Question

Sandford Brokers is trying to promote investments in the shares of two stocks, A and B.

Their quantitative analysts have uncovered the following facts:

Stock A has an average return of 7% and a risk of 4%.

Stock B has an average return of 13% and a risk of 24%

The correlation between the returns of the two assets is - 1 (minus one)

The brokerage is approached by a client who is willing to investment $ 11 million in a portfolio consisting of only these two stocks.

His only condition is that he wants a guaranteed return on his investment with no uncertainty.

As the Head Trader of Boutique Brokers your task is to:

Either give the client a watertight explanation as to why his condition cannot be satisfied

Or

Give him an investment strategy which shows how much to invest in each stock as well the guaranteed return he will get.

In either case, you will need to accompany your recommendation with all relevant deductions, calculations and graphs.

Answer 1

We have the following Figures

Stock A - Return 7% Risk 4%

Stock B - Return 13% Risk 24%

Correlation Between the Return -1

Case I :- Why condition of the Investor as to guaranteed return cannot be satisfied :-

As mentioned in the Quantitative details, the Average return of stock A is 7% with Risk (standard deviation) of 4% and Average return of stock B is 13% with Risk (standard deviation) of 24%; which implies the following:

• Stock A yields on an average 7% of return on the investment but there is risk that this return may vary by 4% either upside or downside. i.e. the average return of 7% is not the guaranteed return.
• Stock B yields on an average 13% of return on the investment but there is risk that this return may vary by 24% either upside or downside. i.e. the average return of 13% is not the guaranteed return.

Conclusion :-

Thus, Investor's condition for guaranteed return with no uncertainty cannot be satisfied.

Case II :- Suggested investment Strategies :-

The investment strategy depends on the Risk taking capacity of the investor. Amounts to be invested in each stock and the return on the portfolio are calculated as per the Minimum Risk Portfolio Formula, calculation and amounts of which are explained in the images attached.

Note - Calculations are done considering up to 4(four) Decimal points.