01@Modern Portfolio Theory and Investment Analysis Hongfei Yan Feb. 21, 2017

Contents @ Modern Portfolio Theory and Investment Analysis, 9th Edition Part 1: Introduction (P1-14) Chapter 1: Introduction Chapter 2: Financial Securities Chapter 3: Financial Markets Part 2: Portfolio Analysis Part 3: Models of Equilibrium in the Capital Markets Part 4: Security Analysis and Portfolio Theory Part 5: Evaluating The Investment Process ISLR_Print6

01 Introduction 1.1 Outline of the Book 1.2 The Economic Theory of Choice: An Illustration under Certainty 1.3 Conclusion 1.4 Multiple Assets and Risk

Everyone owns a portfolio (group) of assets This portfolio is likely to contain real assets, such as a car, a house, or a refrigerator, as well as financial assets, such as stocks and bonds. The composition of the portfolio may be the result of a series of haphazard and unrelated decisions, or it may be the result of deliberate planning. we discuss the basic principles underlying rational portfolio choice and what this means for prices determined in the marketplace. We confine our attention to financial assets, although much of the analysis we develop is equally applicable to real assets.

A choice from among an enormous number of assets. Considers the number of possible assets and the various possible proportions in which each can be held, the decision process seems overwhelming. Analyze how decision makers can structure their problems so that they are left with a manageable number of alternatives. Later sections of the book deal with rational choice among these alternatives, methods for implementing and controlling the decision process, and equilibrium conditions in the capital markets to which the previous analysis leads.

1.1 Outline of the Book Part 1 provides background material on securities and financial markets. Part 2 deals with the subject of portfolio analysis. Part 3 deals with models of equilibrium prices and returns in the capital markets. Part 4 deals with some issues in investment analysis. Part 5 is concerned with evaluating the investment process.

Part 2 includes four sections Portfolio analysis is concerned with finding the most desirable group of securities to hold, given the properties of each of the securities. Section 1 Mean Variance Portfolio Theory Section 2 implementation and simplification of portfolio theory Section 3 the selection of that one portfolio Section 4 impact of the opportunity to diversify a stock portfolio across international boundaries.

Section 1 of Part 2 Titled “Mean Variance Portfolio Theory” deals with Determining the properties of combinations (portfolios) of risky assets given the properties of the individual assets, delineating the characteristics of portfolios that make them preferable to others, and, finally, showing how the composition of the preferred portfolios can be determined.

Section 2 of Part 2 concerned with the implementation and simplification of portfolio theory. The topics covered include simplifying the quantity and type of input needed to do portfolio analysis and simplifying the computational procedure used to find the composition of the efficient portfolios.

Section 3 of Part 2 deals with the selection of that one portfolio that best meets the needs of an investor. We discuss not only techniques that rely on utility maximization but also other techniques suggested in the literature.

Section 4 of Part 2 deals with the impact of the opportunity to diversify a stock portfolio across international boundaries. As the reader might suspect, any increase in the set of possible investment opportunities should increase portfolio performance.

Part 3 Models of Equilibrium in the Capital Markets The first two chapters of Part 3 deal with some alternative forms of equilibrium relationships. Different assumptions about the characteristics of capital markets and the way investors behave lead to different models of equilibrium. The third chapter in this part of the book deals with empirical tests of how well these theoretical models describe reality. The final chapter in Part 3 presents both the theoretical basis of and empirical evidence on the newest theory of relative prices: the Arbitrage Pricing Theory.

Part 5 Evaluating the Investment Process The first chapter in this section contains a description of the principal types of mutual funds and reviews two specific types, closed-end funds and exchange- traded funds, in some detail. The second chapter deals with the evaluation of portfolio performance with an emphasis on open-end mutual funds. In this chapter we discuss the best methods of evaluating portfolio performance and how well-managed portfolios have performed. In contrast to the voluminous literature on portfolio performance, almost nothing has been written about how to evaluate the other steps in the investment process. For example, very little has been written about how to evaluate forecasts of security analysts or how to evaluate the valuation process. The third chapter in this part of the book deals with these problems. The final chapter of the book integrates the material contained in the earlier parts. http://wiki.mbalib.com/wiki/Mutual_funds

1.2 The Economic Theory of Choice: An Illustration under Certainty All decision problems have certain elements in common. Any problem involves the delineation of alternatives, the selection of criteria for choosing among those alternatives, and, finally, the solution of the problem. Furthermore, individual solutions can often be aggregated to describe equilibrium conditions that prevail in the marketplace. A large part of this book will be concerned with following these steps for the selection of risky assets. But before we start this problem, let us examine a simpler one, under certainty, to illustrate the elements of the solution to any economic problem.

This framework for analysis carries over to more complex problems. Consider an investor who will receive with certainty an income of $10,000 in each of two years. Assume that the only investment available is a savings account yielding 5% per year. In addition, the investor can borrow money at a 5% rate. How much should the investor save and how much should he or she consume each year? The economic theory of choice proposes to solve this problem by splitting the analysis into two parts: first, specify those options that are available to the investor; second, specify how to choose among these options. This framework for analysis carries over to more complex problems.

1.2 The Economic Theory of Choice: An Illustration under Certainty 1.2.1 The Opportunity Set 1.2.2 The Indifference Curves 1.2.3 The Solution 1.2.4 An Example: Determining Equilibrium Interest Rate

1.2.1 The Opportunity Set One option available is to save nothing and consume $10,000 in each period. This option is indicated by the point B in Figure 1.1. Save all income in the first period and consume everything in the second. Another possibility is to consume everything now and not worry about tomorrow. This would result in consumption of $10,000 from this period’s income plus the maximum the investor could borrow against next period’s income.

Note that points A, B, and C lie along a straight line Note that points A, B, and C lie along a straight line. This did not happen by accident. In fact, all of the enormous possible patterns of consumption in periods 1 and 2 will lie along this straight line.

the equation for a straight line and is the line shown in Figure 1.1. The investor is left with a large number of choices. refer to the set of choices facing the investor as the opportunity set. how an investor selects the optimum consumption pattern from the opportunity set.

1.2.2 The Indifference Curves an investor chooses among the opportunities shown in Figure 1.1 by specifying a series of curves called utility functions or indifference curves. A representative set is shown in Figure 1.2. These curves represent the investor’s preference for income in the two periods. The name “indifference curves” is used because the curves are constructed so that everywhere along the same curve the investor is assumed to be equally happy. In other words, the investor does not care whether he obtains point A, B, or C along curve I1.

This ordering results from an assumption that the investor prefers more to less. Choices along I1 will be preferred to choices along I2, and choices along I2 will be preferred to choices along I3, and so on. The curved shape results from an assumption that each additional dollar of consumption forgone in period 1 requires greater consumption in period 2. For example, if consumption in period 1 is large relative to consumption in period 2, the investor should be willing to give up a dollar of consumption in period 1 in return for a small increase in consumption in period 2. In Figure 1.2 this is illustrated by deta1 for the amount the investor gives up in period 1 and deta2 for the amount the investor gains in period 2. However, if the investor has very few dollars of consumption in period 1, then a large increase in period 2 is required to be indifferent about giving up the extra consumption in period 1. This is represented by the deta1’ in period 1 (which is the same size as deta1) and the deta2’ in period 2 (which is much larger than deta2).

1.2.3 The Solution The indifference curves and the opportunity set represent the tools necessary for the investor to reach a solution. The optimum consumption pattern for the investor is determined by the point at which a number of the set of indifference curves is tangent to the opportunity set (point D in Figure 1.3).

The investor will move to higher indifference curves until the highest one that contains a feasible consumption pattern is reached.

1.2.4 An Example: Determining Equilibrium Interest Rates look at the investor’s possible decision to see how it can help in determining equilibrium conditions in the market. The optimum decision could occur in three sections of Figure 1.3: A to B, point B, or B to C. If the optimum occurs in the segment AB, then the investor lends money at the 5% rate. If the optimum occurs at point B, then the investor is neither a borrower nor a lender. Finally, if the optimum occurs in segment BC, then the investor borrows against future income at the 5% rate.

In this simple framework, equilibrium in the marketplace is easy to determine. At a 5% interest rate this investor wishes to lend $2,000, the difference between $10,000 in income and $8,000 in consumption. Summing across all investors who wish to lend when the interest rate is 5% gives one point on the supply curve. Similarly, summing across investors who wish to borrow at a 5% interest rate gives one point on the demand curve. As the interest rate changes, the amount our hypothetical investor wishes to lend also changes. In fact, if the interest rate is low enough, the investor may change from a lender to a borrower.

By varying the interest rate, the supply and demand curve can be traced out, and the equilibrium interest rate can be determined. The equilibrium interest rate is that rate at which the amount investors wish to borrow is equal to the amount investors wish to lend. This is often called a market clearing condition. The equilibrium interest rate depends on what each investor’s decision problem looks like, or the characteristics of a figure like Figure 1.3 for each investor. Figure 1.3 depends on the investor’s income in the two periods and the investor’s tastes or preferences. Thus, in this simple world, equilibrium interest rates are also determined by the same influences: investors’ tastes and investors’ income.

1.3 Conclusion This simple example has revealed the elements that are necessary to analyze a portfolio problem. We need two components to reach a solution: a representation of the choices available to the investor, called the opportunity set, and a representation of the investor’s tastes or preferences, called indifference or utility curves. With these two components we solved this simple problem and can solve the more realistic problems that follow. In addition, this simple example taught us that by aggregating across investors, we can construct models of equilibrium conditions in the capital markets. Now we turn to an examination of why and how this framework must be modified to deal realistically with multiple investment alternatives.

1.4 Multiple Assets and Risk If everyone knew with certainty the returns on all assets, then the framework just presented could easily be extended to multiple assets. If a second asset existed that yielded 10%, then the opportunity set involving investment in this asset would be the line A’BC’ shown in Figure 1.4. Its intercept on the vertical axis would be 10,000 + (1.10)(10,000) = $21,000, and the slope would be -(1.10). If such an asset existed, the investor would surely prefer it if lending and prefer the 5% asset if borrowing. The preferred opportunity set would be A’, B, C.

Additional assets could be added in a straightforward manner Additional assets could be added in a straightforward manner. But this situation is inherently unstable. Two assets yielding different certain returns cannot both be available because everyone will want to invest in the higher-yielding one and no one will purchase the lower-yielding one. We are left with two possibilities: either there is only one interest rate available in the marketplace or returns are not certain. Because we observe many different interest rates, uncertainty must play an important role in the determination of market rates of return. To deal with uncertainty, we need to develop a more complex opportunity set.

The remainder of this book is concerned with the development of the framework necessary to solve the more complex asset choice problems in the presence of risk. In the next two chapters we deal with the basic notions of the investor’s opportunity set under risk.