Topic $7$ Portfolio Management

Exercise $1$: Expected Return of an individual investment

Let us take an investment A$,$ which has a $20\%$ probability of giving a $15\%$ return on

investment, a $50\%$ probability of generating a $10\%$ return, and a $30\%$ probability of

resulting in a $5\%$ loss.

The probabilities of each potential return outcome are derived from studying

historical data on previous returns of the investment asset being evaluated.

Exercise $2$: Expected Return of an individual investment

Suppose that an investor is considering whether to purchase:

$$ Shares of company ABC or

$$ Shares of company LMN or

$$ Shares of company XYZ$.$

Following months of analysis and research, the investor found out that the expected

returns of the three stocks are as follows:

Probability of

event

Return

Company ABC

Return

Company LMN

Return

Company XYZ

$2/1010\%15\%20\%$

$3/1030\%30\%3\%$

$5/103\%-20\%0\%$

In which company should the investor put his$/$her capital in order to maximise

his$/$her expected return.

Topic $7$ Portfolio Management

Exercise $3$: Expected Return of a portfolio

Let$$s assume the portfolio is comprised of investments in three assets $$ X$,$ Y$,$ and Z$.$

$$2,000$ is invested in X$,$ $$5,000$ invested in Y$,$ and $$3,000$ is invested in Z$.$ Assume

that the expected returns for X$,$ Y$,$ and Z have been calculated and found to be $15\%,$

$10\%,$ and $20\%,$ respectively.

Investment Amount invested Expected Return

X $$2,00015\%$

Y $$5,00010\%$

Z $$3,00020\%$

Total $$10,000$

Exercise $4$: Expected Return of a portfolio

Assume that an investor is considering between the following two portfolio

investments.

Weight Portfolio A Portfolio B

Asset $1$ E$($R$)20\%12\%7\%$

Asset $2$ E$($R$)20\%2\%6\%$

Asset $3$ E$($R$)20\%25\%9\%$

Asset $4$ E$($R$)20\%-9\%12\%$

Asset $5$ E$($R$)20\%10\%6\%$