Answer:
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.