A (non-technical) Summary of Portfolio Theory and Capital Market Theory

I would like to provide everyone with some historical context for the upcoming portfolio theory and capital market theory topics we will cover, starting next Tuesday, March 16. The required reading for these topics is my Portfolio and Capital Market Theory note, and next Tuesday’s quiz is based on that reading. I also listed as “optional” readings Chapters 4 (Portfolio Theory and Risk Management) and 5 (Capital Market Theory) on the Finance 4335 readings page.

One of the better non-technical summaries of portfolio theory and capital market theory that I am aware of appears as part of a press release put out by The Royal Swedish Academy of Sciences in commemoration of the Nobel prizes won in 1990 by Harry Markowitz on the topic of portfolio theory, and by William F. Sharpe on the topic of capital market theory (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 for your further consideration below:

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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.

Case studies of how (poorly designed) insurance creates moral hazard

In my moral hazard lecture, I discuss how contract designs and pricing strategies can “fix” the moral hazard that insurance might otherwise create. Insurance is socially valuable if it enables firms and individuals to manage properly the risks that they face. However, insurance can also have a potential “dark side.” The dark side is that too much insurance and/or incorrectly priced insurance can create moral hazard by insulating firms and individuals from the financial consequences of their decision-making. Thus, in real-world insurance markets, we commonly observe partial rather than full insurance coverage. Partial insurance ensures that policyholders have incentives to mitigate risk. Real-world insurance markets are characterized by pricing strategies such as loss-sensitive premiums (commonly referred to as “experience-rated” premiums), and premiums that are contingent upon the extent to which policyholders invest in safety.

In competitively structured private insurance markets, we expect that the market price for insurance will (on average) be greater than or equal to its actuarially fair value. Under normal circumstances, one does not expect to observe negative premium loadings in the real world. Negative premium loadings are incompatible with the survival of a private insurance market since this would imply that insurers cannot cover capital costs and would, therefore, have incentives not to supply such a market.

This brings us to the National Flood Insurance Program (NFIP). The NFIP is a federal government insurance program managed by the Federal Emergency Management Agency (also known as “FEMA”). According to Cato senior fellow Doug Bandow’s (admittedly dated, but still quite accurate) blog posting entitled “Congress against Budget Reform: Voting to Hike Subsidies for People Who Build in Flood Plains”,

“… the federal government keeps insurance premiums low for people who choose to build where they otherwise wouldn’t. The Congressional Research Service figured that the government charges about one-third of the market rate for flood insurance. The second cost is environmental: Washington essentially pays participants to build on environmentally fragile lands that tend to flood.”

Thus, the NFIP provides a fascinating case study concerning how subsidized flood insurance exacerbates rather than mitigates moral hazard. It does this by encouraging property owners to take risks (in this case, building on environmentally fragile lands with high flood risk) which they otherwise would not be inclined to take if they had to pay the full expected cost of such risks.

There are many other examples of moral hazard created by insurance subsidies. Consider the case of crop insurance provided to farmers by the U.S. Department of Agriculture. The effective premium loading on federally provided crop insurance is typically quite negative (often -60% or more), thus putting crop insurance on a similar footing to flood insurance in terms of cost compared with actuarially fair value. Just as mis-priced flood insurance effectively encourages property owners to build in floodplains, mis-priced crop insurance motivates farmers to cultivate acreage which may not even be all that fertile.

I could go on (probably for several hundred more pages–there are many other egregious examples which I could cite), but I think I will stop for now…

Moral Hazard Class Problem and Solution

The “Moral Hazard Lecture–March 9, 2021” video features a class problem that carefully examines how to go about designing a so-called “incentive-compatible” contract between a corporate owner (the principal) and manager (the agent). The key insight is that moral hazard can be mitigated by ensuring that both the principal and the agent have “skin in the game”.  In this class problem, this is accomplished by offering the corporate manager an incentive compensation scheme involving a cut in salary that is supplemented by a bonus if certain profit targets are met.

The class problem is available at http://risk.garven.com/wp-content/uploads/2020/10/Moral-Hazard-Class-Problem.pdf, and its solution is available at http://fin4335.garven.com/spring2021/moralhazardsolutions.pdf.

The Next Topic in Finance 4335: Moral Hazard

The next two lectures in Finance 4335 are devoted to the discussion of two important problems related to asymmetric informationmoral hazard and adverse selection.

In finance, the moral hazard problem is commonly referred to as the “agency” problem. Many, if not most real-world contracts involve two parties – a “principal” and an “agent”. Contracts formed by principals and agents also usually have two key features: 1) the principal delegates some decision-making authority to the agent and 2) the principal and agent decide upon the extent to which they share risk.

The principal has good reason to be concerned whether the agent is likely to take actions that may not be in her best interests. Consequently, the principal has strong incentives to monitor the agent’s actions. However, since it is costly to closely monitor and enforce contracts, some actions can be “hidden” from the principal in the sense that she is not willing to expend the resources necessary to discover them since the costs of discovery may exceed the benefits of obtaining this information. Thus, moral hazard is often described as a problem of “hidden action”.

Since it is not economically feasible to perfectly monitor all of the agent’s actions, the principal needs to be concerned about whether the agent’s incentives line up, or are compatible with the principal’s objectives. This concern quickly becomes reflected in the contract terms defining the formal relationship between the principal and the agent. A contract is said to be incentive-compatible if it causes principal and agent incentives to coincide. In other words, actions taken by the agent usually also benefit the principal. In practice, contracts typically scale agent compensation to the benefit received by the principal. Thus, in insurance markets, insurers are not willing to offer full coverage contracts; instead, they offer partial insurance coverage which exposes policyholders to some of the risks that they wish to transfer. In turn, partial coverage reinforces incentives for policyholders to prevent/mitigate loss.

Similarly, in a completely different setting, consider the principal/agent relationship which exists between the owner and manager of a business. If the manager’s effort level is high, then the owner may earn higher profits compared with when the manager’s effort level is low. However, if managerial pay consists of a fixed salary and lacks any form of incentive compensation (e.g., bonuses based upon meeting or beating specific earnings targets), then the manager may be inclined to not exert extra effort, which results in less corporate profit. Thus, compensation contracts can be made more incentive-compatible by including performance-based pay in addition to a fixed salary. This way, the owner and manager are both better off because incentives are better aligned.

On the Determinants of Risk Aversion

This week, we begin a series of five Finance 4335 class meetings (scheduled for February 2-16) devoted to decision-making under risk and uncertainty. We shall study how to measure risk, model consumer and investor risk preferences, and explore implications for the pricing and management of risk. We will focus especially on the concept of risk aversion. Other things equal, risk averse decision-makers prefer less risk to more risk. Risk aversion helps to explain some very basic facts of human behavior; e.g., why investors diversify, why consumers purchase insurance, etc.

A few years ago, The Economist published a particularly interesting article about various behavioral 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, low tolerance for risk is linked to past emotional trauma.

Calculus, Probability and Statistics, and a preview of future topics in Finance 4335

Probability and statistics, along with the basic calculus principles covered last Thursday, are foundational for the theory of pricing and managing risk with financial derivatives, which is what this course is all about. During yesterday’s class meeting, we introduced discrete and continuous probability distributions, calculated parameters such as expected value, variance, standard deviation, covariance, and correlation, and applied these concepts to measure expected returns and risks for portfolios comprising risky assets. During tomorrow’s class meeting, we will take a deeper dive into discrete and continuous probability distributions, in which the binomial and normal distributions will be showcased.

While I have your attention, let me briefly explain what the main “theme” will initially be in Finance 4335.  Starting on Tuesday, February 2, we will begin our discussion of decision theory. Decision theory addresses decision-making under risk and uncertainty, which at the very heart of risk management. Initially, we’ll focus attention on variance as our risk measure. Most of the basic finance theories, including portfolio, capital market, and option pricing theories, define risk as variance. We’ll learn that while this is not necessarily an unreasonable assumption, circumstances may arise where it is not an appropriate assumption. Since individuals and firms encounter multiple sources of risk, we also need to take into consideration the portfolio effects of risk. Portfolio theory implies that risks often “manage” themselves by canceling each other out. Thus the risk of a portfolio is typically less than the sum of the individual risks which comprise the portfolio.

The decision theory provides a useful framework for thinking about concepts such as risk aversion and risk tolerance. The calculus comes in handy by providing an analytic framework for determining how much risk to retain and how much risk to transfer to others. Such decisions occur regularly in daily life, encompassing practical problems such as deciding how to allocate assets in a 401-K or IRA account, determining the extent to which one insures health, life, and property risks, whether to work for a startup or an established business and so forth. There’s also ambiguity when we have incomplete information about risk. This course will at least help you think critically about costs, benefits, and trade-offs related to decision-making whenever you encounter risk and uncertainty.

After the first midterm (scheduled for Tuesday, February 23)., the rest of the semester will be devoted to various other risk management topics, including the demand for insurance, asymmetric information, portfolio theory, capital market theory, option pricing theory, and corporate risk management.

Also featured as one of “50 Things That Made the Modern Economy”: The Index Fund

Besides insurance, Tim Harford also features the index fund in his “Fifty Things That Made the Modern Economy” radio and podcast series. This 9-minute long podcast lays out the history of the development of the index fund in particular and the evolution of so-called passive portfolio strategies in general. Much of the content of this podcast is sourced from Vanguard founder Jack Bogle’s September 2011 WSJ article entitled “How the Index Fund Was Born” (available at https://www.wsj.com/articles/SB10001424053111904583204576544681577401622). Here’s the description of this podcast:

“Warren Buffett is the world’s most successful investor. In a letter he wrote to his wife, advising her how to invest after he dies, he offers some clear advice: put almost everything into “a very low-cost S&P 500 index fund”. Index funds passively track the market as a whole by buying a little of everything, rather than trying to beat the market with clever stock picks – the kind of clever stock picks that Warren Buffett himself has been making for more than half a century. Index funds now seem completely natural. But as recently as 1976 they didn’t exist. And, as Tim Harford explains, they have become very important indeed – and not only to Mrs Buffett.”

Warren Buffett is one of the world’s great investors. His advice? Invest in an index fund

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

From November 2016 through October 2017, Financial Times writer Tim Harford presented an economic history documentary radio and podcast series called 50 Things That Made the Modern Economy. This same information is available in book form under the title “Fifty Inventions That Shaped the Modern Economy“. While I recommend listening to the entire series of podcasts (as well as reading the book), 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.

“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.”

On the ancient origin of the word “algorithm”

The January 26th assigned reading entitled “The New Religion of Risk Management” (by Peter Bernstein, March-April 1996 issue of Harvard Business Review) provides a succinct synopsis of the same author’s 1996 book entitled “Against the Gods: The Remarkable Story of Risk“. Here’s a fascinating quote from page 33 which explains the ancient origin of the word “algorithm”:

“The earliest known work in Arabic arithmetic was written by al­Khowarizmi, a mathematician who lived around 825, some four hun­dred years before Fibonacci. Although few beneficiaries of his work are likely to have heard of him, most of us know of him indirectly. Try saying “al­Khowarizmi” fast. That’s where we get the word “algo­rithm,” which means rules for computing.”

Note: The book cover shown above is a copy of a 1633 oil-on-canvas painting by the Dutch Golden Age painter Rembrandt van Rijn.