Category Archives: Finance

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  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):


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.

On the Determinants of Risk Aversion

In January 2014, The Economist published a particularly interesting article about the determinants of risk aversion, entitled “Risk off: Why some people are more cautious with their finances than others”. Here are some key takeaways from this article:

1. Economists have long known that people are risk-averse; yet the willingness to run risks varies enormously among individuals and over time.

2. Genetics explains a third of the difference in risk-taking; e.g., a Swedish study of twins finds that identical twins had “… a closer propensity to invest in shares” than fraternal ones.

3. Upbringing, environment and experience also matter; e.g., . “…the educated and the rich are more daring financially. So are men, but apparently not for genetic reasons”.

4. People’s financial history has a strong impact on their taste for risk; e.g., “… people who experienced high (low) returns on the stock market earlier in life were, years later, likelier to report a higher (lower) tolerance for risk, to own (not own) shares and to invest a bigger (smaller) slice of their assets in shares.”

5. “Exposure to economic turmoil appears to dampen people’s appetite for risk irrespective of their personal financial losses.” Furthermore, a low tolerance for risk is linked to past emotional trauma.

Interview With Meir Statman (extra credit opportunity)

Meir Statman has very important things to say about decision-making under risk and uncertainty; I introduced Professor Statman to you in my previous blog posting entitled “Your Tolerance for Investment Risk Is Probably Not What You Think.”  Here is an extra credit opportunity for Finance 4335 based upon a 1 hour, 25 minute podcast (recorded in July 2017) hosted by Barry Ritholtz’s Masters of Business podcast (link provided below) entitled “Interview with Meir Statman.”

You may earn extra credit by listening to and reporting on Mr. Ritholtz’s interview with Meir Statman about behavioral finance.   In order to receive extra credit for this assignment, you must submit (via email sent to a 1-2 page executive summary of what you learned from this podcast; it is due by no later than 5 p.m. on Monday, September 18.  This extra credit assignment will replace your lowest quiz grade in Finance 4335 (assuming the extra credit grade is higher).

Bloomberg View columnist Barry Ritholtz interviews Meir Statman, the Glenn Klimek Professor of Finance at Santa Clara University. His research focuses on behavioral finance. He attempts to understand how investors and managers make financial decisions and how these decisions are reflected in financial markets. His most recent book is “Finance for Normal People: How Investors and Markets Behave,” published by Oxford University Press. This commentary aired on Bloomberg Radio.

Your Tolerance for Investment Risk Is Probably Not What You Think

This WSJ article is authored by Professor Meir Statman,  the Glenn Klimek Professor of Finance at Santa Clara University.  Professor Statman’s research focuses on behavioral finance, which is a very important topic in decision theory that I hope to cover during tomorrow’s meeting of Finance 4335.
The questions financial advisers ask clients to get at the answer actually measure something completely different—often leading to misguided investment strategies.

Harvey’s Test: Businesses Struggle With Flawed Insurance as Floods Multiply

This WSJ article provides a fairly comprehensive look at the financial implications for #Harvey for small business. What’s particularly disconcerting is that NFIP is already for all intents and purposes technically insolvent (current debt to the US Treasury stands at around $25 billion) and Congress is supposed to reauthorize funding for the program’s next five years by September 30. On the lighter side of things, it’s fun to see a couple of academic colleagues’ names in print in this article; specifically, Erwann Michel-Kerjan of the Organization for Economic Cooperation and Development Board on Financial Management of Catastrophes and Ben Collier, who is a faculty member at Temple University’s Fox School of Business.

Hurricane will strain a National Flood Insurance Program out of step with needs of small businesses in era of extreme weather.

Risk and Uncertainty – on the role of Ambiguity

This WSJ article from last spring addresses how to measure uncertainty and also explains the subtle, yet important differences between risk and uncertainty. Risk reflects the “known unknowns,” or the uncertainties about which one can make probabilistic inferences. Ambiguity (AKA “Knightian” uncertainty; see reflects the “unknown unknowns,” where the probabilities themselves are a mystery.

A researcher whose work foreshadowed the VIX now has his eye on an entirely different barometer of market uncertainty—ambiguity.

Catastrophe Bonds Fall as Hurricane Harvey Bears Down on Texas

Good article from Bloomberg on how catastrophe (AKA “cat”) bonds are a unique asset class for investors and how such bonds disrupt traditional reinsurance markets.  For a broader perspective of these topics, also see the August 2016 WSJ article entitled “The Insurance Industry Has Been Turned Upside Down by Catastrophe Bonds” and my blog posting entitled “Cat Bonds“.

Cat bonds represent a form of securitization in which risk is transferred to investors rather than insurers or reinsurers. Typically, an insurer or reinsurer will issue a cat bond to investors such as life insurers, hedge funds and pension funds. The bonds are structured similarly to traditional bonds, with an important exception: if a pre-specified event such as a hurricane occurs prior to the maturity of the bonds, then investors risk losing accrued interest and/or the principal value of the bonds. This is why these bonds are falling in price – investors expect that the payment triggers tied to storms like #Harvey will reduce the payments received by holders of these bonds.

Bonds tied to weather risks tumbled the most in seven months as Hurricane Harvey advances on Texas’s Gulf Coast.

Place Your Bets: When Will the U.S. Hit the Debt Ceiling?

This is an excellent article on how asset prices impound political risks, and the role of so-called “prediction markets” in assessing political event probabilities (in this case, the likelihood of the U.S. defaulting on its debt).

Prediction markets add a crowdsourced opinion to the chaos of Washington.

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