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"Portfolio analysis" redirects here. For theorems about the mean-variance efficient frontier, see Mutual fund separation theorem. For non-mean-variance portfolio analysis, see Marginal conditional stochastic dominance. Modern portfolio theory (MPT) is a theory of finance which attempts to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return, by carefully choosing the proportions of various assets. Although MPT is widely used in practice in the financial industry and several of its creators won a Nobel memorial prize for the theory,[1] in recent years the basic assumptions of MPT have been widely challenged by fields such as behavioral economics. MPT is a mathematical formulation of the concept of diversification in investing, with the aim of selecting a collection of investment assets that has collectively lower risk than any individual asset. That this is possible can be seen intuitively because different types of assets often change in value in opposite ways.[2] For example, to the extent prices in the stock market move differently from prices in the bond market, a collection of both types of assets can in theory face lower overall risk than either individually. But diversification lowers risk even if assets' returns are not negatively correlated—indeed, even if they are positively correlated.[3] More technically, MPT models an asset's return as a normally distributed function (or more generally as an elliptically distributed random variable), defines risk as the standard deviation of return, and models a portfolio as a weighted combination of assets, so that the return of a portfolio is the weighted combination of the assets' returns. By combining different assets whose returns are not perfectly positively...

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...The Development of Modern Finance "A Short History of Value" David Roubaud & Jean-Charles Bagneris 10/2011 The Main Steps of the Theory Building • Portfolio Selection (Markowitz, 1952) • CAPM (Sharpe, 1963) • Financing and Dividend Decisions Neutrality (Modigliani et Miller, 1958, 1961,1963) • Efficient Markets (Fama, 1965, 1970) • Options Pricing Theory (Black & Scholes, 1973, Myers, 1977) • Agency Theory (Jensen, Meckling, 1976) • Efficient Markets II (Fama, 1991) • Behavioural Finance (Kahneman & Tversky, 1979, Shiller, 1981, 2000) Portfolio Selection • Investors are rationals and risk averse • Diversification lowers specific risk • Any portfolio is a combination of the market portfolio and the riskless asset The CAPM Capital Asset Pricing Model • Systematic risk of an asset is measured by its beta coefficient • The model calibrates the risk-return relationship • Simple, elegant and linear model => big success • Low explaining power (strong assumptions) • Alternative models are difficult to use 1 The Development of Modern Finance 2 Financial Markets Efficiency "At any given point in time, assets prices on financial markets account for all available information." • Strong assumptions on: – markets organization – investors behaviour • One consequence of EMH is Random Walk Hypothesis • Assumptions are not always true: 3 forms of efficiency (strong, semi-strong, weak) The irrelevance of financing and dividends decisions In a world without taxes and with perfect financial......

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...‘ Investment Analysis & Portfolio Management Sharpe’s Single Index Model Practice Sheet -2 | |1. Betas of two stocks are 0.73 and 1.20 respectively. If the standard deviation of the market returns is 15.49%, the covariance between | | | |the two stock’s return is | | | |(a) 175.20(%)2 (b) 210.20(%)2 (c) 288.20(%)2 (d) 328.76(%)2 (e) 345.60(%) | | | | | | | |2. The index model for two stocks A and B is estimated as follows: | | | |RA = 2% + 0.65RM + eA , RB= 4% + 1.10RM + eB | | | |[pic] =25% | | | |(2 A = 0.15 and (2B = 0.30 (in relation to return on the market index) | | | |(The symbols are in standard notation) | | | |The correlation coefficient between the returns on two stocks is ...

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...Subject: Sound sheep funds ranking Per your request, I have compared the five funds based on the sharpe ratio, and Jensen alpha calculations. I also compared the result to the earlier analysis done based on average return, standard deviation and beta. Sharpe ratio, measures investment performance of the portfolio compared to risk taken. It’s most appropriate to use when evaluating diversified portfolios. Sharpe ratio penalizes non-diversified portfolios by also taking into account unsystematic risk. The high sharpe ratio represents the better performance for taking on additional risk. Wallflower Value Fund (WVF) shows the highest performance. The lowest is Mega Multinational Fund (MMF) (figure 1). Figure 1 Jensen's alpha is the excess return above or below the security market line. It can be interpreted as a measure of portfolio’s excess return over the market. A positive alpha shows the portfolio has a relatively high return given its level of systematic risk. Figure 2 below shows that the highest alpha belongs to WVF. Figure 2 In both ranking Wallflower Fund is showing the best return. The same reasoning was established when assessing the portfolio based on the average return, beta and stdev in the past. The beta of the fund is close to 1.0, the slope beta is slightly above 1.0, the Stdev relative to the average return is reasonable. Base on the alpha and sharpe’s calculation, the fund is receiving a high return while managing the risk. If we......

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...Fidelity Large Cap Stock Fund and S&P 500 are similar funds. These two funds heavily invest in large market capitalization company common stock, topping 80% of its entire portfolio. Fidelity Large Cap Stock Fund consists of normally 11 different sectors for equities listed in highest portfolio weight with first five sectors making 80% of the portfolio: • Financials • Information Technology • Health Care • Energy • Industrials • Consumer Discretionary • Consumer Staples • Telecommunication Services • Materials • Utilities • Other Current year-to-date performance of the Fidelity Large Cap Stock Fund (FLCSX) was overall positive at 16.24% year-to-date return. The financial sector contributed and played a big part in making the successful performance this year resulting from a good portfolio mixture of securities and its positive gain. This mixture consists of some of the high return securities such as; JPMorgan Chase, MetLife and Charles Schwab returning, 29.38%, 48.68% and 54.99% respectively. The historic performance has shown that both MetLife and Charles Schwab performed well responding to the rising interest rates, and these two companies did not fail to positively react to the recent increase in interest rates. Both companies’ share price went up by more than 20%. Thanks to the uptick in interest rates due to many speculation of slow economy recovery in the market. S&P 500 also had a strong year-to-date return at 13.82%. Both FLCSX and S&P 500......

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...risk, aggregate risk, or undiversifiable risk, is the risk associated with aggregate market returns. By contrast, unsystematic risk, sometimes called specific risk, idiosyncratic risk, residual risk, or diversifiable risk, is the company-specific or industry-specific risk in a portfolio, which is uncorrelated with aggregate market returns. Unsystematic risk can be mitigated through diversification, and systematic risk can not be.[1] Systematic risk should not be confused with systemic risk, the risk of loss from some catastrophic event that collapses the entire financial system. Contents [hide] * 1 Example * 2 Systematic risk and portfolio agement * 3 References * 4 See also | ------------------------------------------------- [edit]Example For example, consider an individual investor who purchases $10,000 of stock in 10 biotechnology companies. If unforeseen events cause a catastrophic setback and one or two companies' stock prices drop, the investor incurs a loss. On the other hand, an investor who purchases $100,000 in a single biotechnology company would incur ten times the loss from such an event. The second investor's portfolio has more unsystematic risk than the diversified portfolio. Finally, if the setback were to affect the entire industry instead, the investors would incur similar losses, due to systematic risk. Systematic Risk: It is the risk which is due to the factors which are beyond the control of the people working in the market and that's......

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...long as the correlation coefficient is below 1.0, the portfolio will benefit from diversification because returns on component securities will not move in perfect lockstep. The portfolio standard deviation will be less than a weighted average of the standard deviations of the component securities. 2. The covariance with the other assets is more important. Diversification is accomplished via correlation with other assets. Covariance helps determine that number. 3. a and b will have the same impact of increasing the Sharpe ratio from .40 to .45. 4. The expected return of the portfolio will be impacted if the asset allocation is changed. Since the expected return of the portfolio is the first item in the numerator of the Sharpe ratio, the ratio will be changed. 5. Total variance = Systematic variance + Residual variance = β2 Var(rM) + Var(e) When β = 1.5 and σ(e) = .3, variance = 1.52 × .22 + .32 = .18. In the other scenarios: a. Both will have the same impact. Total variance will increase from .18 to .1989. b. Even though the increase in the total variability of the stock is the same in either scenario, the increase in residual risk will have less impact on portfolio volatility. This is because residual risk is diversifiable. In contrast, the increase in beta increases systematic risk, which is perfectly correlated with the market-index portfolio and therefore has a greater impact on portfolio risk. 6. a. Without doing any......

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...the models to be discussed, i.e. Markowitz, Single Index, CAPM, and APT, have one single goal that is accomplished by using them. This goal is to make a portfolio, or individual securities, as efficient and well performing as possible by finding the optimal weights, highest return, and lowest risk. The Harry Markowitz model of 1952, or the mean-variance model, was one of the earliest models created to compare and contrast securities outcomes. This model uses the weights, standard deviation, and covariance for each security, creating a weighted covariance matrix, therefore forecasting a very accurate estimate of what return and risk the securities or portfolio would give. The Single-Index model, introduced by William Sharpe in 1963, is a simplified variation of the Markowitz model. Using the same premise of estimating in order to forecast optimal portfolios and securities, the single-index model instead uses beta and alpha substitutes for the standard deviation and covariance portions. Beta, measures the volatility of the portfolio or security comparatively to the market as a whole, i.e. the sensitivity to the market, and alpha, measures risk-adjusted performance (comparative to the appropriate benchmarks). These two combined simplify the process of the Markowitz model, while still gaining a result of the optimal portfolio. The Capital Asset Pricing model, or ‘CAPM’, produced by John Lintner in 1965, is a product that branched from the Single-Index model. While it does not...

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...Priest J. Gordon FIN 6300 – Managerial Finance West Texas A&M University Spring 2013 Diversification 1. According to the article, what is a personal beta? (4 points) A personal beta is one’s professional sensitivity to the stock market. 2. List one job you think would create the highest personal betas (4 points) and one job that would create the lowest personal betas(4 points). Briefly explain your choices. (4 points) A commission stock broker or financial advisor would have an extremely high beta considering that their profession is 100% tied to the stock market. Conversely, a Civil Engineer working for the Corps of Engineers would have no professional relation to the stock market and therefore a very low beta. 3. According to the article, use no more than two sentences to explain how a person with high personal beta should invest her financial capital? (4 points) She should withdraw from the stock market and look at other low risk opportunities. Her high beta exposes her to too much risk already before she invests any capital. 4. How does the weather in the United States last year compare to normal? (4 points) According to the article, who benefits and who loses because of this weather? (4 points) This has been a very mild winter for the majority of the country. Only the West Coast & New England area are experiencing their normal temp ranges for this time of year. The cities and states who pay for snow removal and preparations definitely benefit from the warmer weather....

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...FIN 475 Spring 2014 Cases in Financial Management Case 2 Prepared For Dr. Haskins By Kaylynn Burgess, Cody Jochim, and Richard Caldecott February 20, 2014 1. The case gave a table that had the rate or return under certain conditions and from that we found the expected returns, standard deviations, and coefficients of variations for the assets. For the expected returns we took the probability and multiplied that by the rate of return for each type of economy, and then added them all up. To get standard deviation you must first calculate the variance. For that we took the rate of return minus expected return, squared that difference, multiplied that by the probability, and then summed them up. The get the standard deviation we took the square root of the variance. To get the coefficient of variations we took the standard deviation and divided it by the expected return. | T-Bills | Market | Games Inc. | Outplace Inc. | Expected Return | 6% | 10% | 13% | 12% | Standard Deviation | .03824 | .0875 | .2259 | .1308 | CV | .6374 | .8746 | 1.7374 | 1.0897 | We ranked the assets from least risky to most risky by their standard deviation and coefficient of variation and the ranks were the same. The T-Bills were the least risky followed by the market, Outplace Inc., and then Games Inc. In the investing world, the coefficient of variation allows you to determine how much risk you are assuming in comparison to the amount of return you can expect from your......

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...------------------------------------------------- ------------------------------------------------- ------------------------------------------------- ------------------------------------------------- ------------------------------------------------- ------------------------------------------------- ------------------------------------------------- ------------------------------------------------- ------------------------------------------------- ------------------------------------------------- ------------------------------------------------- ------------------------------------------------- ------------------------------------------------- ------------------------------------------------- Efficient Portfolio Construction ------------------------------------------------- Prepared For: Pallabi Siddique Assistant Professor Department of Finance University of Dhaka ------------------------------------------------- Prepared By: Yasir bin yousuf Roll-16-036 Sec-B Department of Finance University of Dhaka ------------------------------------------------- Date of submission: ------------------------------------------------- November 24,......

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...returns on security and APT on International level demonstrating Factors Those are statistically significant 1.0 Multifactor model Pardalos (1997) defines multifactor model as a financial model which uses multiple factors during computation to explain a given market phenomena or at a given equilibrium market prices. The model is also useful in explaining both the individual and portfolio market securities. This is capable through comparison of two or more factors which are being analyzed to determine the relationship between the securities performance and the variables. Formula can be used to express the relationship Return on equity (Ri), Market return (Rm), factor search (F 1, 2…) 2.0 Arbitrage pricing theory (APT) The relationship between literature theories and the stock market behavior is the Asset Pricing model (Levy and Thierry 2005). Consigli and Wallace (2000) in their study, indicates that both are used in whenever securities are being given price and the individual assets risk are also being priced and can also be used in between portfolio to give a more insights of business activities and behavior hence helps in calculating related discounts security interest rates and also helps investors to take calculated risk before making decisions concerning type of investment they need to take. Arbitrage pricing Theory and model was initially discussed by Merton but later Ross (1976) offered further verifiable...

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...distribution (magnitude), p = price, E = expectation (which captures and combines the probability that different outcomes can/will happen) and m = SDF and captures the relation with other factors and the reward required to bear the risk inherent in x (it indicates how much (marginal) utility the outcome has, which captures the role of when we like the payoff more, the conditions matter; it captures the premium needed for this specific risk). The SDF can be derived from the utility function, this gives: . The problem with this is determining marginal utility. In many cases, the SDF is a linear function of a factor (CAPM): That factor f captures when returns in situation A may be more pleasant than the same returns in situation B. Portfolio theory (Risk & return: theory – empirics) Uses assumption A1 and A2, and more: Investors: A3. Agents maximize utility, and do so for 1 period. (Rationality: agents are capable to find the very best solution for their problem, and are willing to do so). A4. Utility is a function of expected return and variance (and nothing else). Market conditions: A5. No distortion from costs, transaction fees, inflation or taxes. If trading has costs, the optimum shifts (another allocation becomes optimal as fees eat...

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...Investment Portfolio Project University of Phoenix Introduction needs to go here | | |5 Yr Average | | | |Return | |T-bond |25% |0.02 | |Microsoft |20% |-0.33 | |Time Warner |10% |0.11 | |Disney |20% |0.02 | |Motorola |10% |-0.05 | |Home Depot |15% |-0.02 | | | | | |Average Return |-0.042 | |Risk Free | |-1.72 | | | | | | | |-1.76 | |STDEV | |0.15 | | | | | |Sharpe | |-11.65 | | | | | | | |5 Yr Average | | | |betas | | | |Return | | | | | |T-bond |25% |0.02 | | |Microsoft |1 | |Microsoft ......

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...price- $36.29 52 week range - $30.82-36.90 Expenses – 0.5% Management fees 0.38% Other expenses – 0.12% Type of Fund: open-ended fund. Class R shares are generally available only to retirement plans. Class R-5 are generally available only to fee-based programs or through retirement plan intermediaries. No dealer compensation is paid from fund assets on sales of Class R-5 or R-6 shares. I like that the expenses are low. It is a lower risk fund. Although it is a growth fund, it doesn’t seem to fluctuate that much. American Funds Capital World G/I R5 (RWIFX) 36.29 0.08(0.22%) Nov 27 Add to Portfolio Risk as of Oct 30, 2012 Get Risk for: Risk Overview Morningstar Risk Rating: 3 Number of Years Up 7 Number of Years Down 2 Best 1 Yr Total Return(Dec 30, 2003): 39.47% Worst 1 Yr Total Return(Dec 30, 2008): -38.21% Risk (Modern Portfolio Theory) Statistics 3 Years Statistic RWIFX Category Alpha (against Standard Index) 4.13 5.19 Beta (against Standard Index) 0.87 0.85 Mean Annual Return 0.68 0.76 R-squared (against Standard Index) 95.16 86.55 Standard Deviation 17.40 17.88 Sharpe Ratio 0.47 0.53 Treynor Ratio 7.89 10.04 5 Years Statistic RWIFX Category Alpha (against Standard Index) 2.91 2.36 Beta (against Standard Index) 0.87 0.89 Mean Annual Return 0.02 -0.03 R-squared (against Standard Index) 96.30 89.30 Standard Deviation 20.80 22.04...

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...FINANCIAL INSTITUTIONS AND PORTFOLIO MANAGEMENT FINANCIAL INSTITUTIONS AND PORTFOLIO MANAGEMENT Introduction The household has two sources of income namely the husband earning $100,000 per year as a middle level manager in a fortune 500 Company and the wife who is an attorney and also earns $100,000 per year. The couple has no children and as such they do not have expenses such as school fees, upbringing costs for the children. The couple is middle aged and as such their appetite to risk is relatively lower than their younger counterparts and relatively higher than their older counterparts. This report shall therefore create an investment plan for the couple which shall include the portfolio that the couple should invest in order to realize their investment goals and also to help them minimize the risk associated with such an investment. The report shall peg the performance of the portfolio created against a benchmark and shall then discuss the rationale behind the benchmark portfolio selected. The report shall discuss the portfolio performance over the last five years and determine the average weekly returns of the portfolio over the same period and compare it with the returns of the benchmark portfolio. The report shall then calculate the standard deviation of the portfolio and discuss the factors that led to the performance of the portfolio and the benchmark portfolio such as the economy, market specific factors, industry specific factors, as well as country......

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