# Fenner Smith is contemplating dividing his portfolio between two assets, a risky asset that has an expected

## Question:

(a) If Mr. Smith invests x percent of his wealth in the risky asset, what will be his expected return?

(b) If Mr. Smith invests x percent of his wealth in the risky asset, what will be the standard deviation of his wealth?

(c) Solve the above two equations for the expected return on Mr. Smith’s wealth as a function of the standard deviation he accepts.

(d) Plot this “budget line” on the graph below.

(e) If Mr. Smith’s utility function is u (rx, σx) = min {rx, 30 − 2σx}, then Mr. Smith’s optimal value of rx is ______, and his optimal value of σx is ______. (You will need to solve two equations in two unknowns. One of the equations is the budget constraint.)

(f) Plot Mr. Smith’s optimal choice and an indifference curve through it in the graph.

(g) What fraction of his wealth should Mr. Smith invest in the risky asset?

Expected Return

The expected return is the profit or loss an investor anticipates on an investment that has known or anticipated rates of return (RoR). It is calculated by multiplying potential outcomes by the chances of them occurring and then totaling these... Portfolio

A portfolio is a grouping of financial assets such as stocks, bonds, commodities, currencies and cash equivalents, as well as their fund counterparts, including mutual, exchange-traded and closed funds. A portfolio can also consist of non-publicly...

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