# Insights gleaned from our coverage of portfolio and capital market theory

The topics covered during the course of the last couple of Finance 4335 class meetings (portfolio and capital market theory) rank among the most important finance topics; after all, the scientific foundations for these topics won Nobel prizes for Markowitz (portfolio theory) and Sharpe (capital market theory). The following outline pretty much summarizes what we covered in class on Thursday, October 12 and Tuesday, October 17:

• Portfolio Theory
1. Mean-variance efficiency
2. Portfolio Mean-Variance calculations
3. Minimum variance portfolio (n = 2 case)
4. Efficient frontier (n = 2 case under various correlation assumptions)
• Capital Market Theory
1. Efficient frontiers with multiple number (“large” n) of risky assets (aka the “general” case)
2. Portfolio allocation under the general case
• degree of risk aversion/risk tolerance determines how steeply sloped indifference curves are
• indifference curves for investors with high (low) degrees of risk tolerance (aversion) are less steeply sloped than indifference curves than for investors with low (high) degrees of risk tolerance (aversion)).
• Optimal portfolios (i.e., portfolios that maximize expected utility) occur at points of tangency between indifference curves and efficient frontier.
3. Introduction of a risk-free asset simplifies the portfolio selection problem since the efficient frontier is now a straight line rather than an ellipse in $E({r_p}), {\sigma _p}$ space. The same selection principle holds as in the previous point (point 2); i.e., investors determine optimal portfolio by finding the tangency between highest indifference curve and the efficient frontier. The point of tangency occurs on the capital market line (CML) where the Sharpe ratio is maximized; everyone chooses some combination of the risk-free asset and the market portfolio, and risk tolerance determines whether the point of tangency involves either a lending (low risk tolerance) or borrowing (high risk tolerance) allocation strategy.
4. The security market line (SML), aka the CAPM, is deduced by arbitrage arguments. Specifically, it must be the case that all risk-return trade-offs (as measured by the ratio of “excess” return ($E({r_j}) - {r_f}$) from investing in a risky rather than risk-free asset, divided by the risk taken on by the investor (${\sigma _{j,M}}$) are the same. If not, then there will be excess demand for investments with more favorable risk-return trade-offs and excess supply for investments with less favorable risk-return trade-offs). “Equilibrium” occurs when markets clear; i.e., when there is neither excess demand or supply, which is characterized by risk-return ratios being the same for all possible investments. When this occurs, then the CAPM obtains: $E({r_j}) = {r_f} + {\beta _j}(E({r_M}) - {r_f})$.

# A Summary of Portfolio and Capital Market Theory (source: The Royal Swedish Academy of Sciences)

During tomorrow’s Finance 4335 class meeting, we will complete our study of portfolio and capital market theory. The portfolio theory topic won Professor Harry Markowitz the Nobel Prize in Economics in 1990, and Professor William F. Sharpe shared the 1990 Nobel Prize with Markowitz for his work on capital market theory.

The very best summary of portfolio theory and capital market theory that I am aware of appears as part of an October 16, 1990 press release put out  by The Royal Swedish Academy of Sciences in commemoration of the prizes won by Markowitz and Sharpe (see http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/1990/press.html).  I have included an appropriately edited version of that press release below (it is important to also note that University of Chicago Finance Professor Merton Miller was cited that same year along with Markowitz and Sharpe for his work on the theory of corporate finance; I include below only the sections of the Royal Swedish Academy press release pertaining to the work by Messrs. Markowitz and Sharpe on the topics of portfolio and capital market theory):

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Financial markets serve a key purpose in a modern market economy by allocating productive resources among various areas of production. It is to a large extent through financial markets that saving in different sectors of the economy is transferred to firms for investments in buildings and machines. Financial markets also reflect firms’ expected prospects and risks, which implies that risks can be spread and that savers and investors can acquire valuable information for their investment decisions.

The first pioneering contribution in the field of financial economics was made in the 1950s by Harry Markowitz who developed a theory for households’ and firms’ allocation of financial assets under uncertainty, the so-called theory of portfolio choice. This theory analyzes how wealth can be optimally invested in assets which differ in regard to their expected return and risk, and thereby also how risks can be reduced.

A second significant contribution to the theory of financial economics occurred during the 1960s when a number of researchers, among whom William Sharpe was the leading figure, used Markowitz’s portfolio theory as a basis for developing a theory of price formation for financial assets, the so-called Capital Asset Pricing Model, or CAPM.

Harrv M. Markowitz
The contribution for which Harry Markowitz now receives his award was first published in an essay entitled “Portfolio Selection” (1952), and later, more extensively, in his book, Portfolio Selection: Efficient Diversification (1959). The so-called theory of portfolio selection that was developed in this early work was originally a normative theory for investment managers, i.e., a theory for optimal investment of wealth in assets which differ in regard to their expected return and risk. On a general level, of course, investment managers and academic economists have long been aware of the necessity of taking returns as well as risk into account: “all the eggs should not be placed in the same basket”. Markowitz’s primary contribution consisted of developing a rigorously formulated, operational theory for portfolio selection under uncertainty – a theory which evolved into a foundation for further research in financial economics.

Markowitz showed that under certain given conditions, an investor’s portfolio choice can be reduced to balancing two dimensions, i.e., the expected return on the portfolio and its variance. Due to the possibility of reducing risk through diversification, the risk of the portfolio, measured as its variance, will depend not only on the individual variances of the return on different assets, but also on the pairwise covariances of all assets.

Hence, the essential aspect pertaining to the risk of an asset is not the risk of each asset in isolation, but the contribution of each asset to the risk of the aggregate portfolio. However, the “law of large numbers” is not wholly applicable to the diversification of risks in portfolio choice because the returns on different assets are correlated in practice. Thus, in general, risk cannot be totally eliminated, regardless of how many types of securities are represented in a portfolio.

In this way, the complicated and multidimensional problem of portfolio choice with respect to a large number of different assets, each with varying properties, is reduced to a conceptually simple two-dimensional problem – known as mean-variance analysis. In an essay in 1956, Markowitz also showed how the problem of actually calculating the optimal portfolio could be solved. (In technical terms, this means that the analysis is formulated as a quadratic programming problem; the building blocks are a quadratic utility function, expected returns on the different assets, the variance and covariance of the assets and the investor’s budget restrictions.) The model has won wide acclaim due to its algebraic simplicity and suitability for empirical applications.

Generally speaking, Markowitz’s work on portfolio theory may be regarded as having established financial micro analysis as a respectable research area in economic analysis.

William F. Sharpe

With the formulation of the so-called Capital Asset Pricing Model, or CAPM, which used Markowitz’s model as a “positive” (explanatory) theory, the step was taken from micro analysis to market analysis of price formation for financial assets. In the mid-1960s, several researchers – independently of one another – contributed to this development. William Sharpe’s pioneering achievement in this field was contained in his essay entitled, Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk (1964).

The basis of the CAPM is that an individual investor can choose exposure to risk through a combination of lending-borrowing and a suitably composed (optimal) portfolio of risky securities. According to the CAPM, the composition of this optimal risk portfolio depends on the investor’s assessment of the future prospects of different securities, and not on the investors’ own attitudes towards risk. The latter is reflected solely in the choice of a combination of a risk portfolio and risk-free investment (for instance treasury bills) or borrowing. In the case of an investor who does not have any special information, i.e., better information than other investors, there is no reason to hold a different portfolio of shares than other investors, i.e., a so-called market portfolio of shares.

What is known as the “beta value” of a specific share indicates its marginal contribution to the risk of the entire market portfolio of risky securities. Shares with a beta coefficient greater than 1 have an above-average effect on the risk of the aggregate portfolio, whereas shares with a beta coefficient of less than 1 have a lower than average effect on the risk of the aggregate portfolio. According to the CAPM, in an efficient capital market, the risk premium and thus also the expected return on an asset, will vary in direct proportion to the beta value. These relations are generated by equilibrium price formation on efficient capital markets.

An important result is that the expected return on an asset is determined by the beta coefficient on the asset, which also measures the covariance between the return on the asset and the return on the market portfolio. The CAPM shows that risks can be shifted to the capital market, where risks can be bought, sold and evaluated. In this way, the prices of risky assets are adjusted so that portfolio decisions become consistent.

The CAPM is considered the backbone of modern price theory for financial markets. It is also widely used in empirical analysis, so that the abundance of financial statistical data can be utilized systematically and efficiently. Moreover, the model is applied extensively in practical research and has thus become an important basis for decision-making in different areas. This is related to the fact that such studies require information about firms’ costs of capital, where the risk premium is an essential component. Risk premiums which are specific to an industry can thus be determined using information on the beta value of the industry in question.

Important examples of areas where the CAPM and its beta coefficients are used routinely, include calculations of costs of capital associated with investment and takeover decisions (in order to arrive at a discount factor); estimates of costs of capital as a basis for pricing in regulated public utilities; and judicial inquiries related to court decisions regarding compensation to expropriated firms whose shares are not listed on the stock market. The CAPM is also applied in comparative analyses of the success of different investors.

Along with Markowitz’ portfolio model, the CAPM has also become the framework in textbooks on financial economics throughout the world.

# Overview:

Baylor has a student-managed investment fund comprised of large capitalization (large-cap) stocks which is now valued at approximately \$7.5 million.  Students in the class are directly responsible for managing the portfolio, while learning the techniques used by professionals to analyze and select individual stocks. Each student will also learn how to use Bloomberg, FactSet, Thomson Eikon and other resources commonly used in the investment management industry.

# The Class:

Time:              Mondays, 5:00-7:30pm
Location:         Hodges Financial Markets Center
Structure:        Designed after the operational format of a funds management firm and built around student participation.

The course primarily consists of market sector teams preparing and presenting to the class detailed reports on stocks in their sector.  Every class member is involved in the discussion of each stock.  Following the presentation and discussion, the team makes a recommendation on the stocks they presented.  The class votes and the decisions of the class are implemented.

For a better understanding of the course, you are welcome to sit through all or part of a class session this semester!  Just come to the Financial Markets Center before 5:00pm any Monday evening.

# Professors:

• Brandon Troegle, CFA®, is a Managing Director and portfolio manager with Hillcrest, focusing on the firm’s securities selections across various strategies. Before joining Hillcrest, Brandon was an equity analyst at Morningstar. Prior to Morningstar, he worked for Luther King Capital Management and Bank of America.
• Wesley Wright, CFA®, is a Portfolio Manager at Hillcrest Asset Management focusing on the firm’s International Value Strategy. Prior to joining Hillcrest, Wesley was a Portfolio Manager at Dreman Value Management in New York where he managed the firm’s International Value product and U.S. All Cap Value product.

How to Apply:  By 5:00pm, Monday, October 23, submit the following:

1. Cover letter stating why you wish to take the course
2. Unofficial transcript ( Note:  Applicants must have completed an investments course (e.g., FIN 4365 or FIN 5365) or take it concurrently with the Practicum.)
3. Resume

Submit documents to Dr. Bill Reichenstein, Department of Finance, Insurance & Real Estate, FOS 320.36.

Enrollment is limited to 15 graduate and undergraduate students with strong academic records and an interest in investments.  Applicants will be evaluated by a Finance faculty committee chaired by Dr. Bill Reichenstein, Professor of Finance and Chair of the Board of Trustees of the Phil Dorr Investment Fund.

Contact Dr. Bill Reichenstein at Bill_Reichenstein@baylor.edu or by phone at 710-6146, or go to: http://www.baylor.edu/business/financial_markets.

# Moral Hazard and Insurance

I realized after today’s class meeting that there were some (potentially confusing) errors in some of the equations I presented on this topic. In my new one-page (PDF-formatted) teaching note entitled “Moral Hazard and Insurance,” I provide a useful and succinct summary of our analysis in today’s meeting of Finance 4335.

# Office Hours & Problem Sets

Hello Class,

I should have your final problem sets graded by Friday, so if you wish to pick them up to help with your studies, I plan on hosting office hours between 12:00 to 2:00 pm on Friday at the Financial Markets Center. I may also be available after 5:00 that day, if you wish to ask questions or pick up your problem sets then you should email me beforehand. Provided you study problem sets 3 & 4 as well as the practice midterm, you should be well prepared for the exam, which is structured in the same manner.

However, if you do not understand how to apply the concepts learned in class, nor how to utilize derivatives or standard normal distributions, this and other exams will prove quite difficult. I recommend at a minimum using a graphing calculator such as  TI-84, TI-89, or TI-Nspire CAS, but it is not necessary, albeit very helpful. Furthermore, DO NOT round any intermediate calculations, otherwise you may get the wrong answer.

There have been times when the precision level of the final answer results in very difficult outcomes if the intermediate calculations are rounded. Additionally, show all relevant work, or you may not receive partial credit. Answers that are close but mechanically wrong are still incorrect, but answers that are close due to rounding error may receive credit depending on the severity. Make sure you always answer the question asked, not tangential information.

I believe that each of you are capable of performing well in the class, as long as you do the appropriate practice and check your work carefully. Many of you have performed exceptionally on the problem sets so far, but some of you likely will need to dedicate significant time to really understand the material. Furthermore, even if you did well on the problem sets, you should still study them to ensure you have not forgot the material. Good luck!

-Alexander Law

# Insurance featured as one of “50 Things That Made the Modern Economy”

During the past year, Financial Times writer Tim Harford has presented an economic history documentary radio and podcast series called 50 Things That Made the Modern Economy.  While I recommend listening to the entire series of podcasts, I would like to call your attention to Mr. Harford’s episode on the topic of insurance, which I link below.   This 9-minute long podcast lays out the history of the development of the various institutions which exist today for the sharing and trading of risk, including markets for financial derivatives as well as for insurance. Here’s the description of this podcast:

“Legally and culturally, there’s a clear distinction between gambling and insurance. Economically, the difference is not so easy to see. Both the gambler and the insurer agree that money will change hands depending on what transpires in some unknowable future. Today the biggest insurance market of all – financial derivatives – blurs the line between insuring and gambling more than ever. Tim Harford tells the story of insurance; an idea as old as gambling but one which is fundamental to the way the modern economy works.”

Insurance is as old as gambling, but it’s fundamental to the way the modern economy works
bbc.co.uk

# Rules for calculating (math) derivatives

Here’s a particularly useful list of rules for calculating (math) derivatives (taken from the “Optimization” reading assignment):

# SAP CEO Interview on the importance of taking time to read The Wall Street Journal

As SAP CEO Bill McDermott explains in the video below, taking time to read the Wall Street Journal (WSJ) is all about intellectual curiosity. Furthermore, I will frequently post links to WSJ articles throughout the course of the semester which help to bridge the gap between Finance 4335 specifically (as well as your business studies generally) and the “real” world. WSJ subscription instructions are available at http://risk.garven.com/2017/05/04/how-to-obtain-a-fall-2017-wall-street-journal-subscription/.

# How to know whether you are on track with Finance 4335 assignments

At any given point in time during the semester, you can ensure that you are on track with Finance 4335 assignments by monitoring due dates that are published on the course website. See http://fin4335.garven.com/readings/ for due dates pertaining to reading assignments, and http://fin4335.garven.com/problem-sets/ for due dates pertaining to problem sets. Also keep in mind that short quizzes will be administered in class on each of the dates indicated for required readings. As a case in point, since the required readings entitled “Optimization” and ” How long does it take to double (triple/quadruple/n-tuple) your money?” are listed for Thursday, August 24, this means that a quiz based upon these readings will be given in class on that day.

Important assignments for the first day of class (Thursday, August 24) include: 1) filling out and emailing the student information form as a file attachment to risk@garven.com, 2) subscribing to the Wall Street Journal, and 3) subscribing to the course blog. A completed Student information form is graded as a problem set and receives 100 points; if you don’t turn in a Student information form, then you will receive a 0 for this “problem set”. Furthermore, I count completion of tasks 2 and 3 above toward your class participation grade in Finance 4335.