Portfolio Optimisation how to Maximise Returns and Minimise Risk

Portfolio Optimisation (Part 1)

A Tale of Two Stocks

The concept of portfolio optimisation becomes most accessible when approached through a straightforward example before expanding to the broader principles.

Consider two well-known Indian companies operating in entirely different sectors: a large-cap information technology firm with a predicted annual return of 22 per cent, and a prominent biotechnology company forecasting a return of 15 per cent. An investor places equal amounts of capital into both. What is the expected return of this two-stock portfolio?

With equal allocation, each stock carries a weight of 50 per cent. Applying the expected return formula introduced in earlier chapters produces the following.

50 per cent multiplied by 22 per cent, plus 50 per cent multiplied by 15 per cent = 11 per cent plus 7.5 per cent = 18.5 per cent.

The portfolio is expected to generate an annual return of 18.5 per cent under equal weighting.

How Weights Shift Returns

The equal split is just one of countless possible allocations. Consider what happens when the weights are adjusted.

If 30 per cent is allocated to the technology firm and 70 per cent to the biotechnology company, the expected return becomes 30 per cent multiplied by 22 per cent, plus 70 per cent multiplied by 15 per cent, which equals 6.6 per cent plus 10.5 per cent, totalling 17.1 per cent.

Reversing those proportions to 70 per cent in the technology firm and 30 per cent in the biotechnology company produces 70 per cent multiplied by 22 per cent, plus 30 per cent multiplied by 15 per cent, which equals 15.4 per cent plus 4.5 per cent, totalling 19.9 per cent.

The difference between a 40/60 split and a 60/40 split in favour of the higher-returning stock amounts to approximately 1.4 percentage points in expected annual return. Across a corpus of several lakhs of rupees, that difference becomes financially meaningful. The core insight is straightforward: as the weights assigned to stocks in a portfolio change, both the expected return and the associated risk change with them.

What Portfolio Optimisation Actually Means

Extending this logic from two stocks to a portfolio of ten or fifteen stocks opens up an enormous range of possible weight combinations. Each unique combination of weights produces a distinct portfolio with its own risk and return characteristics. An equal-weighted portfolio where each of ten stocks receives a 10 per cent allocation is one possibility. A concentrated portfolio where one stock receives 35 per cent and the remaining nine share the balance is another. The number of mathematically possible combinations is, for practical purposes, limitless.

Portfolio optimisation is the discipline of navigating this vast space of combinations intelligently, rather than arbitrarily, to arrive at weights that serve a specific investment objective. Two objectives are most commonly pursued.

The first is maximising returns for a given level of accepted risk. The second is minimising risk for a given level of desired return.

These two objectives are not always compatible, which is precisely what makes portfolio optimisation a substantive analytical challenge rather than a simple calculation.

Key Concepts in Portfolio Optimisation

Three concepts form the foundation of portfolio optimisation and are worth understanding clearly before the methodology is applied in practice.

The Minimum Variance Portfolio is the combination of weights that produces the lowest possible level of portfolio risk, regardless of the return it generates. For investors whose primary concern is capital preservation and risk aversion, this portfolio represents the most conservative end of the spectrum. It does not necessarily deliver the highest return, but it delivers the least volatility.

The Maximum Return Portfolio is the combination of weights that produces the highest achievable expected return from the available set of stocks. This portfolio occupies the opposite end of the spectrum. Greater return potential comes with greater risk, and the maximum return portfolio will carry higher volatility than the minimum variance portfolio built from the same stocks.

The concept of fixed variance with multiple portfolios adds an important layer of nuance. For any given level of portfolio risk, it is possible to construct more than one portfolio. Some of those portfolios will deliver higher returns than others at that same risk level. To illustrate, suppose a target portfolio risk of 16 per cent is established. One combination of weights might deliver an expected return of 32 per cent at that risk level. Another combination of weights, carrying the identical risk of 16 per cent, might deliver only 13 per cent. Both portfolios carry the same risk. Their returns differ substantially.

This observation reveals that simply controlling risk is insufficient. The goal is to identify, at each level of risk, the combination of weights that delivers the highest possible return. The set of all such optimal portfolios, plotted across the full range of possible risk levels, forms a curve known in portfolio theory as the efficient frontier.

Understanding the efficient frontier and how to construct it using the tools developed throughout this module is the subject of the chapters that follow.