The project that we have done based on the Markowitz and Sharp methodologies that allow investors to build an efficient portfolio. An efficient portfolio is defined as the portfolio that maximizes the expected return for a given amount of risk (standard deviation), or the portfolio that minimizes the risk subject to a given expected return.

Markowitz method determines the asset allocation that produces the highest expected return for each unit of risk. The calculation is based on forecasts of each asset's long-term return and volatility and correlations among the various assets. Method showed how the variances of individual stock returns and the correlations of those returns can be combined to calculate a value for the variance of a portfolio made up of those stocks. Based on the received data of possible asset allocation we were able to draw an efficient frontier.

The efficient frontier is the curve that shows all efficient portfolios in a risk-return framework.
The general solution to the shortcomings of the Markowitz method for estimate stock portfolio risk is the use of common factor models. The most known common factor model is Sharp’s single-index model. The single-index model assumes that there is only 1 macroeconomic factor that causes the systematic risk affecting all stock returns and this factor can be represented by the rate of return on a market index, such as the S&P 500. According to this model, the return of any stock can be decomposed into the expected excess return of the individual stock due to firm-specific factors, commonly denoted by its alpha coefficient (α), the return due to macroeconomic events that affect the market, and the unexpected microeconomic events that affect only the firm.

To build covariance matrix we used the regression analysis to get α vector, residual standard deviation and, as a result, residual variance that we needed to build the covariance matrix inverse of variance -...

...Construction of an Efficient Portfolio
Prepared for:
Pallabi Siddiqua
Assistant Professor
Department of Finance
University of Dhaka
Prepared by:
Alamgir Kabir
ID. No. 15-154
Section: B
Department of Finance
University of Dhaka
Date of Submission: 22ndNovember, 2012
Letter of Transmittal
22ndNovember, 2012
Pallabi Siddiqua
Assistant Professor
Department of Finance
University of Dhaka
Subject: Report on “construction of portfolio of 10 listed securities in DSE and interpretation.
Dear Madam,
I am glad to submit the report on “construction of portfolio of 10 listed securities in DSE and interpretation”. I would like to inform you that this report is very helpful for me to know about the construction of an efficient portfolio which will lead me to analyze the stock market and choose perfect stock from the huge number of stocks in the market and it will also help me to be capable of behaving with the market according to its trend.
I am very thankful to you for giving me such realistic opportunity to make an assignment on this topic. I earnestly request you to call me if you think any further work should be done on the topic that you have chosen for me.
Sincerely Yours,
Alamgir Kabir
ID. No. 15-154
Section: B
Department of Finance
University of Dhaka
Acknowledgement
Preparation of this report would be...

...PORTFOLIOCONSTRUCTION USING SHARPE METHOD
A PROJECT REPORT
Table of Contents
Executive Summary 3
Introduction 4
The traditional Approach 4
The Modern Approach 4
Need for Study 5
Objective 5
Limitations 5
Literature Review 6
Research Methodology 8
Analysis and Interpretation 10
Findings 13
Recommendations 13
Conclusions 13
Bibliography 14
Executive Summary
An equity portfolio consists of two or more securities. Individual securities have risk and return characteristics of their own. The portfolio which consists of these securities may or may not have the collective properties of the individual securities. By constructing a portfolio we are trying to reduce the risk and increase the return, than investing in a single stock.
Risk is the variability of return. More dispersion or variability about a security’s expected return means the security was riskier than one with less dispersion. The risk of a portfolio can be reduced by having securities in which the risk of one security can be cancelled by the other. If we consider a portfolio of two securities, the important point is finding two securities in which every time one security performs poorly, the other security performs well. This will provide reasonable return to its investor, even if some of the stocks in the portfolio perform poorly.
In this project we are taking...

...Introduction
The Capital Asset Pricing Model (CAPM) has been one of the most widely used techniques in the global investing community for calculating the required return of a risky asset. This project aims to test whether CAPM is a valid model for predicting the price/return of some selected companies listed on the S&P 500 Index. Also we investigate, whether there appear to be some deviations from the model and look for plausible reasons to explain these. For the purpose of the project, actual monthly returns of sample companies listed on NYSE for the period July 2008 to June 2013 are compared with the CAPM based (predicted) returns for the corresponding time period. The benchmark for the risk free rate Rf is taken as USA 5 year Treasury Bill Return corresponding to the relevant monthly time periods. For estimating market return R , changes in the S&P 500 index for each relevant time period is used. Stability tests are also conducted to assess the consistency of results over the entire range of data.
The conclusions arrived at through data analysis might lead to useful recommendations about how and to what extent CAPM can be used as tool for predicting stock returns and facilitating investment decisions.
Theoretical Background & Literature Review
CAPM developed by Sharpe (1964), Lintner (1965) and Mossini (1965) builds upon the “Portfolio Theory” introduced by Harry Markowitz (1959). CAPM presents the basis for...

...spun off a number of funds, with different investment objectives and different target investors. This has complicate investment process, making it very important for investors to understand the nuances of building a good mutual fund portfolio.
Portfolioconstruction of a mutual fund:
The broader points to keep in mind, when constructing a portfolio, are the financial goals to be achieved and the targeted duration till their achievement. Both these aspects affect the selection of an investment instrument, the amount of money allocated to it and the tenure of the investment, as your risk-to-return ratio would vary accordingly.
Theoretically, investments targeting a high priority financial goal with a shorter duration, should be of lower risk. Conversely, when the goal has a longer tenure, its investments can carry a higher risk and a higher return. As mutual funds cater to both these kinds of needs, constructing a mutual fund portfolio around them can be easier, with the following points being kept in mind:
Right mix of asset classes: Mutual funds invest into equity, debt and gold, or a mixture of these asset classes. It is often observed that investors’ mutual fund portfolios tend to be lopsided in favour of one asset class. Either the portfolio comprises a large amount of equity-oriented mutual funds or debt oriented funds. In the younger years, investors can allocate...

...Chapter 10
Arbitrage Pricing Theory and Multifactor Models of Risk and Return
Multiple Choice Questions
1. ___________ a relationship between expected return and risk.
A. APT stipulates
B. CAPM stipulates
C. Both CAPM and APT stipulate
D. Neither CAPM nor APT stipulate
E. No pricing model has found
Both models attempt to explain asset pricing based on risk/return relationships.
Difficulty: Easy
2. ___________ a relationship between expected return and risk.
A. APT stipulates
B. CAPM stipulates
C. CCAPM stipulates
D. APT, CAPM, and CCAPM stipulate
E. No pricing model has found
APT, CAPM, and CCAPM models attempt to explain asset pricing based on risk/return relationships.
Difficulty: Easy
3. In a multi-factor APT model, the coefficients on the macro factors are often called ______.
A. systemic risk
B. factor sensitivities
C. idiosyncratic risk
D. factor betas
E. B and D
The coefficients are called factor betas, factor sensitivities, or factor loadings.
Difficulty: Easy
6. Which pricing model provides no guidance concerning the determination of the risk premium on factor portfolios?
A. The CAPM
B. The multifactor APT
C. Both the CAPM and the multifactor APT
D. Neither the CAPM nor the multifactor APT
E. None of the above is a true statement.
The multifactor APT provides no guidance as to the...

...CHAPTER – 1
INTRODUCTION TO THE STUDY
Abstract
The study was carried at Share Khan, Coimbatore during March 2014. The aim of the study is to construct an optimum equity portfolio with stocks that form a part of the S&P BSE SENSEX (S&P Bombay Stock Exchange Sensitive Index), using Sharpe’s Single Index model. Daily close price of all the 30 securities of BSE Sensex for the period of 1 year from January 2013 to December 2013 is taken for analysis. In thismodel the securities' inclusion in the portfolio is directly related to its excess return-to-beta ratio. Then they are ranked from highest to lowest order. The number of securities selected depends on a unique Cut- off rate such that all securities with higher ratios will be included. Percentage of investment in each of the selected security is then decided on the basis of respective weights assigned to each security.
Investments
Investment refers to an asset or item that is purchased with the hope that it will generate income or appreciate in the future. In an economic sense, an investment is the purchase of goods that are not consumed today but are used in the future to create wealth. In finance, an investment is a monetary asset purchased with the idea that the asset will provide income in the future or appreciate and be sold at a higher price.
Equity market investments typically yield high returns, particularly if invested over longer periods of time,...

...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...

...Investment Management Division
The Intuition Behind Black-Litterman ModelPortfolios
s In this article and as our title suggests, we demonstrate a method for understanding the intuition behind the Black-Litterman asset allocation model. s To do this, we use examples to show the difference between the traditional meanvariance optimization process and the Black-Litterman process. We show that the mean-variance optimization process, while academically sound, can produce results that are extreme and not particularly intuitive. In contrast, we show that the optimal portfolios generated by the Black-Litterman process have a simple, intuitive property: − The unconstrained optimal portfolio is the market equilibrium portfolio plus a weighted sum of portfolios representing an investor’s views. − The weight on a portfolio representing a view is positive when the view is more bullish than the one implied by the equilibrium and other views.
− The weight increases as the investor becomes more bullish on the
view as well as when the investor becomes more confident about the view.
December 1999
Goldman Sachs Investment Management
Investment Management Research
Goldman Sachs Quantitative Resources Group
Guangliang He Robert Litterman (212) 357-3210 (212) 902-1677
Copyright 1999 Goldman, Sachs & Co. All rights reserved. The information in this publication...