The purpose of this article is to provide a brief explanation of Markowitz’s modern portfolio theory and how you can use it to more effectively allocate your investment portfolio.

Perhaps equally important to what will be covered is what is excluded: this is not a mathematical derivation of the model. For a thorough explanation of the math behind the model, see this article in Wikipedia. The objective of this article is to show how you can apply modern portfolio theory in real life to create an optimized portfolio.

Throughout chapters 1 through 4, we will refer to Excel files that will contain either the templates and the data. We will also include instructional videos that will provide guidance on using the Excel files and applying the concepts behind modern portfolio theory. In Chapter 5, we introduce R–a free open-source tool that is a more powerful and flexible alternative to Excel.

We have purposefully started this series by using Excel since most people are the most familiar with this tool. However, we hope that you’ll read our chapter on R (and associated pages, posts, and video tutorials) and find that the process of downloading return data, plotting an efficient frontier, and finding the optimal portfolio much easier and faster. In addition, R allows for flexibility that cannot be achieved in Excel. We have provided all of the code necessary to get up and running with R in a matter of minutes. We hope you find our series a compelling reason for using R as an alternative to Excel.

## Introduction

In its simplest form, portfolio theory is about finding the balance between ** maximizing your return** and

**. The objective is to select your investments in such as way as to diversify your risks while not reducing your expected return. It is actually simple to apply and effective. While it does not replace the role of an informed investor, it can provide a powerful tool to complement an actively managed portfolio.**

*minimizing your risk*Models should never be blindly applied–see any number of articles on the role of models in the collapse of LTCM or other large funds. But an understanding of how the portfolio theory works will enable you to make more informed decisions about which mutual funds to include in your 401k or which ETF’s to buy for your individual investor account.

Your portfolio (401k, IIA, etc.) probably consists of a number of stocks, bonds, ETF’s, and mutual funds. The mix of these assets constitutes your portfolio allocation. How your portfolio is allocated determines its performance. During the first quarter of every year, investors typically spend a few hours reallocating their retirement accounts. Most allocation decisions are based on past performance, gut feelings, or some arbitrary selection process. In this series, we’ll introduce you to the modern portfolio theory and demonstrate how you can use Microsoft Excel to construct an efficient and optimal portfolio.

## Definitions and Assumptions

Before we begin to explain portfolio theory and its application, let’s begin by defining a number of key terms. A common nomenclature is essential to correctly interpreting this series.

- 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.

## Organization of this Series

We’ve organized this site to be accessible to both students and professionals. For students, we’ve tailored the articles to answer common questions and provide context and real-world examples to the theory taught in the classroom. For professionals, we aimed to make this a practical, hands-on, exercise with plenty of actual case studies.

- Chapter 1 – Introduction to Portfolio Theory
- A practical explanation of the ideas behind the theory
- Definitions, assumptions, limitations, and other important points to keep in mind

- Chapter 2 – Example Portfolio Data Set
- The mix of investments we’ll use throughout the articles to illustrate how to use the theory
- Historical returns and volatility

- Chapter 3 – Covariation Analysis–or simply, how related are the movements in individual investments
- Chapter 4 – Efficient Frontier
- What is the minimum risk for an expected return
- Comparison with example portfolios

- Chapter 5 – Using R as an Alternative to Excel
- Chapter 6 – Tracking Portfolio Performance
- How does our mean variance optimized portfolio perform against traditional allocations?

## Why is this Important?

So why do you care about modern portfolio theory, a dead economist named Markowitz, or something called an efficient frontier? Simply because you can use this approach to lower your risk (portfolio variance) while maintaining (or increasing) your expected returns. Which of the following portfolios would you prefer?

- A mix of stocks and bonds that returned an average of 7% per year, but varied by as much as 10% per year (i.e., returns varied typically between -3% and +17%)
- A mix of stocks and bonds that returned an average of 7% per year, but varied by only 2% per year (i.e., returns varied typically between 5% and 9%)

Although an annual return of 17% sounds good, keep in mind that it is also as likely that you’ll lose 3%! A less volatile return of between 5% and 9% may be less exciting but will get you closer to your retirement goals faster.