Category Archives: Finance

The Next Topic in Finance 4335: Moral Hazard

Next Tuesday’s meeting of Finance 4335 will be devoted to a discussion of the concept of moral hazard. 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 risk 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.

Synopsis of today’s meeting of Finance 4335

During today’s Finance 4335 class meeting, we compared and contrasted two methods for calculating risk premiums.

Under the so-called “exact” method, one 1) calculates expected utility, 2) sets expected utility equal to the utility of the certainty-equivalent of wealth, 3) solves for the certainty-equivalent of wealth, and 4) gets the risk premium by calculating the difference between expected wealth and the certainty-equivalent of wealth. The Arrow-Pratt method is an alternative method for calculating the risk premium based upon Taylor series approximations of expected utility of wealth and the utility of the certainty equivalent of wealth (the derivation for which appears on pp. 6-8 of Both approaches for calculating risk premiums are perfectly acceptable for Finance 4335.

The value added of Arrow-Pratt is that it analytically shows how risk premiums depend upon two factors: 1) the magnitude of the risk itself (as showed by variance), and 2) the degree to which the decision-maker is risk averse. For example, we showed that the Arrow-Pratt coefficient for the logarithmic investor (for whom U(W) = ln W) is twice as large as the Arrow-Pratt coefficient for the square root investor (for whom U(W) = W.5); 1/W for the logarithmic investor compared with .5/W for the square root investor. Thus, the logarithmic investor behaves in a more risk averse than the square root investor; other things equal, the logarithmic investor will prefer to allocate less of her wealth to risky assets and buy more insurance than the square root investor. Another important insight yielded by Arrow-Pratt (at least for the utility functions considered so far in Finance 4335) is decreasing absolute risk aversion (DARA). Other things equal, an investor with DARA preferences becomes less (more) risk averse as wealth increases (decreases). Such an investor increases (reduces) the dollar amount that she will put at risk as she becomes wealthier (poorer).

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

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 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 Determinants of Risk Aversion

This coming Tuesday, we begin a series of five Finance 4335 class meetings (scheduled for September 10-24) 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, a low tolerance for risk is linked to past emotional trauma.

Plans for next week’s Finance 4335 class meetings, along with a preview of future topics

We will devote next week in Finance 4335 to tutorials on probability and statistics. These tools are critically important to in the measurement of risk and development of risk management strategies for individuals and firms alike. Next Tuesday’s class meeting will be devoted to introducing discrete and continuous probability distributions, calculating parameters such as expected value, variance, standard deviation, covariance, and correlation, and applying these concepts to measure expected returns and risks for portfolios comprising risky assets. The following Thursday will provide a deeper dive into discrete and continuous probability distributions, in which we showcase the binomial and normal distributions.

While I have your attention, let me briefly explain what the main “theme” will initially be in Finance 4335 (up to the first midterm exam on Tuesday, October 1). Starting on Tuesday, September 10, 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 basic finance models (e.g., portfolio theory, the capital asset pricing model (CAPM), and option pricing theory) implicitly or explicitly assume that risk = variance. We’ll learn that while this is not necessarily an unreasonable assumption, circumstances can 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 keep 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, 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.

Volatility, now the whole thing

I highly recommend John Cochrane’s January 2019 article entitled “Volatility, now the whole thing” which builds and expands upon yesterday’s implied volatility topic in Finance 4335. For what it’s worth, Dr. Cochrane is a senior fellow at Stanford University’s Hoover Institution and was formerly a finance professor at Univ. of Chicago. Cochrane’s article provides a broader framework for thinking critically about the implications of volatility for future states of the overall economy. This article is well worth everyone’s time and attention, so I highly encourage y’all to read it!

Milton Friedman on CEOs

As an antidote to yesterday’s Business Roundtable decision to throw Friedman’s shareholder-centric model under the bus in favor of “… the more politically au courant “stakeholder” model”, The Wall Street Journal editorial board reminds us about Milton Friedman’s famous 1970 New York Times Magazine article entitled “The Social Responsibility of Business is to Increase its Profits” (linked to in this article and also from

The late, great economist anticipated the Business Roundtable.