We will devote next week in Finance 4335 to tutorials on probability and statistics. These tools are critically important 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, September 29). Starting on Tuesday, September 1, 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, 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.