Consider an investment that pays off $300 or $1,100 per $1,000 invested with equ
ID: 2734948 • Letter: C
Question
Consider an investment that pays off $300 or $1,100 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 answers as whole numbers and enter percentages to the nearest decimal place. Enter a negative sign (-) to indicate a negative number if necessary.
Expected Value
Percentage
Standard Deviation
Expected Return
Invest $1,000
$
%
N/A
Invest $2,000
$
%
(Click to select)N/AQuadrupledDoubledRemained the same
Invest $3,000
$
%
(Click to select)N/ARemained the sameTripledDoubled
Expected Value
Percentage
Standard Deviation
Expected Return
Invest $1,000
$
%
N/A
Invest $2,000
$
%
(Click to select)N/AQuadrupledDoubledRemained the same
Invest $3,000
$
%
(Click to select)N/ARemained the sameTripledDoubled
Explanation / Answer
investment probability outcome of investment(X) outcome*probability X- expected return square of C- expected return P*(X- expected returns) 1000 0.5 300 150 -400 160000 80000 0.5 1100 550 1030 1060900 530450 expected return 700 variance 610450 percentage 70 standard deviation 781.313 standard deviation investment probability outcome of investment(X) outcome*probability X- expected return square of C- expected return P*(X- expected returns) 2000 0.5 600 300 -800 640000 320000 0.5 2200 1100 2060 4243600 2121800 expected return 1400 variance 2441800 percentage 140 standard deviation 1562.626 standard deviation investment probability outcome of investment(X) outcome*probability X- expected return square of C- expected return P*(X- expected returns) 3000 0.5 9000 4500 2850 8122500 4061250 0.5 3300 1650 2685 7209225 3604613 expected return 6150 variance 7665863 percentage 615 standard deviation 2768.729 standard deviation