Question

An investor puts $2,000 into an investment that will pay $2,500 one-fourth of the time; $2,000 one-half of the time, and $1,750 the rest of the time. What is the investor's expected return?

An investment pays $1,500 half of the time and $500 half of the time. Its expected value and variance respectively are

An investment pays $1,200 a quarter of the time; $1,000 half of the time; and $800 a quarter of the time. Its expected value and variance respectively are

Answer 1

a). Expected Value = [Wi x Vi]

= [(0.25 x $2,500) + (0.50 x $2,000) + (0.25 x $1,750)

= $625 + $1,000 + $437.50 = $2,062.50

Expected Return = [Expected Value / Initial Investment] - 1

= [$2,062.50 / $2,000] - 1 = 1.03125 - 1 = 0.03125, or 3.125%

b). Expected Value = [Wi x Vi]

= [(0.50 x $1,500) + (0.50 x $500)]

= $750 + $250 = $1,000

Variance = [Wi x (E(V) - Vi)²]

= [0.50 x ($1,000 - $1,500)²] + [0.50 x ($1,000 - $500)²]

= $125,000 + $125,000 = $250,000

c). Expected Value = [Wi x Vi]

= [(0.25 x $1,200) + (0.50 x $1,000) + (0.25 x $800)

= $300 + $500 + $200 = $1,000

Variance = [Wi x (E(V) - Vi)²]

= [0.25 x ($1,000 - $1,200)²] + [0.50 x ($1,000 - $1,000)²] + [0.25 x ($1,000 - $800)²]

= $10,000 + $0 + $10,000 = $20,000