IE 5441: Financial Decision Making

Transcription

1 IE IE 5441: Financial Decision Making Professor Department of Industrial and Systems Engineering College of Science and Engineering University of Minnesota

2 IE Lecture Hours: Tuesday, Thursday 12:20-14:15 Question Hour: Thursday 4:00-5:00 pm Office: ISyE 130E; Tel. (612) Teaching Assistant: Mr. Xiang Gao Question Hour: Tuesday 4:00-5:00 pm Office: Shepherd Lab 485; Tel. (612)

3 IE Text Book: David G. Luenberger, Investment Science, Oxford, 1st Edition 1998; 2nd Edition 2013 Grade composition: 10% 4 (homework) + 20% (mid-term) + 40% (final exam) Course Webpage:

4 IE Chapter 1. Introduction

5 IE Cash Flows t = 0 t = 1 t = 2 t = N 1 t = N time cash flows

6 IE Investments and Markets The comparison principle Suppose that your savings account generates an annual interest rate of 6%. You have got $100,000 in that account. A friend of yours needs some money urgently. He proposes to borrow your $100,000 now and pay back in the following scheme: Year 1 Year 2 Year 3 $10,000 $50,000 $60,000 Do you want to do it? (assuming there is no default risk, and no moral obligations as well).

7 IE Arbitrage A slightly more general principle underlying financial decision making is that there is no free lunch in a free and transparent financial market. Arbitrage Type A: an investment opportunity that produces an immediate positive reward without any required payments in the future. Arbitrage Type B: an investment opportunity that requires no cost but has a positive probability of yielding positive payoff(s) in the future and no probability of yielding negative payments. A fundamental principle in financial decision theory is that neither Type A nor Type B arbitrage opportunity should exist in the financial market.

8 IE Dynamics Investment is a dynamic process. Investors exchange possible cash flows due to their varied preferences through the financial market. Time-dimension plays an important role in financial decision problems.

9 IE Risk Aversion It is tempting to believe that the fair price for an outcome is its expected value. St Petersburg Paradox. Let us consider a coin-tossing game. The rule is as follows. We toss a fair coin. If the head appears on the first toss, then the game is over and you get $1. If the head appears on the second toss, then you get $2. In general, if the head appears on the k-th toss, then you get $2 k. The question is: How much should you pay to play this game?

10 IE Typical investment problems Pricing Pricing of financial assets is a fundamental problem in investment: Given an investment with known payoff characteristics (may be random), what is its reasonable price? Methods used to solve pricing problems: Comparison; No arbitrage arguments; Utility functions.

11 IE Hedging Hedging is the process of reducing the financial risks that either arise in the course of normal business operations or are associated with investments. Example. Imagine a large bakery. The bakery wins a contract to supply a large quantity of bread to another company at a fixed price. The profit of the bakery depends on the price of the flour, which fluctuates over time. The bakery wishes to be in the baking business, not in the flour speculation business. How can the baker solve this uncertainty problem?

12 IE Risk assessment and management Risk is part of life. When we buy a house we face the risk of losing its value, and we also face the risk of rising interest rate if we take a mortgage. When we invest in a foreign country, the exchange rate poses a risk. Also, there is clearly a default risk. How to model the losses? How to assess the risks? How to quantify the risks? These are truly important problems to solve.

13 IE Pure investment problems Investment problems often appear as portfolio selection problems. The following ingredients are important in solving portfolio selection problems: Assess one s preferences, or utility function; Taking the time-dynamics into account; Understand the constraints; Model the uncertainties correctly; Estimate the problem parameters. In this course, we will explore these aspects of financial decision-making mentioned in this brief summary.