An investor is considering two investment, an office building and bonds. He can only invest on of them. The possible return from each investment and their probability are as follows: Office Building Return Probability $50000 0.3 60000 0.2 80000 0.1 10000 0.3 0 0.1 Bonds Return Probability $30000 0.6 40000 0.4 1) Calculate the expected return and variance of investing in office building. 2) Calculate the expected return and variance of investing in bonds. 3) If you were the investor, which one you will choose base on the expected return? Briefly

1) Calculate the expected return and variance of investing in office building.

expected return:

$50,000 x 0.3 = $15,000

$60,000 x 0.2 = $12,000

$80,000 x 0.1 = $8,000

$10,000 x 0.3 = $3,000

$0 x 0.1 = $0                      

expected return = $38,000

$50,000 - $38,000 = -$12,000² = $144,000,000

$60,000 - $38,000 = -$22,000² = $484,000,000

$80,000 - $38,000 = -$42,000² = $1,764,000,000

$10,000 - $38,000 = -$28,000² = $784,000,000

$0 - $38,000 = -$38,000² = $1,444,000,000        

expected variance: (0.3 x $144,000,000) + (0.2 x $484,000,000) + (0.1 x $1,764,000,000) + (0.3 x $784,000,000) + (0.1 x $1,444,000,000) = $43,200,000 + $96,200,000 + $176,400,000 + $235,200,000 + $144,400,000 = $695,400,000

standard deviation = √$895,800,000 = $26,370

2) Calculate the expected return and variance of investing in bonds.

expected return:

$30,000 x 0.4 = $12,000

$40,000 x 0.6 = $24,000  

expected return = $36,000

$30,000 - $36,000 = -$6,000² = $36,000,000

$40,000 - $36,000 = $4,000² = $16,000,000

expected variance: (0.4 x $36,000,000) + (0.6 x $16,000,000) = $14,400,000 + $9,600,000 = $24,000,000

standard deviation = √$24,000,000 = $4,899

3) Based on the expected return we should choose investing in a building, but if we consider the variance and the standard deviation of the investments, I would choose investing in bonds. The difference in expected returns is not that large (only $2,000) but the variance and standard deviations of investing in the office buildings is quite large, meaning that the risk is very high.

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