UNIVERSITY OF ILLINOIS AT CHICAGO Liautaud Graduate School of Business Department of Finance Professor Hsiu-lang Chen 1 Practice Problem I In choices under uncertainty, individuals maximize his or her expected utility U! Part I. Expected Utility (Lecture 1) A casino company offers a simple game which is described as follows: The prize of the game depends on two unbiased coins you toss. If both heads appear, you get $200. If both tails appear, you get $100. Otherwise, you get $150. 1. The company offers you a promotion as follows: A cash of $145 or a chance to win the prize of the coin game. Your utility function is U(W)= -1/W. What is your choice? What is the lowest cash offer that you are willing to quit from playing the game? 2. After the promotion period ends, the company charges the entry fee $145 for the game. One day, a group of tourists, who all exhibit utility function U(W)= -1/W, visit the casino, but no one plays the coin game. To induce them to play, the company decides to raise the payoff, instead of lowering the entry fee. What will be the smallest compensatory risk premium the company has to offer? 3. Suppose now the utility function is U=E(r)-0.5A 2. (Inputs should be in a decimal format.) The company still charges the entry fee $145 for the game. For an investor with A=0.75, will the investor prefer this coin game to an instant risk-free rate of 1%?

Part II. Construction of Feasible Investment Opportunity Set and the Efficient Frontier (Lecture 3) 1. Consider two securities for the potential portfolio inclusion: E(r1)=25%,E(r2)=10%, 1=75%, 2=25%, 12 Draw all feasible investment combinations given these two risky assets in a plane of P, E(rp)} in Excel for four cases: (1) 12 =1, (2) 12 = 0.2, (3) 12 = - 0.2, (4) 12 = -1. What does the Efficient Frontier look like?

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Part of this practice problem is constructed based on the homework assignment by Professor Schaumburg at Kellogg School of Management where I was visiting during my sabbatical...

...PaperThis assignment needs to consist of a portfolio analysis in a Microsoft Word document that is not to exceed three pages. You must also include your portfolio analysis in either Word or Excel. You must show how you calculated the answers.
1. Select four stocks from finance.yahoo.com, google.finance.com, or moneycentral.msn.com. One should be a clothing manufacturer, one should be a retailer, one should be an automobile manufacturer, and one should be a restaurant or food producer.
2. Obtain the closing price, the change in price from the previous day, and the beta.
3. Calculate the return on holding the stock for a day (this should be the change in price over the closing price).
4. Calculate a portfolio return with weights of 0.25 for each stock.
5. Calculate a weighted beta with weights of 0.25 for each stock.
6. Write up the implications of the portfolio return and risk with respect to what you learned about beta and the CAPM in 2-3 pages.
Answer:
Market Risk:
Market risk is the risk that reflects the effect of the project on a well-diversified stock portfolio. This is the risk which depends on the variance and correlation of the project or a particular stock with the stock market. Portfolio risk is the risk that one still bears after achieving full diversification, Portfolio risk is often called systematic or market risk as well.
The market risk of a stock...

...Assignment Portfolio Theory and Management
Individual Assignment
Introduction
This report exams the performance of fund 49 from different perspectives. Then, I composed a portfolio for client Jim using fund 49 and other four asset classes. The report contains five parts, first part identifies the style of fund 49 and pick out its corresponding benchmark. Second part conducts performance evaluation by different ratios. Third part compares fund 49 and fund 50 from different aspects. Forth part exams whether Jim’s objectives under some assumptions can be achieved or not and also provides possible alternative scenarios to him.
1. If we want to know the fund style, we should use different style benchmarks to exam what my fund style is. Usually, according to factor model, we should run regression between Rf and six benchmarks together and exam the relationship between my fund and six benchmarks. Then we constrain α=0, Ʃβi=1 and 0<βi<1. So picking out the largest and most significant β is the way to define the fund style.
Rf=α+βL-B*FL-B+βL-G*FL-G+βL-V*FL-V+ΒM/S-B*FM/S-B+ΒM/S-G*FM/S-G+ ΒM/S-V*FM/S-V+ Ɛ
Unlike U.S financial market which contains substantial difference between value and growth, in Australian, the different styles have high correlation with each other.
So we can just use Jensen measure involves running regressions between six different Australian Equity Benchmarks less risk free rate (cash) and my fund 49 less...

...derivatives blew up, and other foundations were laid bare. Even the core of investing theories related to portfolios has come under pressure. Yet the belief in Modern Portfolio Theory has remained strong amongst the investors.
Modern Portfolio Theory (MPT) is a theory that tells investors how to minimise risks associated with investment and at the same time, maximise return on the investments by proper resource allocation and diversifying theirportfolios – it is based on the theory that risk can be lessened by diversifying into uncorrelated asset classes. However, unless the correlations of the various asset classes are predictable, the reduction of risk may be lost.
Investors expect to be rewarded for the level of risk they are taking in a particular market. According to the theory, it's possible to construct an "efficient frontier" of optimal portfolios offering the maximum possible expected return for a given level of risk and there are four basic steps involved in portfolio construction: Security Valuation, Asset Allocation, Portfolio Optimization and Performance measurement.
This theory of portfolio selection was coined by Harry Markowitz in his paper ‘Portfolio Selection’ which was published in the Journal of Finance in March, 1952. Even before Markowitz in 1952, investors were familiar with the notion being able to reduce exposure to...

...Portfolio Investment
1
Abstract The objective of this work is to optimize portfolios and to evaluate their performances. CAPM and APT models are important models that use statistical measures in order to achieve the objective. Throughout this work we improved our knowledge regarding portfolio theory and its application. Literature and Data For information we used the book Investments and PortfolioManagement by Bodie, Kane and Marcus as well as material given during the lectures. We used Microsoft Excel to elaborate data and the sources were given during the labs.
Assignment 1
Introduction: The goal is to explore and compare different methods such as CAPM, APT and portfolio theory. Methodology: In this assignment we exploit theories such as the Portfolio Theory, Mean-Variance Theory and the CAPM. So, we are assuming all the hypotheses that these theories assume. Among all, we are assuming that average return is a good measure of return and the risk could be calculated with the standard deviation. When we use CAPM, we are implying that the only risk is the Beta with the market (systematic risk) because we can reduce the risk of each asset to zero, with a well-diversified portfolio. In APT, we assume there are other important risks related to other factors. So, the main difference between APT and CAPM is that while CAPM only considers the market as the...

...Post-Modern Portfolio Theory
PMPT Definition, Investment Strategy, and Differences With MPT
By Kent Thune
See More About
alternative investing
build a portfolio
mutual fund analysis
See More About
alternative investing
build a portfolio
mutual fund analysis
Definition: Post-Modern Portfolio Theory (PMPT) is an investing theory and strategic investment style that is a variation of Modern Portfolio Theory (MPT). Similar to MPT, PMPT is an investing method where the investor attempts to take minimal level of market risk, through diversification, to capture maximum-level returns for a given portfolio of investments.
PMPT History and Difference With MPT
PMPT is the culmination of research from many authors and has expanded over several decades as academics at universities in many countries tested these theories to determine whether or not they had merit. The term post-modern portfolio theory was first used in 1991 to describe portfolio construction software created by engineers Brian M. Rom and Kathleen Ferguson. Rom and Ferguson first publicly described their ideas about PMPT in the 1993 Journal of Investing article, Post-Modern Portfolio Theory Comes of Age.
The difference between PMPT and MPT is the way they define risk and build portfolios based upon this risk. MPT sees risk as symmetrical; the portfolio...

...Frame the issue. Discuss the advantages and limitations of optimal portfolio allocation.
HMC defined their Policy Portfolio to correspond to their benchmark, according to the modern portfolio theory (Markowitz, 1952), whose goal is to minimize the variance for a given return. The main advantage of the optimal portfolio allocation lies in its ability to provide weights on how to invest a given amount of money based on a few inputs. Optimal portfolio allocation is easy to implement, yet it faces some issues and limitations. As discussed in class, the model assumes normality in the returns, since the optimization only depends on the mean and the variance. HMC team should however take into account that the distribution of returns is not normal and that there might be outliers issues. HMC partly takes these into account by controlling the risk for the aforementioned outliers using stress test (Exhibit 7). Another important matter to point out is that the model uses historical data as input, and these data might very well not be constant or accurate. Correlation may indeed change both over time and between classes of assets. However HMC examined short-term and long-term historical records and talked with investment management firms specialized in this type of analysis in order to get the most accurate data. Finally, HMC is doing well using the optimizer as a proxy for the investment decision....

...
Assignment No 6
Diversification in Stock Portfolios
Introduction
Diversification is one of the key components of a successful investment portfolio. Almost all
experts advise the avoidance of concentrating all of your investments in one type. However,
many investors forget about diversification once they see a financially attractive stock and
concentrate all of their assets in it. Other investors make a similar mistake and being influenced
by their emotions fail to listen to their common sense whispering "Diversify".
Many companies have attracted their employees to investing in company stock as part of their
retirement plan through the provided matching of contributions. As a result most investors end
up concentrating their assets in company stock and forgetting about the importance of
diversification. Investing in your company's stock is not something bad. However, you should
own not only your company's stock, because if something bad happens with your company you
risk not only losing your job but all of your assets. Through diversifying your stocks among
different industries you decrease to a great extent the risk of losing your money..
Portfolio Diversification
You can use index funds or exchange traded funds to track a broader market index. This gives
you exposure to many different types of companies, without your...

...Asset Selections: 6
Feedback & Control: 6
Assignment 2: 7
Transactions History 7
Portfolio Performance Vs. index Performance 9
1. Portfolio Performance vs. Dow Jones ETF Performance 10
Assignment 3 11
Portfolio Returns vs. Market Return 11
Assignment 1:
Introduction
Ayyad Co. is a financial institution, created by a group of five individuals investing their savings until their retirement age which is in 15 years. They decided to allocate USD 200,000 per person and then manage their portfolio by themselves to achieve their investment objectives. The purpose of this Investment Policy Statement is to establish guidelines for the Company’s investment portfolio. The statement also incorporates investment objectives that will be used for monitoring the progress of the Portfolio’s investment program.
Investment Objectives:
The investment objectives which are set by the company board of directors can be described by the following:
1- Annual absolute rate of return equal to 12%.
2- 2% higher than the composite benchmark consisting of market indexes weighted according to the expected target asset allocations stipulated by the Portfolio’s investment guidelines.
Risk Policy
1. Diversification: across and within asset classes is the primary means by which the company expects the Portfolio to avoid undue risk of large losses over long time periods. To protect the...