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?

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

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 $9.50\mathrm{\%}$.

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.

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.