...healthcare system can determine the appropriate portfolio mix based on their desired expected level of return and risk they are willing to accept. I. Mixes of STP & LTP Suppose different hospitals within the Partners system chose different mixes of the “risk-free” STP (short term pool) and the baseline LTP (long term pool), whose future expected returns and risks are shown in Exhibit 3. On Exhibit 3, plot the returns and risks of the various potential portfolios that can be formed by allocating funds between the STP and baseline LTP. What shape does a line drawn through these portfolios take? Why? In contrast, what would the risk-return opportunities available to the hospitals be if they could invest only in the STP and US Equities? Exhibit 1a plots the expected returns for the mix of portfolios with the “risk-free” STP and the baseline LTP. A straight line can be drawn through these portfolios as the expected return and standard deviation (i.e. volatility) increases with the greater weight allocation to the LTP. The straight line is observed due to these portfolios being comprised of a risk-free asset (i.e. STP) and a risky asset (i.e. LTP). Due to the composition, the expected return and risk are linearly related to the weight in the risky asset. It should be noted that the highest Sharpe ratio is from the portfolio that invests 90% in STP and 10% in LTP. Exhibit 1b plots the risk-return opportunities if only STP and US Equities are invested in. This chart...
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...Computational Finance Fall 2012 Daniel Egger Handout No. 2 Basic Statistics ! ! 2.1 Topics Covered 2.2 Mean and Median of a Data Set 2.3 Variance and Standard Deviation of a Data Set 2.4 Covariance and Correlation of two Data Sets 2.5 Standard Units (Z‐Scores) and their use for Calculating Correlation 2.6 Slope (Beta) and Y‐Intercept (Alpha) of the regression line of one stocks’s annual returns against annual market return 2.7 Calculating the Expected Return, and Volatility, of a Combination of Assets 2.8 Graphing the Efficient Frontier for Risk‐Averse, Profit‐Maximizing Investors 2.2 Mean and Median of a Data Set The Mean is the average of a set of n known values X = {x1 , x2 ,..., xn } . A sample mean can be written: 1 n x = " xi ! n i=1 (Note that if a “sample mean” and a “population mean” need to be distinguished, x is conventionally used for the sample mean, and µ for the population mean. This distinction will not concern us in Introductory Computational Finance). ! The mean may be calculated using the Excel function AVERAGE. ! The Median is the number in the middle of an ordered set of values; half of all values are greater, and half less. When the total number of values is even, the median is the average of the two numbers in the middle. The median may be calculated using the Excel function MEDIAN. 1 ! 2.3 Variance and Standard Deviation of a Data Set 2 The population Variance of a data set...
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...portfolio loss volatility or to portfolio capital, and compares them with absolute risk contributions. Marginal risk contributions serve essentially for risk-based pricing with an ‘ex ante’ view of risk decisions, while absolute risk contributions are the basis for the capital allocation system. Marginal risk contributions to capital are the correct references for risk-based pricing. Pricing based on marginal risk contributions charges to customers a mark-up equal to the risk contribution times the target return on capital. The mark-up guarantees that the return on capital for the entire portfolio will remain in line with the target return when adding new facilities. However, prices based on marginal risk contributions are lower than prices based on absolute risk contributions. This is a paradox, since the absolute risk contributions are the ones that sum to capital. In fact the new facility diversifies the risk of those existing facilities prior to the entrance of any new one. Therefore, adding a new facility results in a decline in all absolute risk contributions of existing facilities. Because of this decline, the overall return of the portfolio remains on target. However, the ex-ante measure of risk-based performance, on the marginal contribution and the ex-post measure, on the absolute contribution, differ for the same facility. The Marginal Risk Contributions The marginal contributions of a facility, or a sub-portfolio, to the portfolio loss volatility or to capital...
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...Chapter 6—The Tradeoff Between Risk and Return MULTIPLE CHOICE 1. Which of the following is an example of systematic risk? a. IBM posts lower than expected earnings. b. Intel announces record earnings. c. The national trade deficit is higher than expected. d. None of the above. ANS: C DIF: E REF: 6.4 The Power of Diversification 2. Which of the following is an example of unsystematic risk? a. IBM posts lower than expected earnings. b. The Fed raises interest rates unexpectedly. c. The rate of inflation is higher than expected. d. None of the above. ANS: A DIF: E REF: 6.4 The Power of Diversification 3. What do you call the portion of your total return on a stock investment that is caused by an increase in the value of the stock. a. Dividend yield. b. Risk-free return. c. Capital gain. d. None of the above. ANS: C DIF: E REF: 6.1 Understanding Returns 4. What is one of the most important lessons from capital market history? a. Risk does not matter. b. There is a positive relationship between risk and return. c. You are always better off investing in stock. d. T-bills are the highest yielding investment. ANS: B DIF: E REF: 6.2 The History of Returns 5. What is the purpose of diversification? a. Maximize possible returns. b. Increase the risk of your portfolio. c. Lower the overall risk of your portfolio. d. None of the above. ANS: C DIF: E REF: 6.4 The Power of Diversification NARRBEGIN: Bavarian Sausage Bavarian Sausage You bought a share of Bavarian Sausage stock...
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...relation of its returns with that of the financial market as a whole.[1] An asset with a beta of 0 means that its price is not at all correlated with the market. A positive beta means that the asset generally follows the market. A negative beta shows that the asset inversely follows the market; the asset generally decreases in value if the market goes up and vice versa.[2] The beta coefficient is a key parameter in the capital asset pricing model (CAPM). It measures the part of the asset's statistical variance that cannot be mitigated by the diversification provided by the portfolio of many risky assets, because it is correlated with the return of the other assets that are in the portfolio. Beta can be estimated for individual companies using regression analysis against a stock market index. Contents [hide] * 1 Definition o 1.1 Securities market line * 2 Beta volatility and correlation * 3 Choice of benchmark * 4 Investing * 5 Academic theory * 6 Multiple beta model * 7 Estimation of beta * 8 Extreme and interesting cases * 9 Criticism * 10 See also * 11 Notes * 12 External links [edit] Definition The formula for the beta of an asset within a portfolio is \beta_a = \frac {\mathrm{Cov}(r_a,r_p)}{\mathrm{Var}(r_p)} , where ra measures the rate of return of the asset, rp measures the rate of return of the portfolio, and Cov(ra,rp) is the covariance between the rates of return. The portfolio...
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...Business Research Papers Vol.3 No.2 June 2007, Pp. 362 - 375 362 Stock Return Volatility in Emerging Equity Market (Kse): The Relative Effects of Country and Global Factors Mohammad Faisal Rizwan* and Safi Ullah Khan** This paper focuses on the role of macroeconomic variables and global factors on the volatility of the stock returns in an emerging market like Pakistan. The paper uses two multivariate models, multivariate EGARCH and Vector Auto Regressive (VAR) models to investigate the effect of exchange rate, interest rate, industrial production, money supply, Morgan Stanley Capital International (MSCI) World Index and 6-months LIBOR on stock prices in Pakistan’s equity market. The estimate shows that domestic macroeconomic variables have varying degrees of importance in explaining the relationship between stock returns and volatility in Karachi Stock Exchange. The empirical results also show that the two global factors, MSCI World Index and 6-months LIBOR, variables used in this paper explain the stock returns in KSE. An important conclusion drawn from the results is that macroeconomic variables exhibit asymmetric effects on returns volatility. Overall, the results show that Pakistan’s stock market is partially integrated as shown by the significant role of both country and global factors. Field of Research: Finance 1. Introduction Studies on the link between macroeconomic variables and stock returns are broadly divided into two groups based on the level of market integration...
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...Market Volatility: Measures and Results Gary E. Mullins, Ph.D. University of Wisconsin - Stevens Point | | IntroductionVirtually everyone who is interested in financial markets seems to agree on two things: that markets are now more volatile than ever, and that volatility causes many problems. Let's look at some recent and not-so-recent articles concerning volatility. This week turned out to be slower than expected on the IPO market, as intense volatility on U.S. exchanges prompted many companies to put off much-anticipated debuts. I am writing to you today to address my concerns about trading in a fast market, a current issue of extreme importance to me. I want to give you my perspective and let you know the steps we at Schwab are taking to support investors during this time of market volatility. In recent months, there has been a marked increase in price volatility and volume in many stocks, particularly of companies that sell products or services via the Internet (Internet issuers). In the above quotes, there are two implicit assumptions: that volatility is higher now than it has been in the past, and that this volatility is somehow bad. In the first article, it assumes that (obviously) increased volatility has caused firms to delay their Initial Public Offerings (IPO's). Next, Schwab believes that investors need special support because of the high volatility inherent in today's market. Finally, Barrett appears to be more concerned about volatility for Internet...
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...T H E J O U R N A L THEORY & PRACTICE FOR FUND MANAGERS O F FALL 2013 Volume 22 Number 3 RISKBASED PORTFOLIOS special section The Voices of Influence | iijournals.com Pursuing the Low Volatility Equity Anomaly: Strategic Allocation or Active Decision? ERIK KNUTZEN ERIK K NUTZEN is the chief investment officer at NEPC LLC in Cambridge, MA. eknutzen@nepc.com FALL 2013 JOI-KNUTZEN.indd 75 I n the past several years, asset managers have built investment strategies based on historical evidence that lower volatility stocks earn superior risk-adjusted returns. These approaches are being called low volatility, managed volatility, minimum variance, or similar names. They seek to exploit what has been identified in studies by academics and practitioners alike as an equity pricing anomaly. This anomaly joins previously identified persistent stock market inefficiencies associated with low price-tobook and smaller company shares. This article evaluates the low volatility anomaly, its potential causes, whether it is likely to persist, and the role, if any, of low volatility equity investing in long-term investment programs. Based on historical information, we conclude that the low volatility equity anomaly appears to exist and can be explained by certain behavioral and structural biases of investors. But its continued existence into the future is less certain. We also observe that even well-documented anomalies experience multi-year...
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...index and exacerbates price distortions. Because trading against overvaluation exposes managers to greater risk of deviating from the index than trading against undervaluation, agency frictions bias the aggregate market upwards. They can also generate a negative relationship between risk and return because they raise the volatility of overvalued assets. Socially optimal contracts provide steeper performance incentives and cause larger pricing distortions than privately optimal contracts. buffa@bu.edu, d.vayanos@lse.ac.uk, p.k.woolley@lse.ac.uk. We thank Sergey Chernenko, Chris Darnell, Peter DeMarzo, Ken French, Jeremy Grantham, Zhiguo He, Ron Kaniel, seminar participants at Bocconi, Boston University, CEU, Cheung Kong, Dartmouth, LSE, Maryland, Stanford, and conference participants at AEA, BIS, CRETE, ESSFM Gerzenzee, FRIC, Jackson Hole, and LSE PWC for helpful comments. ∗ 1 Introduction Asset management is a large and growing industry. For example, individual investors held directly 47.9% of U.S. stocks in 1980 and 21.5% in 2007, with the remainder held by financial institutions of various types, run by professional managers (French (2008)). Asset managers’ risk and return is measured against benchmarks, and performance relative to the benchmarks determines the managers’ compensation and the funds they get to manage. In this paper we study how the...
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...depends on it. Another concept is the Capital Asset Pricing Model. There are three main assumptions that underlie the CAPM and allow us to identify the efficient portfolio of risky assets. 1. Securities are traded at competitive market prices 2. Investors choose efficient portfolios 3. Investors have homogenous expectations When these assumptions hold, the market portfolio and the efficient portfolio coincide. The efficient portfolio is the point where the capital market line, which is the line from the risk-free investment through the market portfolio, is tangent to the efficient frontier and represents the highest expected return available for any level of volatility. If we go up the efficient frontier investors can obtain portfolios by borrowing or lending at the risk-free rate. The security market line (SML) shows the expected return for each security as a function of its beta. Beta measures risk. Under the CAPM assumptions all stocks and portfolios should lie on the SML, which implies that the market portfolio is efficient. The second part of the task is an exercise which will...
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...Problem Set 1. Stocks offer an expected rate of return of 18%, with a standard deviation of 22%. Gold offers an expected return of 10% with a standard deviation of 30%. a. In light of the apparent inferiority of gold with respect to both mean return and volatility, would anyone hold gold? If so, demonstrate graphically why one would do so. Explain. Answer: Even though it seems that gold is dominated by stocks, gold might still be an attractive asset to hold as a part of a portfolio. If the correlation between gold and stocks is sufficiently low, gold will be held as a component in a portfolio, specifically, the optimal tangency portfolio. Efficient frontier Efficient frontier b. Given the data above, re-answer part (a) with the additional assumption that the correlation coefficient between gold and stocks equals 1.0. Draw a graph illustrating why one would or would not hold gold in one’s portfolio. Could this set of assumptions for expected returns, standard deviations, and correlation coefficients represent an equilibrium for the financial markets? Explain. Answer: If the correlation between gold and stocks equals +1, then no one would hold gold. The optimal portfolio would be comprised of bills and stocks only. Since the set of risk/return combinations of stocks and gold would plot as a straight line with a negative slope (see the following graph), these combinations would be dominated by the stock portfolio. Of course, this situation could not persist...
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...Corporation, Zecoon, Yokohama Industries, Woodlandoor, Wong Engeenering, White Horse Berhad, Whelcal Holding, Weida, Warisan TC Holding, Yinson Holding Berhad and YTL Power. While, the stock prices of 5 United State public listed company named by Adobe System INC, Alaska Air Group INC, Apple INC, The Aes Corporation and The NewYork Mellon Corporation. For stock prices of 5 United Kingdom public listed company named by Barclay, Bg Group, Big Yellow Group, Black Mount and Bovis Homes and lastly for the stock prices of 5 Indonesia public listed company named by Astra International, Bank Central Asia, Bank Danamon Indonesia, Kimia Farma and Unilever Indonesia. We also are required to demonstrate and explain the computations of annual return, risk, Sharpe ratio, return, covariance, beta, Treynor Ratio, portfolio standard deviation, and build a graph. THEORETICAL CONCEPTS In this assignment, we used the formula of Variances, Annual, Standard Deviation, Covariance, Correlation Coefficient, Beta, Variance Of Portfolio, Risk, Sharpe Ratio, Treynor Risk 1) Variance Variance measures how far a set of numbers is spread out. The variance measures how far each number in the set is from the mean. Variance is calculated by taking the differences between each number in the set and the mean, squaring the differences (to make them positive) and dividing the sum of the squares by the number of values in the set. 2) Annual...
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...portfolio and the five suppositions of portfolio selection need to be explained before the following discussion of the value of portfolios. The article ‘Portfolio Selection’, which was issued on Journal of Finance in 1952 and the book ‘Portfolio Selection: Efficient Diversification of Investments’ which was published in 1959 was known as the opening if the modern portfolio theory. The author of these two literatures is Harry M. Markowitz who was born in 1927, in America, and was awarded the Nobel Prize for Economics in 1990 for his outstanding contribution in economics. Simply speaking, the portfolio theory is that containing various securities and other assets in one collection of the investor, and of this collection could reach the highest return in the given level of risk or the...
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...ARAMIT: The expected rate of return is higher than the estimated rate of return and as a result the share of this company is overpriced. Institute holds more shares and government has no contribution here for investing so there is high risk and another issue for high risk is that the beta is more than one. This company issues bonus shares sometimes. Its P/E ratio represents that the share is fairly valued and the growth of earning is rising slowly. Net asset value per share is good so chance of losing at winding up or bankrupt is very much low. Though there are some positive issues the market is necessary regarding its rate of return so investors should buy shares. This company has a beta of greater than 1, offering the possibility of a higher rate of return, high market volatility but also posing more risk. 2. Berger paints Bangladesh ltd.: The expected rate of return is lower than the estimated rate of return so the share of this company is underpriced. This company does not give bonus shares. Net asset value per share is good so chance of losing at winding up or bankrupt is very much low. Considering all these issues one investor should buy the share of this company as everything is positive for buying though some issues are not in favor but those are negligence. This company has a beta of greater than 1, offering the possibility of a higher rate of return with higher risk. 3. BEXIMCO: The expected rate of return is higher than the estimated rate of return and as a result...
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...and investment. This project also study the relationship between expected return, standard deviation, coefficient of variation, covariance, correlation, beta and capital asset pricing model. One of the financial objectives of business organization is to maximize returns on its investments and operations. Various components of returns make up the returns to proportional with the various types of risks borne and market conditions. Risk can be defined as the chance of financial loss in the common of basic definition. Assets having greater chances of loss are viewed as more risky than those with lesser chances of loss. While for the return obviously assess to risk on the basis of flexibility of return then we need to be certain for what return is and how to measure it. For a company, investments and shares are always being the common equity and fund for them cycling their business every day. They must have their expected return in gaining a profit and a given trust towards their clients. Investment is the application of funds with the target of attaining additional income or growth in terms of value. This project is to calculate the closing daily share prices of five companies from the main market and KLCI for year 2013. Our group has proposed five companies which are Magnum Berhad, Faber Group Berhad, Gamuda Berhad, Scientex Berhad and Public Bank Berhad. The calculation is involve of the expected return, variance, standard deviation, coefficient of variation, covariance...
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