Select Page

Efficient Frontier With Borrowing

So far, portfolios have been constructed from owned funds. With o~ funds, the efficient frontier of Porfirio with one risk-free asset ends at point M. Extending FM beyond M shows further.opportunities for higher return. Are these opportunities real or hypothetical? What should an investor do to exploit these opportunities?

These are real opportunities, which the investor can avail of by borrowing funds at a risk-free rate, R, and investing the same in the risky asset, M. This is known as creating a borrowing portfolio. With borrowings, the weight of the risky asset in the exceeds one. Negative weight for risk-free asset ensures that the sum of weights equals unity. Negative weight for risk-free assets shows that the investor has created a leveraged portfolio by borrowing funds. For example, an investor has Rs 2,00,000. He borrows an additional sum of Rs 1,00,000 and invests it in the risky asset. The weight of the risky asset in the overall portfolio is 1.5 (= Rs 3,00,000/Rs 2,00,000). The weight of the risk-free asset becomes -05 (= 1.5 – 1.), which means borrowings art 50 per cent of the owned funds.

It may be noted that the steepest CAL with borrowing and lending portfolios completely dominates the efficient frontier of risky assets. Thus, CAL tangential to the efficient frontier of risky assets constitutes the new efficient frontier with one risk-free asset. A very Significant conclusion of the model is the optimal risky portfolio (M) for all irrespective of their preference. Investigator’s risk aversion simply determines the exact point along the CAL. A risk-averse Investor assigns greater weight to the risk-free asset in his portfolio than an investor with greater risk tolerance. However, both use identical sets 0; two assets–one risk-free and another risky. This result is called the separation theorem.

Efficient Frontier with One Risk-free Asset