Probability * (Income - Expected Value)^2)
Standard Deviation = Square Root (0.50 * ($1800 - $2200)^2 + 0.50 * ($2600 - $2200)^2)
Standard Deviation = Square Root (160000 + 160000)
Standard Deviation = 400
If $2000 invested Standard deviation will get doubles
Expected return has been doubled by investing $1000 from borrwoing
3. Invest $3000
Expected Value = Probability * (Income - Borrowed Amount)
Expected Value = 0.50 * ($900 + $900 + $900 - $2000) + 0.50 * ($1300 + $1300 + $1300 - $2000)
Expected Value = $1300
Percentage = $300 / $1000 = 30%
Standard Deviation = Square Root (Probability * (Income - Expected Value)^2)
Standard Deviation = Square Root (0.50 * ($2700 - $3300)^2 + 0.50 * ($3900 - $3300)^2)
Standard Deviation = Square Root (360000 + 360000)
Standard Deviation = 600
Expected return has been tripled by investing $2000 from borrwoing