Outside Reading

Chapter 1 is an introduction to the course, and you should read it on your own.

If you have a computer and your copy of ASW came with the CD, then you should also install the Management Scientist at this time. We will develop the same functionality on Excel together.

In reading Chapter 1 please pay particular attention to section 1.2 on decision making (which we will discuss on day one of class) and to the material in Appendix 1.2 on formatting data.

The material in section 1.4 is illustrative of a kind of decision-making you have undoubtedly encountered elsewhere.

In Chapter 2 we will review and extend certain topics from Math 118/Math 238 Statistics - namely the concepts of an event space, probability as a frequency, and subjective probability and marginal distributions.

We will also delve further into probability theory, examining the addition and multiplication laws of probability, and the notions of independent events and conditional probability. Two events are independent when knowing whether or not one event occurs (e.g. it is Monday ) does not effect the probability of another event occurring ( e.g. more than 10% of our employees are absent). When we speak of conditional probability we ask about the probability of one event, given information about another event occurring; for example, what is the probability of more than 10% of the employees being absent, given that we know it is Monday. These ideas are very useful in thinking about how things are or are not related. For example, if we suspect that employee absenteeism is higher on Mondays and Fridays, we might ask if the absenteeism rate is independent of the day of the week.

Conditional probability also allows us to "turn things inside out" in a way which is particularly important for decisions which are made only once, and sharpens your analytic skills. For example, suppose that the Olympic Committee knows that 3% of all athletes who are steroid-free will test positive ("false positives") and that 5% of all athletes who do use steroids test negative ("false negatives"), and that 1.5% of all athletes use steroids. Now let us suppose that we have an athlete who tests positive. What is the probability that this athlete uses steroids? Notice how we have turned things inside out----we know the probability of a positive result, given information about whether or not the athlete uses steroids; we then ask the probability of the athlete using steroids given information about the test result.

The theorem that allows us to make this calculation is called Bayes Theorem and it is particularly useful for decisions which are made once. (What do we do about this particular athlete? Do we buy a particular stock?). We will look at many applications of Bayes Theorem.

The calculations here are relatively simple; they may be done by hand or on a spread sheet.

We will also talk about problems with estimating probabilities, our first insight into behavioral economics. The discussion of risk, including ideas on how to measure it and on risk tolerance, in Units 1 and 2 of the course is fundamental to financial mathematics and portfolio management.

Test.

Problems will be assigned.

Outside Reading>

In this part of the course we will examine how to choose among several alternatives when you have some events that you can't predict completely. For example what size office should you rent for your consulting practice (the alternatives might be small office, medium office or large office) when you don't know how much business the practice will generate? Should you buy technology stocks now when you don't know how that industry will do next year?

We will look at several different ways to approach this problem - the optimistic criterion, the pessimistic criterion, the expected value approach, and the Minimax Regret criterion. In looking at these approaches we will spend a fair amount of time examining the notions of risk, risk tolerance and risk aversion and asking in what situations is one more or less risk tolerant. We will also read from Bernstein Against the Gods and Dembro and Freeman Seeing Tomorrow, two recent books on the matter of risk, and read about how rational/irrational individuals are in making financial decisions, and examine a number of case studies.

We will also ask about when it pays to get more information before making a decision (e.g. doing some market research before launching a product or taking an option to buy a piece of real estate so that we can see more about how an area is developing before committing to the land) and how much that information is worth to us.

We will use both Excel and alternatively The Management Scientist software.

When we turn to Utility Theory we ask about how to evaluate alternatives when our aims are harder to quantify (e.g. quality of life or feeling financially secure). We carry this further in Chapter 18 (Unit 4) when we ask about problems where we have multiple goals, and how to weight them. For example, suppose you want to buy a new car and have multiple goals related to minimizing cost, and maximizing safety and maximizing convenience. How do you weigh the relative importance of those goals and how do you use that to make a decision? Many important decisions, both personal and financial (portfolio management) ones, have multiple goals. We will examine case studies and look at software which can be used for this. Much of this process is art, rather than science. The purpose of the theory is to help you think more clearly about your values and goals.  

Group project on decision making and mutual funds or indices.

NOTE:If you have not had the Investments course yet, you should browse thru Ch. 1-2 of Bodie & Merton (on Reserve in the Library); we will not discuss Ch. 5 in this course, but you will find the material interesting for your own financial life.

Problems will be assigned.

Outside Reading

We will first learn how to evaluate two investments which give different streams of income over many years (the time value of money). This is important in, for example, determining the price of bonds. It is also important for comparing two packages of investments whose outcomes are spread out over time. The time value of money is a simple but enormously useful idea which crops up in many contexts. (For example, should we invest in a computer system which costs $1 million now and saves $350 thousand in labor for each of the next 3 years?). Many of you have learned about this in the Money and Banking or Investments course. We will work though some rather complicated examples.

Next we turn our attention to the Capital Asset Pricing Model (CAP-M) and the various forms of the Efficient Market Hyptothesis, and the measures associated with Modern Portfolio Theory .

An option is the right to buy or sell a stock or other asset at some time in the future. We will introduce the basic idea that if two packages of financial investments have the same results then they should have the same price (Law of One Price or Principle of No Arbitrage). This allows us to price options and other financial derivatives.

We will also examine various trading strategies which use multiple options.

Group or individual projects.