An individual with unit initial wealth will construct a portfolio consisting of fractions 1 − α of a risk-free asset and α of a risky asset. The risk-free asset has return rate rf , a known constant.
The risky asset has return rate r1, a random variable with expected value rbar1 and variance σ1^2 . The return rate for the portfolio is the random variable r = (1 − α)rf + αr1.
Assume utility function U(x) = x − (1/3)x^2 for the individual.

a) Find formulas for E[r] and for E[r^2] in terms of α, rf , rbar1, and σ1^2.
b) After one year the utility of the wealth is U(1 + r). Write out the formula for E[U (1 + r)] = E[ 1 + r −(1/3)(1 + r)^2] in terms of α, rf , rbar1 and σ1^2 .
c) If rf = (1/40), rbar1 = (1/20) and σ1 = (1/5), find α for the portfolio of maximum expected utility.

Gexpressions: practice question 3 of 5 jackson wants to study the popularity of his music video by tracking the number of views the video gets on his website. the expression below represents the total number of views that jackson's video receives n days after he begins tracking the nu views, where b is the rate at which the number of views changes. alb)" select the statement that would accurately describe the effect of tripling a, the initial number of views before jackson beginst the rate at which the number of views changes, b, will triple. the total number of views the video has after n days, a(b)", will not change. the total number of days since jackson begins tracking views, n, will be reduced by one-third. the total number of views the video has after n days, alb)", will triple. submit

The volume of the sun is approximately 1 × 10^18 cu km, while the volume of jupiter is approximately 1 × 10^15 cu km. which of the following is true? a. the volume of jupiter is approximately one thousand times the volume of the sun. b. the volume of jupiter is approximately one hundred times the volume of the sun. c. the volume of the sun is approximately one thousand times the volume of jupiter. d. the volume of the sun is approximately one hundred times the volume of jupiter.

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