Consider an investment that pays off $700 or $1,600 per $1,000 invested with equ

Question

Consider an investment that pays off $700 or $1,600 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 devlation 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 percentage values as percentages not decimals (i.e., 23% not O.23). Enter a negative sign (-) to indicate a negative number if necessary. Expected Value Percentage Standard Deviation Expected Return Invest $1,000 Invest $2,000 Click to select Invest $3,000 (Click to select

Explanation / Answer

Investment If you just invest your own $1000, the EV = 0.5(700)+0.5(1600)=1,150 or 15% and the SD = 450 If you borrow an additional $1000, the EV = 0.5(1400-1000) +0.5(3200-1000) = 1,300 or 30%. You have doubled the expected return. The SD = (.5(400-1300)^2 +.5(2200-1300) ^2)^1/2 = 900 The standard deviation has also doubled. If you borrowed $2000 to invest a total of $3000, the EV = 0.5(2100-2000) +0.5(4800- 2000) = 1,450 or 45%. You have tripled the expected return versus the un-leveraged investment. The SD = (.5(100-1450)^2 +.5(2800-1450) ^2)^1/2 = 1350 The standard deviation has tripled versus the un-leveraged investment

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