Modern Portfolio Theory (MPT)

Introduction

The foundation of modern portfolio theory (MPT) was introduced by Harry Markowitz in 1952. Thirty-eight years later, Harry Markowitz, Merton Miller and William Sharpe were awarded Nobel Prize for what has become a broad theory for portfolio selection. Modern portfolio theory (commonly referred as mean variance analysis) established a whole new terminology which became a norm among investment managers. (Gupta, Francis Markowitz, Fabozzi, Frank. 2002) It has wide application in different areas of financial management such as: asset allocation through mean variance optimization, bond portfolio immunization, optimal investment trust or manager selection, international asset allocation decisions, portfolio risk management and hedging strategies.

The core concept of the Portfolio Theory is based on asset diversification and directly relies on the conventional wisdom which advice to avoid putting all eggs in one basket (Papers4you.com, 2006). In its simplest form MPT provides a framework to construct efficient portfolios by selection of the investment assets, considering risk appetite of the investor. MPT employs statistical measures such as correlation and co variation to quantify the effect of the diversification on the performance of portfolio. In it is essence MPT attempts to analyze how different investments are interrelated to each other. What happens if one investment goes broke? Does it mean that all other investments will go broke as well? How to minimize the negative effect of the downfall in one particular investment asset?

According to Markowitz (1952) investors should focus on selecting portfolios based on their overall risk-reward characteristics instead of merely compiling portfolios from securities that each individually has attractive risk-reward characteristics. In a nutshell, inventors should select portfolios not individual securities. (Risk glossary) While the theory behind MPT is quite straightforward, the implementation of efficient asset allocation can become quite complicated. The model employs a wide range of different factors such as security returns, volatilities and correlation between asset classes for constructing efficient mean variance frontier. The frontier is considered to be efficient because every point on this frontier is a portfolio that gives the greatest possible return for certain risk level. (Gupta, et al, 2002) Since asset allocation decisions are so important, majority of the financial advisors determine optimal portfolios for their clients, both institutional and private.

While the implementation of the mean variance analysis requires specific skill and knowledge, the main concepts are relatively easy and can be easily presented to the wide audience (Papers4you.com, 2006). Surprisingly, MPT has wide implications in everyday life as well, since all of us are somehow involved into investment decisions. Everyone has to think about securing funds for the future education or pension, investing into property or buying a new car, and allocating some money for the coming vocation. How to justify these decisions, what would be the optimal solution? Familiarity with portfolio theory allows bringing up the ideas employed by professional investors into everyday life.

AssumptionThere are two assumption of Modern Portfolio Theory:

Return: For many assets, this may include both capital appreciation (the price of the stock rises) and dividends. For debt instruments, the return may include price appreciation (for example, when interest rates fall), the periodic interest payments, or the payment of the principal. Expected returns may be based on historical performance; however, it is important to think critically about whether past performance is likely to continue in the future. (For example, do you really expect to see a 50% rise in technology stocks year-over-year for the next 10 years?)

Risk: This is perhaps the most contentious definition. In the context of this series, risk is the measure of variability in the expected return. We will use simple statistical tools to quantify risk. Risk is typically based on past volatility; however, as with returns, investors should think critically about the assumptions underlying the estimates of risk. If anything, the recent credit crisis has shown that two assets that appeared to be unrelated (uncorrelated, which we’ll cover later) may actually move together quite quickly under certain economic conditions.

Application

While some investors may consider MPT an intuitive method for constructing portfolios, the actual applications of MPT generally differ from that of the theory along several notable dimensions.

1. While MPT is designed to utilize expected return and volatility assumptions, historical data is most often utilized in practice due to the potential difficulty of making precise, forward looking return and standard deviation estimates.

2. The number of asset classes included in portfolio construction may have meaningful effects on the composition of the optimal portfolio.

3. Because optimal portfolios based on MPT, at times, can be relatively undiversified (i.e., concentrated in certain asset classes), portfolios are constructed with asset class constraints (e.g., no more than 20% in small cap stocks).

In general, both the use of historical data and asset class constraints are understandable from a practical standpoint. However, their widespread use when constructing MPT based portfolios may lead to actual portfolio returns and volatility over a given time period that differ meaningfully from those expected for optimal portfolios. Additionally, these optimal portfolios may adjust their asset class exposure somewhat slowly over time even as market conditions change meaningfully. Likewise, the specific asset classes included in the optimization process are likely to have a significant impact on the final composition of the optimal portfolio.

Criticism/ Limitations

The MPT is based on some Selection Model in a realistic and practical case; we have to point to some critical issues that can threaten the applicability and validity of MPT. We analyzed the fit of the assumptions of MPT to the decision problem of global sourcing decision making. A number of design choices were made resulting in limitations that have to be discussed to understand their implications to management and research.

1. Parameterization Risk: Some errors will occur regardless of the accuracy in the estimation procedure. Practitioners should use a sensitivity analysis to identify parameters that are critical for the portfolio allocation.

2. Model Risk: Choosing MPT and a specific preference function as the basis for our model implies some model risks

3. Capacity constraints: In practice, the capacity of sites will typically be limited due to already running projects and limited space, funds and human resources.

4. Income Uncertainty: By just focusing on costs and risks and assuming that the income of each project is contractually fixed, the decision problem becomes manageable.

Conclusion

Having discussed important limitations of our model, we want to conclude the discussion with a more general perspective on the generalizability and the breadth of the application, while Modern Portfolio Theory enjoys widespread use in the investment industry; investors should keep in mind several potential issues that may arise with the theory’s actual application. First, the use of historical data to generate inputs implies that future asset class returns and volatility will

reflect those of the past when, in fact, return and volatility statistics within a given asset class can vary greatly even over longer-term time periods. Second, the asset classes utilized in the optimization process can have a meaningful impact on the composition of the optimal portfolio. As such, it is important to understand why certain asset classes are included or excluded in the modeling process. Lastly, imposing asset class constraints could result in portfolios which may not truly be optimal as defined by MPT and potentially lead to muted portfolio adjustments in response to changing market conditions. Ultimately, the successful application of MPT will depend on an investor’s ability to accurately forecast future returns and volatility statistics, utilize the “correct” mix of asset classes, and effectively impose constraints without resulting in portfolios considered “sub-optimal.”

Reference

1. Markowitz, Harry M. (1952). Portfolio selection, Journal of Finance, 7 (1), 77-91.2. Gupta, Francis Markowitz, Harry M.Fabozzi, Frank J. (2002) The Legacy of Modern

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