Consider an investment that pays off $500 or $1,200 per $1,000 invested with equ
ID: 2744557 • Letter: C
Question
Consider an investment that pays off $500 or $1,200 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 $ 850 % 350 N/A Invest $2,000 $ % Invest $3,000 $ %
Explanation / Answer
If you just invest your own %1000, the EV = 0.5(500)+0.5(1200) = $850 and the SD = 350
If you borrowed an additional $1000, the EV = 0.5(1000-1000)+0.5(2400-1000) = 700
The SD = 0.5(0-700)2+0.5(1400-700)2= 700, the Sstandard deviation is doubled
If you borrowed $2000 to invest a total of $3000, the
EV = 0.5(1500-2000)+0.5(3600-2000)=550
The SD = 0.5(-500-500)2+0.5(1600-550)2=1050, the standard deviation is tripled