...The optimal risky portfolio asked me to shortsell the market for -1.6081 and invest 280.1% of my investable wealth in the active portfolio. Within the active portfolio itself, among 16 different tickers that I chose, my optimal weights were to invest in Kraft, General Mills, Visa, and Walmart. Running a regression of Risky Portfolio HPR against Market Portfolio HPR, we obtain the below line fit plot. Though the fit may not look all that bad, it is actually quite low with a R^2 of roughly 0.3. This does not come as too big of a surprise, though, as the risky portfolio utilizes active portfolio management that itself aims to break from the market. Also, the 16 tickers I used in this exercise could not possibly reflect all of the movements of the S&P market index. To extend our analysis of the relationship between the risky portfolio and market portfolio, we consult the following graph modeling their quantitative movements over roughly the past four months. As one would expect, the Risky HPR fluctuates a lot wilder than the Market HPR does. However, it does not consistently stray in any one direction away from 0%. Interestingly, looking at the dollar paths tells us a completely unexpected story. Usually we would expect an actively managed, risky portfolio to generate higher returns (barring transaction fees) than a passive, market portfolio. Yet here, we see that the dollar path of the market in fact outgrows the dollar path of the risky portfolio. In fact, by the...
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...long haul contributing is the conservation of capital. Warren Buffett, ostensibly the world's most excellent mogul, has one standard when contributing - never lose cash. This doesn't mean you ought to offer your venture property the minute they enter losing region, yet you ought to remain definitely mindful of your portfolio and the losses you're ready to persevere in an exertion to expand your riches. While it is difficult to stay away from danger completely when putting resources into the business sectors, these five strategies can help protect your portfolio. One of the foundations of Modern Portfolio Theory (MPT) is diversification. In a business downturn, MPT pupils accept a generally expanded portfolio will beat a thought one. Speculators make deeper and all the more extensively broadened portfolios by owning countless in more than one asset class, along these lines decreasing unsystematic danger. This is the hazard that accompanies putting resources into a specific organization instead of deliberate danger, which is the danger connected with putting resources into the businesses by and large. As per some money related specialists, stock portfolios that incorporate 12, 18 or even 30 stocks can take out most, if not all, unsystematic danger. Shockingly, methodical danger is constantly present and can't be differentiated away. On the other hand, by including non-associating asset classes, for example, securities, items, monetary standards and land to a gathering...
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...2. Mean-variance portfolio theory (2.1) Markowitz’s mean-variance formulation (2.2) Two-fund theorem (2.3) Inclusion of the riskfree asset 1 2.1 Markowitz mean-variance formulation Suppose there are N risky assets, whose rates of returns are given by the random variables R1 , · · · , RN , where Rn = Sn(1) − Sn (0) , n = 1, 2, · · · , N. Sn(0) Let w = (w1 · · · wN )T , wn denotes the proportion of wealth invested in asset n, N with n=1 wn = 1. The rate of return of the portfolio is N RP = n=1 wnRn . Assumptions 1. There does not exist any asset that is a combination of other assets in the portfolio, that is, non-existence of redundant security. = (1 1 · · · 1) are linearly independent, otherwise 2. µ = (R1 R2 · · · RN ) and RP is a constant irrespective of any choice of portfolio weights. 1 2 The first two moments of RP are N N µP = E[RP ] = n=1 E[wn Rn] = n=1 N wnµn, where µn = Rn, and 2 σP = var(RP ) = N N N wiwj cov(Ri, Rj ) = i=1 j=1 i=1 j=1 wiσij wj . Let Ω denote the covariance matrix so that 2 σP = wT Ωw. For example when n = 2, we have (w1 w2 ) σ11 σ12 σ21 σ22 w1 w2 2 2 2 2 = w1 σ1 + w1w2(σ12 + σ21) + w2 σ2 . 3 Remark 2 1. The portfolio risk of return is quantified by σP . In mean-variance analysis, only the first two moments are considered in the portfolio model. Investment theory prior to Markowitz considered the maximization of µP but without σP . 2. The measure of risk by variance would place equal weight on the upside deviations and downside...
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...Assumptions of Portfolio Theory • Investors are rational. • Investors are basically risk averse. • Investors wants to maximize the returns from his/her investments for a given level of risk. • Investor portfolio includes all of his/her assets and liabilities. • The relationship between the returns of assets in the portfolio is important since the returns from these investments interact with each other. Risk Aversion • Portfolio Theory assumes investors are basically risk averse. • Risk aversion means an investor, given a choice between two assets with equal rates of return, will select the asset with the lower level of risk. • Does not imply everybody is risk averse. • Most investors when committing large sums of money in developing an investment portfolio are risk averse. • This means investors expect a positive relationship between expected return and expected risk. Definition of Risk • Risk is the uncertainty of future outcomes. • Probability of an adverse outcome. Markowitz Portfolio Theory • Developed by Harry Markowitz in the 1950s. • Won a Nobel Prize for his work. • Basic portfolio model derived the expected rate of return for a portfolio of assets and an expected risk measure. Markowitz Portfolio Theory • He used variance of the rate of return as a measure of portfolio risk under a reasonable set of assumptions. • He also derived the formula for computing variance of a portfolio. Assumptions of Markowitz Model • Investors consider each investment...
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...fundamentals of the modern portfolio theory In the first paragraph we show the crucial differences between the modern portfolio theory and pre-Markowitz one, summarize the mathematical framework of the MPT and critically evaluate the core assumptions building the MPT. This paragraph is devoted to the second stage of the portfolio selection process assuming that all input parameters of the model are true. 2.1 Definition of the modern portfolio theory Harry Markowitz is highly regarded as a pioneer in theoretical justification of investor’s behavior and development of optimization model for portfolio selection process. In 1990, Markowitz shared a Nobel Prize for his contributions to financial economics and corporate...
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...To reiterate some of the assumptions that Ellie mentioned earlier plus a few more. These misleading assumptions have been proven wrong so they weaken the theory. * Assumptions: * All investors act rationally and are risk-averse. Proven wrong by behavioural economists. * Investors all have access to the same sources of information for investment decisions False because market is asymmetrical with information – due to insider trading and some investors are more informed than others. Many online publications charge members to access their sites, such as The Wall Street Journal or Bloomberg. So investors who don’t pay the additional fee are not as informed. * Investors base decisions solely on expected return and risk (derived from historical returns). The drawback is that optimal asset allocations are highly sensitive to small changes in inputs, especially expected returns. Portfolios may not be well diversified. * Investors can borrow and lend at a risk-free rate. The drawback is that borrowing rates are always higher than lending rates. Certain investors are restricted from purchasing securities on margin. * Investors can buy securities of any size. False as some securities have minimum order sizes. And securities cannot be bought or sold in fractions. Also, each investor has a credit limit so they cannot lend or borrow unlimited amounts of shares. * Single-period perspective. Investors rarely have a single-period perspective...
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...Modern Portfolio Theory in the Modern Economy: MPT During the Credit Crisis 0f 2008 Abstract There are various theories of risk and return as it pertains to measuring and predicting investment return in a portfolio- one of the oldest and most prominent being Modern Portfolio Theory .An example of a hypothetical portfolio utilizing the principles of MPT invested during the credit crisis of late 2008/early 2009 will be utilized in part. In direct application, does Modern Portfolio theory hold strong during a major financial crisis? Past research will be compared to present the mechanics and applications of MPT order to answer the questions poised and to create hypothetical portfolios based on past fund performance during the time period of 2007 -2010. It is expected that a portfolio using MPT would not have performed significantly better than any other less diversified investment. Contents Introduction……………………………………..........................................................................4-7 Credit Crisis Thesis Statement Modern Portfolio Defined Prior Research Prediction Method…………………………………………………….........................................................8-9 Parameters/ Source of Portfolios Results……………………………………………………......................................................10-19 A. Application/ graphs Conclusion…………………………………………...............………………………............19-20 Restatement of Thesis Discussion of Results Limitations Recommendation References……………………………………………………………………...
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...PORTFOLIO THEORY Let us begin our discussion on Portfolio Theory with an example of two investments (assets or securities) – Ace and Bravo. Their return expectations are given in the table below. You will notice that both Ace and Bravo are risky investments because they do not offer a certain return. You can begin by comparing the expected return and risk of Ace and Bravo: State of Probability Return Economy of occurrence Ace Bravo Boom 0.2 +20 -15 Growth 0.6 +5 +5 Recession 0.2 -10 +25 1. What kind of a correlation do you observe between the two securities? 2. Calculate the expected return and standard deviation of both Ace and Bravo. Interpret the results. Expected Return = E(R) = ∑ ri.pi for each state of the economy Standard Deviation = σ = √ [∑(ri – E(R))2 .pi] Thus calculated, we have the following results: |Security |Expected Return |Expected Risk | | | |(measured by σ) | |Ace |5% |±9.49% | |Bravo |5% |±12.65% | Ace is better than Bravo when viewed in the risk-return framework, because it offers...
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...6053 BAUSAE Personal Finance Portfolio Report on Trading Investment Strategy Oct-Nov 2012 Nicola Kirk-420355 Word count-2870 Contents Justification of Strategy 3-4 EMH Portfolio Performance 5-9 Taxation Calculations Evaluation of portfolio performance 10-11 Jensen Treynor Sharpe Appendix 12 Bibliography 13 Justification of strategy After receiving the inheritance of £100,000 the first major financial decision was to select an account to invest the total amount in. I placed it in an instant access account with Derbyshire Building Society with an annual interest rate of 2.5% AER which included a 1% bonus for the first year. This allowed unlimited free withdrawals and a minimum balance of £1(after the initial opening balance of £1,000). This is a very low risk investment, as the first £85,000 would be protected also giving a small but constant and reliable income from the interest. In addition to this the account can be very easily liquidated when required. Hargreaves Lansdown was the stockbroker chosen for all trading as they offered competitive rates. They charge £11.95 for 0-9 transactions, £8.95 for 10-19 transactions and £5.95 for 20+ transactions. When deciding what assets to invest in I decided not to invest in currency, as they are extremely volatile, unpredictable and wouldn’t give as significant a return due...
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... 5 Padma Oil---------------------------------------------------------------------------------------Page 5 Singer Bangladesh-----------------------------------------------------------------------------Page 6 South East Bank-------------------------------------------------------------------------------Page 7 Standard Ceramics----------------------------------------------------------------------------Page 7 Square Pharmaceuticals-----------------------------------------------------------------------Page 8 Findings and Analysis Arithmetic Mean and Standard Deviation--------------------------------------------------Page 9 Correlation Coefficient and Covariance----------------------------------------------------Page 9 Portfolio Risk and Return-------------------------------------------------------------------Page 11 Efficient Frontier-----------------------------------------------------------------------------Page 13 Calculated Beta and Comparison with Market Beta-------------------------------------Page 14 Required Return using CAPM--------------------------------------------------------------Page 15...
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...| 0.21 | -0.07 | REITs | 0.56 | 0.45 | 0.21 | 1 | -0.01 | Commodities | -0.05 | 0.01 | -0.07 | -0.01 | 1 | | | | | | | Covariance with: | | US Equity | Foreign Equity | Bonds | REITs | Commodities | US Equity | 0.02455489 | 0.017194378 | 0.003944923 | 0.010635542 | -0.001422053 | Foreign Equity | 0.017194378 | 0.02322576 | 0.001381201 | 0.008311896 | 0.000276606 | Bonds | 0.003944923 | 0.001381201 | 0.01014049 | 0.002563016 | -0.001279394 | REITs | 0.010635542 | 0.008311896 | 0.002563016 | 0.01468944 | -0.000219978 | Commodities | -0.001422053 | 0.000276606 | -0.001279394 | -0.000219978 | 0.03294225 | Question 4 Portfolio weights for given Expected returns (generated via Solver) | Min Variance | Portfolio 1 | Portfolio 2 | Portfolio 3 | Portfolio 4 | Portfolio 5 | Portfolio 6 | Portfolio 7 | Portfolio 8 | Expected Return | 0.077691577 | 0.08 | 0.085 | 0.09 | 0.095 | 0.1 | 0.105 | 0.11 | 0.115 | Variance | 0.072897979 | 0.073085745 | 0.074755718 | 0.078050518 | 0.082776348 | 0.088704786 | 0.095612388 | 0.103302919 | 0.111614658 | Slope | 1.065757625 | 1.0946047 | 1.137036767 | 1.153099335 | 1.14767083 | 1.127334888 | 1.098184055 | 1.064829543 | 1.030330622 | | | | | | | | | | | US Equity | -0.069956996 | -0.047943261 | -0.000660991 | 0.046621225 | 0.093903482 | 0.141185707 | 0.188467905 | 0.23575012 | 0.28303232 | Foreign Equity | 0.164559275 |...
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...should be keenly evaluated with the possible risks to help determine a smart alpha investment strategy. According to him, a well performing firm uses smart alpha as its investment strategy, bearing in mind its long run profitability as compared to smart beta strategies. For instance, the smart alpha strategy analyses the risks prone to certain capitalization investment and develops a strategy that would conform to such risk and benefit at the same time. Positive outcome relating to these forms of strategic investments is only determined by keen analysis of market inefficiencies and making use of the vulnerability to gain. This makes Stanyer (2014) to argue that although most investors have been using smart beta to measure their investment portfolios, it is more risk averse than smart alpha. He justifies this using the recent use of smart alpha by most firms to realize and analyse smart beta for their successful investment gains (Stanyer 2014). Superior performance of smart beta on the market Smart beta a passive investment strategy, aiming at minimizing risks in...
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...Beth A. Walker Balancing Risk and Return in a Customer Portfolio Marketing managers can increase shareholder value by structuring a customer portfolio to reduce the vulnerability and volatility of cash flows. This article demonstrates how financial portfolio theory provides an organizing framework for (1) diagnosing the variability in a customer portfolio, (2) assessing the complementarity/similarity of market segments, (3) exploring market segment weights in an optimized portfolio, and (4) isolating the reward on variability that individual customers or segments provide. Using a seven-year series of customer data from a large business-to-business firm, the authors demonstrate how market segments can be characterized in terms of risk and return. Next, they identify the firm’s efficient portfolio and test it against (1) its current portfolio and (2) a hypothetical profit maximization portfolio. Then, using forward- and back-testing, the authors show that the efficient portfolio has consistently lower variability than the existing customer mix and the profit maximization portfolio. The authors provide guidelines for incorporating a risk overlay into established customer management frameworks. The approach is especially well suited for business-to-business firms that serve market segments drawn from diverse sectors of the economy. Keywords: customer portfolio management, market-based assets, financial portfolio theory, return on marketing, market segmentation The advantage...
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...Economics Financial Theory Ben McClure Contact | Author Bio Advertisement No matter how much we diversify our investments, it's impossible to get rid of all the risk. As investors, we deserve a rate of return that compensates us for taking on risk. The capital asset pricing model (CAPM) helps us to calculate investment risk and what return on investment we should expect. Here we look at the formula behind the model, the evidence for and against the accuracy of CAPM, and what CAPM means to the average investor. Birth of a Model The capital asset pricing model was the work of financial economist (and, later, Nobel laureate in economics) William Sharpe, set out in his 1970 book "Portfolio Theory And Capital Markets." His model starts with the idea that individual investment contains two types of risk: Systematic Risk - These are market risks that cannot be diversified away. Interest rates, recessions and wars are examples of systematic risks. Unsystematic Risk - Also known as "specific risk," this risk is specific to individual stocks and can be diversified away as the investor increases the number of stocks in his or her portfolio. In more technical terms, it represents the component of a stock's return that is not correlated with general market moves. Modern portfolio theory shows that specific risk can be removed through diversification. The trouble is that diversification still doesn't solve the problem of systematic risk; even a portfolio of all the shares...
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...Harry Markowitz, who’s earlier work, introduced the theory of modern portfolio and diversification. Along with Markowitz (1952), he began the theory of the model in 1956 when he was trying to find a dissertation topic. He built on Markowitz’s suggestions and set out his developed theory in his book “Portfolio Theory and Capital Markets.” (1970). This essay will try to outline the Capital Asset Pricing Model, explain the theory behind the model and outlay its uses. This will be done by using legal texts, journals and other resources. It is never possible to get rid of all the risk when investing and the actual return on an investment may differ from what the investor expects. For that reason investors always look for a rate of return that will repay them for their risk taking. The Capital Asset Pricing Model (CAPM) is a model that relates risk and return, helping investors calculate the risk of the investment and the return on the investment that should be expected. Haim Levy and Thierry Post (2005, p883) define the model as an “equilibrium asset-pricing model that predicts a linear relationship between expected return and beta.” It would be assumed that if an investor has decided to invest in a number of companies, the risk of the portfolio would be the average risk of each of the investments. However, the portfolio risk is in fact smaller therefore; the overall risk can be reduced by diversifying the investments in a portfolio. This is done by investing in a variety of investments...
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