Modern portfolio theory: Unleashing optimal returns and risk management

Modern Portfolio Theory (MPT) is an investment framework developed by economist Harry Markowitz in 1952.

Modern Portfolio Theory (MPT) is an investment framework developed by economist Harry Markowitz in 1952. It is a mathematical approach that aims to optimise the trade-off between risk and return in a portfolio of assets.

The core principle behind Modern Portfolio Theory is that an investor should not evaluate individual assets in isolation, but rather consider how they interact and combine within a portfolio. MPT posits that investors are rational and risk-averse, striving to maximise profits while minimising risk exposure.

Key concepts of Modern Portfolio Theory include:

• Risk and Return: MPT defines risk as the volatility or variability of returns. It considers the expected return of an asset or portfolio in relation to its standard deviation as a measure of risk. The theory assumes that investors require compensation in the form of higher returns for taking on additional risk.
• Diversification: MPT emphasises the benefits of diversifying a portfolio across multiple assets with different risk-return characteristics. By combining assets that do not move in perfect correlation with each other, the theory suggests that the overall risk of the portfolio can be reduced without sacrificing potential returns.
• Efficient Frontier: The efficient frontier is a graphical representation of all possible portfolios that provide the highest expected return for a given level of risk or the lowest risk for a given level of return. MPT seeks to find the optimal portfolio on the efficient frontier that maximizes expected returns for a given level of risk tolerance or minimizes risk for a given level of expected returns.
• Capital Asset Pricing Model (CAPM): CAPM is an extension of MPT that introduces the concept of systematic risk. It states that an asset's expected return is a function of its sensitivity to systematic risk, measured by beta. The CAPM provides a framework for determining an asset's required rate of return based on its beta and the risk-free rate of return.

Applying MPT with an example

Suppose an investor has a portfolio allocation decision to make between two assets: Asset A, a technology company stock, and Asset B, a government bond. The investor's objective is to achieve a balance between risk and return.

Set Investment Objectives

The investor aims to achieve capital appreciation while considering their risk tolerance. They are willing to accept some level of risk but want to avoid excessive volatility in returns.

Gather Data

The investor collects historical data on the returns of Asset A (technology company stock) and Asset B (government bond) over the past five years. They calculate the average annual return and standard deviation for each asset based on the historical data.

Establish Correlations

The investor examines the historical relationship between Asset A and Asset B to determine their correlation coefficient. Let's assume that the correlation coefficient between the two assets is 0.2, indicating a relatively low positive correlation.

Estimate Expected Returns

Based on their analysis of the technology sector and government bond market, the investor estimates the expected returns for Asset A to be 12 per cent and Asset B to be 3 per cent over the next year.

Assess Risk Measures

The investor calculates the risk measures for each asset. They find that the standard deviation of Asset A is 18 per cent and Asset B is 6 per cent.

Optimise the Portfolio

Using optimisation techniques, the investor seeks to construct an optimised portfolio that balances risk and return. They utilise software or tools that consider the expected returns, risk measures, and correlations between Asset A and Asset B. The optimization process aims to find the portfolio allocation that lies on the efficient frontier, maximizing return for a given level of risk or minimizing risk for a given level of return.

Suppose the optimization process suggests an allocation of 60 per cent to Asset A and 40 per cent to Asset B as the optimal portfolio allocation.

Consider Constraints

The investor takes into account any constraints or requirements they may have. For example, they might have a constraint of not allocating more than 70 per cent of the portfolio to a single asset or sector.

Monitor and Rebalance

The investor regularly monitors the performance of the portfolio. If the allocation deviates significantly from the target allocation due to market movements or changes in investment goals, the investor may consider rebalancing the portfolio. Rebalancing involves selling or buying assets to bring the portfolio back to its desired allocation.

It's important to note that this example is simplified and does not consider additional factors, such as transaction costs, taxes, or the impact of market events. In practice, portfolio optimization using MPT involves more detailed analysis, consideration of a broader range of assets, and potentially using advanced optimization techniques or working with financial professionals to implement and manage the portfolio effectively.