Optimum portfolio

There is no single best portfolio. There is a best portfolio for someone.

The workbook defines an optimum portfolio as a combination of investments having desirable individual risk–return characteristics for a given set of constraints. The phrase that matters is for a given set of constraints. A pension fund that cannot hold unlisted shares, a family office that needs money back in three years, and an endowment with a forty-year horizon face different constraints, so the same investment universe gives each of them a different optimum.

The efficient frontier narrows the choice to portfolios nothing else beats. The optimum portfolio is the one point on that shortlist that fits this investor.

Section 3.8 sets out the portfolio optimisation process. Using the Modern Portfolio Theory framework, the manager must estimate:

1. the expected return of every asset class, security and investment opportunity in the universe;
2. the standard deviation of each asset's expected returns;
3. the correlation coefficients among the entire set, taken a pair at a time.

In addition, any constraints the investor has must be specified. The optimiser then produces the feasible combinations, and the one which meets the investment objectives of the investor is selected.

Two things follow:

• The optimum depends on the inputs, so it inherits estimation risk. A 50-security universe needs 1,225 correlation estimates.
• The optimum depends on the investor. In section 3.11 the workbook says the exact location an investor chooses on the efficient frontier depends on that individual's risk-return utility function.

Chapter 1 frames objectives in terms of both risk and return, and that is why a return target alone never defines an optimum.

All portfolio figures are illustrative.

A family office has Rs 2 crore to allocate. Its investment policy sets two constraints:

• portfolio standard deviation no higher than 12%, and
• no more than 20% in unlisted securities.

The optimiser returns four efficient portfolios:

P3 and P4 are efficient but not feasible for this investor. Of the feasible pair, P2 gives the highest return within the risk ceiling:

Expected gain on P2 = Rs 2 crore × 13% = Rs 26 lakh
Expected gain on P1 = Rs 2 crore × 10% = Rs 20 lakh

P2 is the optimum portfolio for this family office. P4 has a better return for the same 12% risk and would be the optimum for an investor without the unlisted constraint — which is exactly the point. Change the constraint and the optimum moves, even though nothing in the market has changed.

Chapter 3, section 3.8 (Portfolio Optimization process), defines the optimum portfolio and lists the three estimates plus constraints; Exhibit 3.3 shows the process. Section 3.9 follows with estimation risk. Expect a definitional question and one asking which inputs the manager must estimate — returns, standard deviations and pairwise correlations.

• The optimum is investor-specific. It is chosen from feasible portfolios to meet that investor's objectives and constraints; there is no universal optimum.
• An efficient portfolio is not automatically the optimum. It may break a constraint.
• The three estimates are expected return, standard deviation and correlation. Constraints are specified in addition to them.
• Do not confuse the optimum portfolio with the market portfolio. The market portfolio is the single tangency portfolio every investor holds once a risk-free asset exists; the optimum is a choice for one investor.
• A higher-return portfolio is not a better optimum if it breaches the risk limit.