Conclusion Olm
In this chapter we have defined the geometric properties of that set of portfolios all risk-avoiding investors would hold regardless of their specific tolerance for risk. We have defined this set the efficient frontier under alternative assumptions about short sales and the ability of the investor to lend and borrow at the riskless rate. Now that we understand the geometric properties of the efficient frontier, we are in a position to discuss solution techniques to the portfolio problem. This...
Nonstandard Forms of Capital Asset Pricing Models
The CAPM model developed in the previous chapter would provide a complete description of the behavior of capital markets if each of the assumptions set forth held. The test of the CAPM model is how well it describes reality. But even before we examine these tests, it is useful to develop equilibrium models based on more realistic assumptions. Most of the assumptions underlying the CAPM violate conditions in the real world. This does not mean that we should disregard the CAPM model, for the...
Delineating Efficient Portfolios
In Chapter 4 we examined the return and risk characteristics of individual securities and began to study the attributes of combinations or portfolios of securities. In this chapter we look at the risk and return characteristics of combinations of securities in more detail. We start off with a reexamination of the attributes of combinations of two risky assets. In doing so we emphasize a geometric interpretation of asset combinations. It is a short step from the analysis of the combination of...
A Simple Example Of Factor Analysis
In order to provide the reader who has never used any form of factor analysis with a demonstratiomfjiow it works we include a simple example in this appendix. We choose to usefprincipal component analysis fc r the example, because this leads to a solution that is easiest to interpret.'5 We choose 10 years of monthly data on the Morgan Stanley Capital International stock indexes for each of four countries the United States, Canada, France, and Belgium. Remember that principal components analysis...
Simple Techniques for Determining the Efficient Frontier
In Chapters 7 and 8 we examined several models that were developed to simplify the inputs to the portfolio selection problem. Each of these models makes an assumption about why stocks covary together. Each leads to a simplified structure for the correlation matrix or covariance matrix between securities. These models were developed to cut down on the number of inputs and simplify the nature of the inputs needed to forecast correlations between securities. The use of these models was expected to...
Solving Systems Of Simultaneous Equations
To solve large systems of simultaneous equations, one would use any of the large number of standard computer packages that exist for this purpose. However, small systems can be ,olved by hand. The simplest way is by repetitive substitution. Consider the following sys-em of simultaneous equations Equation C.l can be rearranged so that X2 is expressed as a function of Xv This rearrangement yields X2 7-4X, substituting this into Equation C.2 yields 3X, 2 7-4Z, 5 3X, 14-8X, 5 -5X, -9 y -...
Market Rationality
In the prior sections we discussed the speed with which information is incorporated in hare price. We referred to this as informational efficiency. A number of authors are also concerned with whether prices accurately reflect investors' expectations about the present alue of future cash flows. We will refer to this hypothesis as market rationality to distinguish it from informational efficiency, while recognizing that some authors use the word efficiency to apply to both ideas. If markets...
The Shape Of The Portfolio Possibilities Curve
Reexamine the earlier figures in this chapter and note that the portion of the portfolio possibility curve that lies above the minimum variance portfolio is concave while that which lies below the minimum variance portfolio is convex.8 This is not due to the peculiarities of the examples we have chosen but rather is a general characteristic of all portfolio problems. This can easily be demonstrated. Remember that the equations and diagrams we have developed are appropriate for all combinations...
Nonpricetaking Behavior
Up to now we have assumed that individuals act as price takers in that they ignore the impact of their buying or selling behavior on the equilibrium price of securities and, hence, on their See Lintner 79 , Sharpe 118 , Fama 32 , and Gonedes 41 . 18Lintner assumes the negative exponential utility function given by u w e a'wi. The measure of risk aversion is given by ar optimal portfolio holdings. The obvious question to ask is what happens if there are one or more investors, such as mutual...
Short Sales Disallowed
One of the assumptions made in deriving the capital asset pricing model is that the investor can engage in unlimited short sales. Furthermore, short sales were defined in the broadest sense of the term in that the investor was allowed to sell any security whether owned or not and to use the proceeds to buy any other security.' This was a convenient assumption and it simplified the mathematics of the derivation, but it was not a necessary assumption. Exactly the same result would have been...
Financial Securities
This chapter is meant to introduce the reader to the principal financial instruments, their return characteristics, and the indexes that are used to represent their return. The nature of the material means that this chapter is much more descriptive than subsequent chapters. Those readers already familiar with financial instruments and the indexes that can be used to represent their return can skip to Chapter 3. Those readers who have had a prior finance course and are familiar with financial...
The Characteristics of the Opportunity Set Under Risk
In Chapter 1 we introduced the elements of a decision problem under certainty. The same elements are present when we recognize the existence of risk however, their formulation becomes more complex. In the next two chapters we explore the nature of the opportunity set under risk. Before we begin the analysis we present a brief summary or roadmap of where we are going. The existence of risk means that the investor can no longer associate a single number or payoff with investment in any asset. The...
Bibliography
1. Brennan, Michael J. The Optimal Number of Securities in a Risky Asset Portfolio When There Are Fixed Costs of Transacting Theory and Some Empirical Results. Journal of Financial and Quantitative Analysis, X, No. 3 Sept. 1975 , pp. 483-496. 2. Elton, Edwin J., and Gruber, Martin J. Risk Reduction and Portfolio Size An Analytical Solution, Journal of Business, 50, No. 4 Oct. 1977 , pp. 415 137. 3. -. Modern Portfolio Theory 1950 to Date, Journal of Banking and Finance, 21, Nos. 11-12 December...
Multiperiod Capm
i 'p to now we have assumed that all investors make investment decisions based on a single-period horizon. In fact, the portfolio an investor selects, at any point in time, is leally one step in a series of portfolios that he intends to hold over time to maximize his utility of lifetime consumption. Two questions immediately become apparent ' I. What are the conditions under which the simple CAPM adequately describes market equilibrium 1. Is there a fully general multiperiod equilibrium model...
Telser Criteria
With riskless lending and borrowing, employing Telser's criteria leads to three possible solutions 1. The optimum occurs at the intersection of the constraint with the lending and borrowing line. 1. The optimum occurs at infinite borrowing. 3. There is no portfolio that meets the constraint and thus no feasible solution. Figure 11.14 shows the situation where the optimum is the intersection of the constraint with the lending and borrowing line. Figure 11.15 shows the situation where the optimum...
Info Jok
aA dividend entry on the same line as a price indicates that the return between that time period and the previous period consisted of a capital gain or loss and the receipt of the dividend. aA dividend entry on the same line as a price indicates that the return between that time period and the previous period consisted of a capital gain or loss and the receipt of the dividend. A. Compute the rate of return for each company for each month. B. Compute the average rate of return for each company....
Info Rss
63. - Multivariate Tests of the Zero-Beta CAPM, Journal of Financial Economics, 14 Sept. 4. Sxmkowitz, Michael, and Logue, Dennis. The Interdependent Structure of Security Returns. Journal of Financial and Quantitative Analysis, VUI, No. 2 March 1973 , pp. 259-272. i - Sorensen, Eric, Mezrich, Joseph, and Thum, Chee. The Salomon Brothers U.S. Stock Risk Attribute Model, Salomon Brothers Oct. 1989 . fi6. Sorensen, Eric, Salomon, R. S. Davenport, Caroline, and Fiore, Maria. Risk Analysis The...
Riskless Lending And Borrowing With Short Sales Not Allowed
This problem is analogous to the case of riskless lending and borrowing with short sales allowed. One portfolio is optimal. Once again, it is the one that maximizes the slope of the 7This only works for the standard definition of short sales. The Lintner definition of short sales assumes riskless lending and borrowing at a particular rate for each point on the original curved efficient frontier. Figure 6.3 Tangency portfolios for different riskless rates. line connecting the riskless asset and...
Short Sales Allowed With Riskless Lending And Borrowing
The derivation of the efficient set when short sales are allowed and there is a riskless lending and borrowing rate is the simplest case we can consider. From Chapter 5 we know that the existence of a riskless lending and borrowing rate implies that there is a single portfolio of risky assets that is preferred to all other portfolios. Furthermore, in return standard deviation space, this portfolio plots on the ray connecting the riskless asset and a risky portfolio that lies furthest in the...
The Efficient Frontier With Riskless Lending And Borrowing
Up to this point we have been dealing with portfolios of risky assets. The introduction of a riskless asset into our portfolio possibility set considerably simplifies the analysis. We can consider lending at a riskless rate as investing in an asset with a certain outcome e.g., 33Mer on 19 has shown that the efficient set is the upper half of a hyperbola. Figure 5.12 The efficient set when short sales are allowed. a short-term government bill or savings account . Borrowing can be considered as...
An Example Determining Equilibrium Interest Rates
We take another 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, orBto 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, the investor borrows against future income at the 5...