Description. An update of a definitive investment text, Modern Portfolio Theory is a comprehensive guide to asset allocation, portfolio optimization, asset pricing. 5th ed. New York: Wiley, pages, , English, Book; Illustrated, Modern portfolio theory and investment analysis / Edwin J. Elton, Martin J. Gruber. [PDF]A Course in Modern Mathematical Physics (Solutions Manual) by [PDF] Accounting principles 8th Ed (Solutions Manual) by Weygandt.
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Modern Portfolio Theory and Investment Analysis [Edwin J. Elton, Martin J. Gruber, Ninth edition. pages cm Includes bibliographical references and index. The eighth and ninth assumptions deal with the homogeneity of expectations. Help Center; less. pdf. Elton Modern Portfolio Theory and Investment Analysis Selected Solutions to Text Problems Brown and Goetzm 42 Pages. PORTFOLIO THEORY. AND INVESTMENT. ANALYSIS. EIGHTH EDITION. INTERNATIONAL STUDENT VERSION. EDWIN J. ELTON. Leonard N. Stern School.
Skip to main content. Log In Sign Up. Quynie Gauloises. Problem 1 A. Opportunity Set With one dollar, you can download red hots and no rock candies point A , or rock candies and no red hots point B , or any combination of red hots and rock candies any point along the opportunity set line AB. Solving the above equation for X gives: Indifference Map Below is one indifference map.
Graphically, the opportunity set appears as follows: Assuming you like both pizza and hamburgers, your indifference curves will be negatively sloped, and you will be better off on an indifference curve to the right of another indifference curve. Assuming diminishing marginal rate of substitution between pizza slices and hamburgers the lower the number of hamburgers you have, the more pizza slices you need to give up one more burger without changing your level of satisfaction , your indifference curves will also be convex.
Therefore, your optimal choice is the combination of pizza slices and hamburgers that is represented by the point where your indifference curve is just tangent to the opportunity set point A below.
Expected return is the sum of each outcome times its associated probability. Pair E The efficient set is the positively sloped part of the curve, starting at the GMV portfolio and ending at security 4.
Short Selling Allowed Note that the answers to part B. In the no-short-sales case in Part A.
Pair A The efficient set is the positively sloped line segment through security 1 and out toward infinity. Pair B The entire line out toward infinity is the efficient set. Pair D The efficient set is the positively sloped line segment through security 3 and out toward infinity. Pair F The efficient set is the positively sloped part of the curve, starting at the GMV portfolio and extending past security 3 toward infinity.
Pair E assets 2 and 4 : We arrived at the following answer graphically; the analytical solution to this problem is presented in the subsequent chapter Chapter 6.
The tangent portfolio has an expected return of 9. The tangent optimal portfolio has an expected return of Problem 5 A.
The single-index model's formula for security i's own variance is: Problem 6 A. Recall that the formula for a portfolio's beta is: Recall that the definition of a portfolio's alpha is: Problem 5 The formula for a security's expected return using a general two-index model is: The two-index model's formula for the covariance of security i with security j is: Problem 6 For an industry-index model, the text gives two formulas for the covariance between securities i and k.
If firms i and k are both in industry j, the covariance between their securities' returns is given by: Problem 1 The equation for the security market line is: Using those values, an asset with a beta of 2 would have an expected return of: Problem 2 Given the security market line in this problem, for the two stocks to be fairly priced their expected returns must be: Chapter Problem 7 Using the two assets in Problem 1, a portfolio with a beta of 1.
Problem 1 Given the zero-beta security market line in this problem, the return on the zero- beta portfolio equals 0. The return on the market portfolio must therefore be 0. This is depicted in the graph below, where the efficient frontier extends along the ray from RF to the tangent portfolio L, then to the right of L along the curve through the market portfolio M and out toward infinity assuming unlimited short sales.
Note that, unless all investors in the economy choose to lend or invest solely in portfolio L, the market portfolio M will always be on the minimum-variance curve to the right of portfolio L.
Since both M and Z are on the minimum-variance curve, the entire minimum- variance curve of risky assets can be traced out by using combinations portfolios of M and Z. Letting X be the investment weight for the market portfolio, the expected return on any combination portfolio P of M and Z is: Problem 1 From the text we know that three points determine a plane. The APT equation for a plane is: There are many ways to solve a set of simultaneous linear equations.
One method is shown below. Subtract equation a from equation b: The first step is to use portfolios in equilibrium to create a replicating equilibrium investment portfolio, call it portfolio E, that has the same factor loadings risk as portfolio D. Since they have the same risk factor loadings , we can create an arbitrage portfolio, combining the two portfolios by going long in one and shorting the other.
This will create a self-financing zero net investment portfolio with zero risk: We need to short sell either portfolio D or E and go long in the other.
The question is: This gives us: There is no reason to expect any price effects on portfolios A, B and C, since the arbitrage with portfolio D can be accomplished using other assets on the equilibrium APT plane. In other words, the optimum consumption pattern is where the highest feasible indifference curve is just tangent to the opportunity set.
Chapter: 1 2. List the factors that affect risk. Answer: The following are the factors that affect risk: 1. The maturity of an instrument usually, longer the maturity assets are riskier 2. The risk characteristics and creditworthiness of the issuer or guarantor of the investment. The nature and priority of the claims the investment has on income and assets. The liquidity of the instrument and the type of market in which it is being traded.
Chapter: 2 3.
List and discuss the characteristics of various types of financial securities. Answer: A security is a legal contract representing the right to receive future benefits under a stated set of conditions. The various types of financial securities are: A. Money Market Securities Money market securities are short-term debt instruments sold by governments, financial institutions, and corporations. Money market instruments have maturities of one year or less when issued and their transaction size is typically large.
The various types of money market instruments are: 1.
Treasury Bills T-bills : These are the least risky and the most marketable of all money market instruments. T-bills are sold at a discount from face value and pay no explicit interest payments. The difference between the download price and the face value constitutes the return the investor receives. These are considered to be the closest approximations available to a riskless investment.
Redownload Agreements Repos : These refer to an agreement between a borrower and a lender to sell and redownload a U. Both instruments sell at rates that depend on the credit rating of the bank that backs them.
Commercial paper is a short-term debt instrument issued by large, well-known corporations, and rates are determined in part by the creditworthiness of the corporation. Capital Market Securities Capital market securities include instruments with maturities greater than one year, and those with no designated maturity at all.
The types of capital market instruments are: 1. Fixed Income Securities: These securities have a specified payment schedule promising to pay specific amounts at specific times.
In almost all cases, failure to meet any specific payment puts them into default, with all remaining payments missed interest plus principal due immediately. Treasury Notes and Bonds: The federal government issues fixed income securities over a broad range of the maturity spectrum.
Securities with maturity of 1 to 10 years are called Treasury notes, and securities with a maturity beyond 10 years are known as Treasury bonds. Both notes and bonds pay interest twice a year and repay principal on the maturity date. Federal Agency Securities: They are issued by various federal agencies that have been granted the power to issue debt in order to help certain sectors of the economy.
Municipal Bonds: They are debt instruments sold by political entities such as states, counties, cities, and so forth, other than the federal government or its agencies. In contrast to agency bonds, municipal bonds can default and the interest on municipal bonds is exempt from federal and usually state taxes. Corporate Bonds: They promise to pay interest at periodic intervals and to return principal at a fixed date.
The major difference is that these bonds are issued by business entities and thus have a risk of default.