This pack of ECO 316 Week 1 Chapter 5 The Theory of Portfolio Allocation comprises:…
In this group assignment, by historical data analysis, we evaluate the two approaches Mean-Variance and CAPM specific in the stock risk estimation for minimize risk investor. The two approaches are consistent in the stock risk, but differ in the risk of portfolios we construct. Through our observation and the approach assumption analysis which refer to academic literatures, the former one represents more reasonable result ultimately as we conclude in the last 2 pages in this report body.…
The mean-variance theory postulated that in determining a strategic asset allocation an investor should choose from among the efficient portfolios consistent with that investor’s risk tolerance amongst other constraints and objectives. Efficient portfolios make efficient use of risk by offering the maximum expected return for specific level of variance or standard deviation of return. Therefore, the asset returns are considered to be normally distributed. Efficient portfolios plot graphically on the efficient frontier, which is part of the minimum-variance frontier (MVF). Each portfolio on the minimum-variance frontier represents the portfolio with the smallest variance of return for given level of expected return. The graph of a minimum-variance frontier has a turning point that represents the Global Minimum Variance (GMV) portfolio that has the smallest variance of all the minimum-variance portfolios. Economists often say that portfolios located below the GMV portfolio are dominated by others that have the same variances but higher expected returns. Because these dominated portfolios use risk inefficiently, they are inefficient portfolios. The portion of…
In developing investment strategy, there are two primary portfolio management styles – active and passive. Active management is a portfolio management strategy that has a goal of outperforming the market or some other investment benchmark index by making specific investment selections geared towards outperforming the market. Passive management is a strategy of being content to invest in an index fund that will closely replicate the investment weighting and returns of a specific index as the investor is not seeking to create returns in excess of that benchmark. The first style requires much more attention, effort, and diligence in obtaining and analyzing data, while the second requires much less dayto-day attention by its very nature. [9] To outperform the market and exploit market inefficiencies, the investment manager of an active portfolio purchases undervalued assets such as stocks or he short sells assets that are overvalued, or a combination of the two. Instead of always trying to increase value of a portfolio, the investor might also be trying to reduce the risk with respect to a benchmark index fund. [9]…
The construction of the best combination of investment instruments (investment portfolio) is a principal goal of investment policy. This is an optimization problem: select the best portfolio from all admissible portfolios. To approach this problem we have to choose the selection criterion first. The seminal paper of Markowitz [8] opened a new era in portfolio optimization. The paper formulated the investment decision problem as a risk-return tradeoff. In its original formulation it was, in fact, a mean-variance optimization with the mean as a measure of return and the variance as a measure of risk. To solve this problem the distribution of random returns of risky assets must be known. In the standard Markowitz formulation returns of these risky assets are assumed to be distributed according to a multidimensional normal distribution N (µ, Σ), where µ is the vector of means and Σ is the covariance matrix. The solution of the optimization problem is then carried on under implicit assumption that we know both µ and Σ. In fact this is not true and the calculation of µ and Σ is an important part of the solution.…
Here we study the performance of a one-period investment X0 > 0 (dollars) shared among several different assets. Our criterion for measuring performance will be the mean and variance of its rate of return; the variance being viewed as measuring the risk involved. Among other things we will see that the variance of an investment can be reduced simply by diversifying, that is, by sharing the X0 among more than one asset, and this is so even if the assets are uncorrelated. At one extreme, we shall find that it is even possible, under strong enough correlation between assets, to reduce the variance to 0, thus obtaining a risk-free investment from risky assets. We will also study the Markowitz optimization problem and its solution, a problem of minimizing the variance of a portfolio for a given fixed desired expected rate of return.…
Through Markowitz’s model of portfolio selection, we can achieve optimum results from a diversified portfolio by method of efficient diversification. Markowitz’s model involves finding the portfolio weights for a diversified set of assets that will result in the steepest capital allocation line. Increasing the steepness of the CAL…
In our study, we concentrated on the optimal portfolios, the one which has the lowest volatility or risk, for given level of return. The area below the frontier shows the achievable risk-return combinations, there will be at least one portfolio constructible that has the risk and return corresponding to that point. No portfolio on the efficient frontier can dominate any other portfolio on the efficient frontier. All of these portfolios have different return and risk measures, with expected rates of return that increase with higher risk. When we increased the expected return incrementally the weight of BBY and MRK increased until expected return is 2 ,MRK decreasing and BBY increasing afterwards ,whereas weight of WMT, C, IBM and HSY decreased respectively and became 0.Weight of HD is always 0 since it has a very low return/risk ratio compared to others. For the highest return of 2.5 BBY and MRK were optimal combinations since they are highly negatively correlated compared to others. Since BBY is on the efficient frontier, the decision to prefer it or other portfolios to each other depends on risk preference of individuals. The other individual securities are not efficient in these cases since they are on the area below the curve. The portfolios that are closest to the efficient frontier are more diversified since the portfolios on the efficient frontier are the most diversified. As you can see in exhibit 7 the minimum variances that you obtained by making up a portfolio of 7 securities are all below the individual standard deviations for the same level of expected return while they are…
Investors often debate on whether a portfolio should have active or passive exposure to assets. Interestingly, the active-passive exposure is much more than just a binary choice. It actually falls into a 4-box matrix. In this discussion paper, we show how investors can adopt this 4-box matrix to active-passive management. Active management is a function of security selection and market timing factors. The portfolio manager of a diversified active fund, for instance, first selects securities within the investable universe of stocks. The manager then buys and sells these securities on a continual basis. The fund’s objective is to generate higher returns than the benchmark index. Such excess return is called alpha returns and is the reason why active funds charge higher management fees compared with passive funds. Passive management typically refers to index funds. The portfolio manager of such a fund simply takes exposure to pre-defined universe of securities constituting the index. Besides, the manager does not engage in market timing. The 4-box active-passive choice essentially separates the security selection and the market timing factors. Accordingly, active-active decision refers to active management (market timing) of active exposure (security selection). Passive-active decision refers to passive management of active exposure. That is, the investor actively selects securities and holds the portfolio till the investment horizon. Likewise, active-passive decision refers to active management of passive exposure, where the investor actively engages in market-timing her index exposure. Passivepassive decision refers to passive management of passive exposure. Active management is difficult and portfolio managers cannot consistently beat the benchmark index, despite possessing security selection and market timing skills. Alpha, in other words, is a zero-sum game. This means the excess returns of all…
To construct the optimal risky portfolio, we first determine the optimal active portfolio. Using the Treynor-Black technique, we construct the active portfolio:…
In 1960, a doctoral candidate in economics at the University of California, Los Angeles by the name of William F. Sharpe needed a dissertation topic. After reading a 1952 paper on portfolio theory by Harry Markowitz entitled Portfolio Selection, Sharpe had found his idea. Markowitz 's paper presented the notion of an "efficient frontier" of optimal investment that advocated a diversified portfolio to reduce risk. However, his theory did not develop a practical means to assess how various holdings operate together, or correlate. Sharpe took Markowitz 's theoretical work and greatly simplified it by connecting investment risk and reward to a single risk factor (beta) (Burton, 1998). With the publication of his 1963 dissertation A Simplified Model of Portfolio Analysis, Sharpe introduced the world to the Capital Asset Pricing Model (CAPM). Today, CAPM has become an integral part of investment theory and is used on a daily basis by investment practitioners and managers. The concept was deemed so important that in 1990, Sharpe was awarded the Nobel Prize in Economics for his contributions to the development of the CAPM theory. Since its introduction, there have been many questions concerning the relevance of the assumptions upon which the theory is based. CAPM has been and continues to be tested within the academic research, however, although other alternative pricing models have been developed in an attempt to combat the shortcomings of CAPM, the Capital Asset Pricing Model is the most widely used and accepted model within the current financial community.…
Process of Portfolio Management 4.1 Investors Objectives 4.2 Stability of Principal 4.3 Growth of Income 4.4 Capital Appreciation 4.5 Investment Possibilities 4.6 Risk Involved 4.6.1 Equities 4.6.1.1 Diversifiable risk 4.6.1.2 Non-Diversifiable Risk 4.6.2 Bonds 4.6.2.1 Default Risk 5. Techniques of Portfolio Management 5.1 Equity portfolio 5.2 Equity Stock analysis Chapter 2 Objectives & Scope Chapter 3 Methodology - Primary Data - Secondary Data Chapter 4 Data Collection 4.0. Primary Data Collection 4.0.1.…
6. Wikipedia. (2006). Wikipedia Encyclopedia; searched Markowitz, CAPM, MPT, MCAD, Risk, and Diversification. Retrieved January 9, 2007 from http://en.wikipedia.org/…
In this project we are taking Large Capital Securities and Mid Capital Securities to construct an equity portfolio with the help of Sharpe’s model of portfolio construction.…
It is an honor and great pleasure for me to present my report on “Efficient Portfolio Construction”. This report was assigned to us as a partial requirement of the F-407 : Security pricing and portfolio theory course in fourth year second semester.…