IE 5441
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IE 5441: Financial Decision Making
Professor Shuzhong Zhang
Department of Industrial and Systems Engineering
College of Science and Engineering
University of Minnesota
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Lecture Hours:
Tuesday, Thursday 12:20 - 14:15
Question Hour:
Thursday 4:00 - 5:00 pm
Office:
ISyE 130E; Tel. (612) 624 8406
Teaching Assistant:
Mr. Xiang Gao
Question Hour:
Tuesday 4:00 - 5:00 pm
Office:
Shepherd Lab 485; Tel. (612) 625-0157
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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:
http://www.isye.umn.edu/courses/ie5441/index.shtml
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Chapter 1. Introduction
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Cash Flows
··· ···
t=0
t=1
t=2
time
t=N −1
t=N
cash flows
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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).
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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.
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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.
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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 $2k . The question is: How much should you
pay to play this game?
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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.
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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?
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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.
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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.
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