Question

Suppose you visit with a financial adviser, and you are considering investing some of your wealth in one of three investment portfolios: stocks, bonds, or commodities. Your financial adviser provides you with the following table, which gives the probabilities of possible returns from each investment.

a. Which investment should you choose to maximize your expected return: stocks, bonds, or commodities?

b. If you are risk-averse and had to choose between the stock and the bond investments, which would you choose? Why?

Short answer

Part (a) The commodities portfolio should be chosen because it has the highest return of$9.50\%$

Part (b) A risk-averse investor should go for a bond.

Step-by-step solution

Given to part (a)

Stock holdings:

$0.25$is Probability.

$12\%$= Return one

$10\%$= Return two

$8\%$= Return three

$6\%$= Return four

Bond holdings:

$0.6$is probability one

$0.4$is Probability two

$10\%$= Return one

$7.50\%$= Return two

Portfolio of commodities:

$0.2$is Probability one

$0.25$is Probability two

$20\%$= Return one

$12\%$= Return two

$6\%$= Return three

$4\%$= Return four

Explanation to part (a)

Stock portfolio:

The expected return is calculated using the formula:

$Expectedreturn=\left(\begin{array}{l}(\text{Probability}\times \text{Return}1)+(\text{Probability}\times \text{Return 2})\\ +(\text{Probability}\times \text{Return}3)+(\text{Probability}\times \text{Return 4)}\end{array}\right)$

In the given equation, substitute $0.25$for probability, $12$percent for return $1,10$percent for return $2,8$percent for return $3$, and $6$percent for return $4$.

role="math" localid="1647015548316" $Expectedreturn=\left(\right(0.25\times 12\mathrm{\%})+(0.25\times 10\mathrm{\%})+(0.25\times 8\mathrm{\%})+(0.25\times 6\mathrm{\%}\left)\right)$

$=9\mathrm{\%}$

The stock's expected return is $9\%$.

Bond holdings:

The formula for calculating expected return is as follows:

$Expectedreturn=(\mathrm{Probability}1\times \mathrm{Return}1)+(\mathrm{Probability}2\times \mathrm{Return}2)$

In the preceding equation, substitute $0.6$for probability $1,0.4$for probability $2,10$percent for return $1$and $7.50$percent for return $2$.

$Expectedreturn=(0.6\times 10\mathrm{\%})+(0.4\times 7.50\mathrm{\%})$

$=8.8\mathrm{\%}$

Bonds are expected to return $8.8\mathrm{\%}.$

Portfolio of commodities:

$Expectedreturn=\left(\begin{array}{l}(\text{Probability}1\times \text{Return 1)}+(\text{Probability}2\times \text{Return 2)}\\ +(\text{Probability}2\times \text{Return}3)+(\text{Probability}2\times \text{Return 4)}\end{array}\right)$

In the preceding equation, substitute data-custom-editor="chemistry" $0.2$for probability $1,0.25$for probability $2,20$percent for return $1,12$percent for return $2,6\%$for return $3$and $4\%$for return $4$.

role="math" localid="1647017464836" $\begin{array}{r}Expectedreturn=\left(\right(0.2\times 20\mathrm{\%})+(0.25\times 12\mathrm{\%})+(0.25\times 6\mathrm{\%})+(0.25\times 4\mathrm{\%}))\\ \end{array}$

$=9.50\mathrm{\%}$

Commodity returns are expected to be $9.50\mathrm{\%}$.

As a result, the commodities portfolio should be chosen because it has the highest return of $9.50\mathrm{\%}$.

Introduction to part (b)

A bond is a fixed-income investment in which an investor lends money to a company or government that borrows money for a set period of time and pays a preset interest rate.

Explanation to part (b)

Risk-averse refers to someone who avoids high-risk investment situations. If a person is afraid of taking risks, he should invest in bonds rather than stocks because the risk in bonds is lower.

As a result, a risk-averse investor should go for a bond.