Question

A portfolio gives at 10% return with a standard deviation of 18%. You would like the standard deviation to drop to 14%. What should you do? What should you do if you want the standard deviation to rise to 23%.

OUR NOTES give the answers, however, I don't understand how they reached the numbers.

The answer to the first part is to add more risk-free assets until they account for 4/18 of the portfolio

The answer to the second part is use debt to finance an increase in the size of this portfolio by 5/18.

I don't understand this can you please provide a step by step on how these answers were reached.

Thank you

Answer 1

A ration investor views standard deviation as a risk measurement tool for the held portfolio. It also means how much the return would deviate from the mean return of the portfolio. Capital Allocation is the apportionment of funds between risky and risk-free investments such as equity stocks and T-bills. Risk return of the portfolio depends upon proportion of risky and risk-free asset. If the proportion of the risky asset is y, then proportion of risk-free asset would be 1-y.

Portfolio Return= y*risky asset+ Risk-free asset* (1-y)

Underestimation of expected return and standard deviation will artificially decrease the return per unit of the risk.

To return to the proper risk and return relationship of the portfolio, one needs to decrease the amount of risky investments.

Expected Return= 10%, standard deviation = 18%, a standard deviation of 18% means return can vary anywhere between -8% to 28%, hence adding more risk free assets to the portfolio help in lessening of the risk.