Question

5. What is the minimum variance portfolio? Derive its formula. Explain the efficient vs the non-efficient portions of the Portfolio Opportunity Set (POS).

Answer 1

MINIMUM VARIANCE PORTFOLIO:

IN SIMPLER TERMS, MINIMUM PORTFOLIO INVESTMENT MEANS HEDGING THE TOTAL PORTFOLIO RISK FOR THE LEVEL OF RISK ACCEPTED WITH RESPECT TO THE EXPECTED RATE OF PORTFOLIO RETURN. IT IS A WELL-DIVERSIFIED PORTFOLIO. IN OTHER WORDS, IT CONSIST OF RISKY INDIVIDUAL ASSETS WHICH ARE HEDGED TOGETHER TO REDUCE THE RISK INTO LOWEST POSSIBLE LEVEL AND IMPROVING THE RETURN. IT LEVERAGES THE RISK OF INDIVIDUAL ASSET. THUS MVP(MINIMUM VARIANCE PORTFOLIO)MITIGATES THE RISK PROPERLY.

THIS PORTFOLIO STRUCTURING MODEL MAXIMISES RETURNS BY MINIMIZING THE RISK. IT MINIMIZES THE PRICE VOLATILITY OF THE OVERALL PORTFOLIO.

FORMULA: EXPECTED RETURN=WA E(RA)+WB E(RB)

PORTFOLIO VARIANCE=MULTIPLY THE SQUARED WEIGHT OF EACH SECURITY BY THE CORRESPONDING VARIANCE OF THE SECURITY AND ADD TWO MULTIPLIED BY THE COVARIANCE BETWEEN THE SECURITIES.

EFFICIENT VS.NON EFFICIENT PORTION OF PORTFOLIO OPPORTUNITY SET(POS)

PORTFOLIO OPPORTUNITY SET IS THE EXPECTED RETURN OF ALL PORTFOLIO THAT CAN BE CONSTRUCTED FROM A GIVEN SET IOF ASSETS. IT HELPS THE INVESTORS TO CONSTRUCT A PORTFOLIO WITH THE ASSETS HE/SHE HAS WITH HIS/HER RISK TOLERANCE. IT IS THE COLLECTION OF ASSETS WHICH ALLOWS THE POTENTIAL INVESTORS TO CHOOSE AMONG THE PORTFOLIO THAT matches THEIR LEVEL OF RISK TOLERANCE.

EFFICIENT PORTION OF PORTFOLIO IS CALLED AS EFFICIENT FRONTIER WHICH CONSISTS OF THE SET OF ALL EFFICIENT PORTFOLIOS THAT YIELD THE HIGHEST RETURN FOR EACH LEVEL OF RISK. THE EFFICIENT FRONTIER CAN BE COMBINED WITH AN INVESTORS OPTIMAL PORTFOLIO,THE PORTFOLIO WITH THE GREATEST RETURN FOR THE RISK THAT THE INVESTOR IS WILLING TO ACCEPT.

ANINEFFICIENT PORTFOLIO IS ONE THAT DELIVERS AN EXPECTED RETURN THAT IS TOO LOW FOR THE AMOUNT OF THE RISK TAKEN ON. CONVERSELY, AN INEFFICIENT PORTFOLIO ALSO REQUIRES TOO MUCH RISK FOR A GIVEN EXPECTED RETURN. AN INEFFICIENT PORTFOLIO HAS A POOR RISK-TO-REWARD RATIO. PORTFOLIOS BELOW THE EFFICIENT FRONTIER OFFER LOWER RETURNS FOR THE SAME RISK, SO A WISE INVESTOR WOULD NOT CHOOSE SUCH PORTFOLIOS.