24 Functions are not Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods are are are are are are are are are are are are are are are are are are are are are are are are not not not not not not not not not not not not not not not not not not not not not not not not Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods are are are are are are are are are are are are are are are are are are are are are are are are not not not not not not not not not not not not not not not not not not not not not not not not Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods F are are are are are are are are are are are are are are are are are are are are are are are are not not not not not not not not not not not not not not not not not not not not not not not not Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods Methods are are are are are are are are are are are are are are are are are are are are are are are are not not not not not not not not not not not not not not not not not not not not not not not not Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions Functions
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FY 2003/2004 Budget DevelopmentNew Faculty Positions Funded Department Title Name Salary Marketing Assistant Professor Suh, Taewon 75,024 CIS Assistant Professor To Be Named 82,000 Finance & Economics Assistant Professor To Be Named 85,000 Curriculum & Instruction Assistant Professor To Be Named 47,481 Art & Design Assistant Professor Blanco, Ivanette 43,128 Unallocated 7,171 Undergraduate Education 339,804 EAPS Assistant Professor To Be Named 48,000 Mass Communications Assistant Professor To Be Named 42,000 Finance & Economics Assistant Professor To Be Named 91,000 Family & Consumer Science Assistant Professor To Be Named 45,000 CIS & Quantitative Methods Assistant Professor To Be Named 75,000 Anthropology Assistant Professor To Be Named 38,000 Curriculum & Instruction Assistant Professor To Be Named 48,000 Art & Design Assistant Professor To Be Named 48,000 Special Opportunities (3-4) Assistant Professor To Be Named 354,139 Advising and OSFA Savings 789,139 Aquatic Resources Ph.D. Assistant Professor, 12-month Huston ,Michael 95,319 Aquatic Resources Ph.D. Assistant Professor, 12-month To Be Named 85,029 Assistant Professor To Be Named 70,200 Education Ph.D. New Program 250,548 6
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John Lochman – Interim Director, Alabama Life Research Institute Saxon Professor Emeritus of Psychology Director Emeritus, Center for Prevention of Youth Behavior Problems [EC] 2018-2019 Advisory Board • Carol Agomo – Director of Community and Administrative Affairs, UA Division of Community Affairs • David Albright - Hill Crest Foundation Endowed Chair in Mental Health and Associate Professor in School of Social Work • Susan Burket – Alabama Power Foundation Endowed Professor, College of Engineering • Jason DeCaro – Professor of Anthropology, College of Arts and Sciences • Thomas English – Assistant Professor of Management, Culverhouse College of Business • Patrick Frantom – Associate Professor of Chemistry, College of Arts and Sciences • Safiya George – Associate Professor of Nursing, & Assistant Dean for Research, College of Nursing • John Higginbotham – UA Interim Vice President for Research; Director, Institute for Rural Health Research; Professor and Chair of the Department of Community and Rural Medicine, College of Community Health Sciences [EC] • Mathew Jenny – Associate Professor of Biology, College of Arts and Sciences • Debra McCallum – Director, Institute for Social Science Research; Senior Research Social Scientist [EC] • Kagendo Mutua – Professor, Severe and Profound Disabilities and Transition, College of Education • Laura Myers – Director, Center for Advanced Public Safety, College of Engineering; Senior Research Scientist • Patricia Parmelee – Director, Alabama Research Institute on Aging; Professor of Psychology, College of Arts and Sciences [EC} • Jason Parton – Director, Institute for Business Analytics (and Data Analytics Lab); Assistant Professor, Culverhouse College of Commerce [EC] • Edward Sazonov – Associate Professor of Electrical and Computer Engineering, College of Engineering • Xiangrong Shen – Associate Professor of Mechanical Engineering, College of Engineering • Stuart Usdan – Professor and Dean, College of Human Environmental Sciences • Thomas Weida - Associate Dean of Clinical Affairs, Chief Medical Officer for University Medical Center, College of Community Health Sciences • Susan White – Professor & Doddridge Saxon Chairholder in Clinical Psychology, Colege of Arts & Sciences; Director, Center for Prevention of Youth Behavior Problems [EC]
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Determining the Optimal Portfolio • If we can plot the portfolio return vs. Portfolio volatility for all possible allocations (weights), then we can easily locate the optimal portfolio with the highest Sharpe ratio of (Rp - Rf)/(Vol of risky portfolio). • When we only have two risky assets, as in this case, it is easy to construct this graph by simply calculating the portfolio returns for all possible weights. • When we have more than 2 assets, it becomes more difficult to represent all possible portfolios, and instead we will only graph only a subset of portfolios. Here, we will choose only those portfolios that have the minimum volatility for a given return. We will call this graph the variance-return frontier. • Once we solve for this minimum variance frontier, we will show that there exists one portfolio on this frontier that has the highest Sharpe ratio, and thus is the optimal stock portfolio. • Because there exists one specific portfolio with the highest Sharpe ratio, all investors will want to invest in that portfolio. Thus, the weights that make up this portfolio determines the optimal allocation between the risky assets for all investors. 14
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Determining the Optimal Portfolio • If we can plot the portfolio return vs. portfolio volatility for all possible allocations (weights), then we can easily locate the optimal portfolio with the highest Sharpe ratio of (Rp - Rf)/(Vol of portfolio). • When we only have two risky assets, it is easy to construct this graph by simply calculating the portfolio returns for all possible weights. • When we have more than 2 assets, it becomes more difficult to represent all possible portfolios, and instead we will only graph only a subset of portfolios. Here, we will choose only those portfolios that have the minimum volatility for a given return. We will call this graph the minimum variance frontier. • Once we solve for this minimum variance frontier, we will show that there exists one portfolio on this frontier that has the highest Sharpe ratio, and thus is the optimal stock portfolio. • Because there exists one specific portfolio with the highest Sharpe ratio, all investors will want to invest in that portfolio. Thus, the weights that make up this portfolio determines the optimal allocation between the risky assets for all investors.
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How do we get the CAPM from the assumptions? 8  Now, if we look at any portfolio on the efficient frontier, we can think of   it as being the result of maximizing the expected excess return on the portfolio subject to the variance being equal to a certain value. This is equivalent to ensuring that the ratio of (a) the marginal contributions by each asset to portfolio expected excess return to (b) the marginal contributions of each asset to portfolio variance. Hence it must be true for each asset that [E(ri)-rf]/Cov(ri, rP) is the same. Since all investors have the same information, they will all have the same portfolio of risky assets in their overall portfolio. This is the market portfolio. Since investors choose their portfolios optimally, their portfolios are efficient. Hence the market portfolio is also efficient. Hence this relationship is true of the market portfolio. That is, [E(ri)-rf]/Cov(ri, rm) is the same for all assets/portfolios in the market portfolio. But the market portfolio itself can be considered a portfolio within itself. Hence [E(ri)-rf]/Cov(ri, rm) = [E(rm)-rf]/Cov(rm, rm) = [E(ri)-rf]/Var(rm). If we define , it follows that E()-=[)-]
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Identifying the Tangent Portfolio Combinations of the risk-free asset and the tangent portfolio provide the best risk and return tradeoff available to an investor.  This means that the tangent portfolio is efficient and that all efficient portfolios are combinations of the risk-free investment and the tangent portfolio. Every investor should invest in the tangent portfolio independent of his or her taste for risk.  An investor’s preferences will determine only how much to invest in the tangent portfolio versus the risk-free investment.  Conservative investors will invest a small amount in the tangent portfolio.  Aggressive investors will invest more in the tangent portfolio.  Both types of investors will choose to hold the same portfolio of risky assets, the tangent portfolio, which is the efficient portfolio.
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CAPM and the Sharpe Ratio (1/2) • Recall from our earlier analysis, recall that, given the assets in the economy there is only one way to form an optimal portfolio. • Under certain assumptions, the Capital Asset Pricing Model states that this optimal risky portfolio (with the highest Sharpe ratio) must be the market portfolio. – Think of the market portfolio as a portfolio of all assets in the economy. • Strictly speaking, this market portfolio is unobservable. However, in practice (as we have done before), we proxy the market portfolio by a broad index like the S&P 500. • Thus, if the CAPM is correct, then the market portfolio (like the S&P 500) is the portfolio with the highest Sharpe ratio, and all of us should invest in this portfolio. .
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Approximation Errors Optimal Solution for Lymann Brothers Example • R1 = 12.51 (12.51% portfolio return for scenario 1) • R2 = 12.90 (12.90% portfolio return for scenario 2) • R3 = 7.13 ( 7.13% portfolio return for scenario 3) • R4 = 2.51 ( 2.51% portfolio return for scenario 4) • IS = 0 ( 0.0% of portfolio in international stock) • LC =Portfolio 0 ( 0.0% portfolio Lymann Brothers Return vs. S&P of 500 Returnin large-cap Scenario blend) Portfolio Return S&P 500 Return • MC = .332 (33.2% of portfolio in mid-cap 1 12.51 13.00 blend) 2 12.00(16.1% of portfolio in small-cap • SC 12.90 = .161 3 7.13 7.00 blend) 4 2.51 2.00 • IB = .507 (50.7% of portfolio in intermediate BA 452 Lesson B.6 Nonlinear Programming bond) 24  
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Variance  Optimal Solution • R1 = 10.63% portfolio return for scenario 1 • R2 = 12.20% portfolio return for scenario 2 • R3 = 8.93% portfolio return for scenario 3 • R4 = 4.24% portfolio return for scenario 4 • Rbar = 9.00% expected portfolio return • IS = 0.00% of portfolio in international stock • LC = 25.10% of portfolio in large-cap blend • MC = 0.00%of portfolio in mid-cap blend • SC = 14.1% of portfolio in small-cap blend • IB = 60.8% of portfolio in intermediate bond 100.0% of portfolio BA 452 Lesson B.6 Nonlinear Programming 45
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Frontier with KO and PEP • As an example, consider a portfolio of KO and PEP. What should be the optimal combination of KO and PEP? – Refer to excel file on web page. • As we only have two assets here, we can easily tabulate the Sharpe ratio for a range of portfolio weights, and check which portfolio has the highest Sharpe ratio. • The next slide shows the results. In the calculation of the Sharpe ratio, it is assumed that the riskfree rate is constant (which is not strictly true). The portfolio mean and portfolio return are calculated with the usual formulae over the 10-year sample period 1993-2002, with monthly data. • As can be seen, the optimal weight for a portfolio (to get the maximum Sharpe ratio) appears to be in the range of 0.6 in KO. If the exact answer is required, we can easily solve for it using the excel solver. • It can also be observed that, amongst these 11 portfolios, the portfolio with the minimum volatility is one that invests 50% in each of the two stocks. This is the minimum variance portfolio. The minimum variance portfolio may be different from the portfolio with the highest Sharpe ratio. 15
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Portfolios and Single Assets 21 Why is there a difference between asset classes and single assets? Can we come up with a single theory to explain both? To do this, we need to realize that when we put together single assets in a portfolio, the volatility of the portfolio diminishes, the greater is the number of assets in the portfolio. This can be seen once we note two things: One, the return on a portfolio of assets is the average return on the different assets making up the portfolio.  Thus, if we have a portfolio invested equally over 4 assets earning 2%, 4% and 9% respectively, the return on the portfolio is (2+4+9)/3 = 5% Two, as we said earlier, if the different observations used to compute an average are independent, then the standard deviation for the average, s.e. equals s.d./√n, where n is the number of observations and s.d. is the standard deviation of the observations. So if the return on a portfolio is an average, can we say that if a portfolio consists of 100 assets, the standard deviation of the returns on the portfolio is one-tenth of the standard deviation of the returns on an individual asset?
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Avoid Redundant I/O: C An actual piece of code seen at OU: for (thing = 0; thing < number_of_things; thing++) { for (timestep = 0; timestep < number_of_timesteps; timestep++) { read_file(filename[timestep]); do_stuff(thing, timestep); } /* for timestep */ } /* for thing */ Improved version: for (timestep = 0; timestep < number_of_timesteps; timestep++) { read_file(filename[timestep]); for (thing = 0; thing < number_of_things; thing++) { do_stuff(thing, timestep); } /* for thing */ } /* for timestep */ Savings (in real life): factor of 500! Supercomputing in Plain English: Storage Hierarchy Tue Jan 29 2013 86
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Avoid Redundant I/O: C An actual piece of code seen at OU: for (thing = 0; thing < number_of_things; thing++) { for (timestep = 0; timestep < number_of_timesteps; timestep++) { read_file(filename[timestep]); do_stuff(thing, timestep); } /* for timestep */ } /* for thing */ Improved version: for (timestep = 0; timestep < number_of_timesteps; timestep++) { read_file(filename[timestep]); for (thing = 0; thing < number_of_things; thing++) { do_stuff(thing, timestep); } /* for thing */ } /* for timestep */ Savings (in real life): factor of 500! NCSI Parallel & Cluster: Storage Hierarchy U Oklahoma, July 29 - Aug 4 2012 70
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Avoid Redundant I/O An actual piece of code seen at OU: for (thing = 0; thing < number_of_things; thing++) { for (time = 0; time < number_of_timesteps; time++) { read(file[time]); do_stuff(thing, time); } /* for time */ } /* for thing */ Improved version: for (time = 0; time < number_of_timesteps; time++) { read(file[time]); for (thing = 0; thing < number_of_things; thing++) { do_stuff(thing, time); } /* for thing */ } /* for time */ Savings (in real life): factor of 500! OU Supercomputing Center for Education & Research 61
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Is the CAPM testable? 13 Roll pointed out that a) the true market portfolio is not identifiable (because it includes all risky assets) and b) the linear E(R) versus b relation holds for all efficient portfolios and c) tests of the CAPM test for ex-post mean-variance efficiency. Hence even if we accept the validity of the linear risk-return relationship in our empirical tests, we may not have identified a true ex-ante efficient portfolio that can be used for expected return computations. Practically, though, we make do with what we have; empirical tests of the CAPM use diversified portfolios of stocks as proxies for the market portfolio. Still even after making these allowances, we are not able to validate the CAPM. Empirically, we find that if excess returns on stocks are regressed on the excess market return, the intercept is significantly higher than the zero value predicted by the CAPM. The alpha or the beta-adjusted excess return is positive for low-beta securities and negative for high-beta securities. So if the linear expected return-beta relationship does not hold up, is it still true that the observed market portfolio is ex-ante mean-variance efficient? One of the implications of the CAPM is that the CML is the standard for portfolio returns. Since most active mutual funds are not able to outperform the expected return based on the observed market portfolio, we can argue that the observed market portfolio is efficient and use the expected return-beta relationship with respect to the observed market portfolio.
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Capital Asset Pricing Model: CAPM (1/2) • Recall from our earlier analysis, recall that, given the assets in the economy there is only one way to form an optimal portfolio. • Under certain assumptions, the Capital Asset Pricing Model shows that this optimal risky portfolio (with the highest Sharpe ratio) must be the market portfolio. Think of the market portfolio as a portfolio of all assets in the economy. • Strictly speaking, this market portfolio is unobservable. However, we shall proxy it by a broad index of stocks. • Recall that we said that all optimal portfolio allocations are on the line connecting the riskfree rate to the optimal portfolio. Given our proxy for the market portfolio (say, S&P 500 or the Wilshire 5000), we may assume that all optimal portfolios are some combination of the riskfree asset and this index. We will call the graph of these portfolios as the capital market line.
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Faculty Members Faculty David M. Hamby Professor Abi T. Farsoni Assistant Professor Steven Reese Radiation Center Director Kathryn A. Higley Professor, Dept. Head Andrew C. Klien Professor Jose N. Reyes Alexey Soldatov Professor, Assistant Professor, on leave of absence Senior Research Faculty Wade Marcum Assistant Professor Todd S. Palmer Professor Krystina Tack Brian Woods Qiao Wu Medical Physics Associate Professor Professor Program Director Alena Paulenova Associate Professor
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Is the CAPM testable? 12 Roll pointed out that a) the true market portfolio is not identifiable (because it includes all risky assets) and b) the linear E(R)-b relation holds for all efficient portfolio. Tests of the CAPM test for ex-post mean-variance efficiency. Hence even if we accept the validity of the linear risk-return relationship, we may not have identified a true efficient portfolio that can be used for expected return computations. Practically, though, we make do with what we have; empirical tests of the CAPM use diversified portfolios of stocks as proxies for the market portfolio. Empirically, we find that if excess returns on stocks are regressed on the excess market return, the intercept is significantly higher than zero. The alpha or the beta-adjusted excess return is positive for low-beta securities and negative for high-beta securities. So if the linear expected return-beta relationship does not hold up, is it still true that the observed market portfolio is mean-variance efficient? Since most active mutual funds are not able to outperform the observed market portfolio, we can argue that the observed market portfolio is efficient and use the expected return-beta relationship with respect to the observed market portfolio.
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51 1.24 Arithmetic • Rules of operator precedence – Operators in parentheses evaluated first • Nested/embedded parentheses – Operators in innermost pair first – Multiplication, division, modulus applied next • Operators applied from left to right – Addition, subtraction applied last Operator(s) Operation(s) • Operators applied fromOrder leftoftoevaluation right (precedence) () Parentheses *, /, or % Multiplication Division Evaluated second. If there are several, they re Modulus evaluated left to right. + or - Addition Subtraction  2003 Prentice Hall, Inc. All rights reserved. Evaluated first. If the parentheses are nested, the expression in the innermost pair is evaluated first. If there are several pairs of parentheses “on the same level” (i.e., not nested), they are evaluated left to right. Evaluated last. If there are several, they are evaluated left to right.
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