# ECON200: Math for Economists

Unit 3: Financial Theory, Risk, and Applications   *Financial theory is predicated on the concept of inflation, or the general rise in prices over time.  Inflation has the power to erode people’s savings or erase their debts.  The rate of inflation varies over time, and its effects must be factored into a variety of quantitative economic models.  In this unit, we will calculate the real value of a currency in two different ways and select which is best for various models.

Risk is a measurable phenomenon.  Every time a decision is made, there is a risk that the expected outcome will not be the actual result.  In this respect, risk is ever-present because our environment is continually changing.  The fairness of a system can be characterized by a risk and reward calculation, and models of risk tolerance can quantify an individual’s or firm’s appetite for risk.

Arbitrage is a typical example of a risk application.  Generally defined as exploiting price differentials by buying a financial asset in one market and selling it in another, arbitrage involves calculating risk and reward.  Economists will evaluate the similarities and differences in assets and markets over time to arrive at an optimal and potentially risk-free transaction.*

This unit should take approximately 11 hours to complete.

☐    Subunit 3.1: 0.25 hours

☐    Sub-subunit 3.1.1: 0.1 hours

☐    Sub-sub-subunit 3.1.2.1: 0.2 hours

☐    Sub-sub-subunit 3.1.2.2: 0.1 hours

☐    Sub-sub-subunit 3.1.2.3: 0.1 hours

☐    Sub-subunit 3.1.3: 2 hours

☐    Subunit 3.2: 4.75 hours

☐    Subunit 3.3: 3.5 hours

Unit3 Learning Outcomes
Upon successful completion of this unit, the student will be able to: - Develop a toolkit of quantitative methods to solve problems in financial theory and risk. - Apply specific quantitative tools (expected value, probabilities, and algebraic equations) to solve problems in financial theory and risk. - Analyze returns to capital over time with inflation risk, diversification, and probabilities from an algebraic perspective. - Choose between using real and nominal interest rates when building an economic model.

3.1 Inflation   - Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 4: In?ation” Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 4: In?ation” (PDF)

`````` Instructions: Read pages 53–58.

Reading this chapter should you approximately 15 minutes.

attributed to Yoram Bauman, and the original version can be found
[here](http://www.smallparty.org/yoram/quantum/).
``````

`````` Instructions: The above link will bring you to a video lecture
about how real and nominal rates are calculated.

Watching this video should take approximately 3 minutes.

displayed on the webpage above.
``````

`````` Instructions: The above link will bring you to a video lecture

Watching this video should take approximately 10 minutes.

displayed on the webpage above.
``````

`````` Instructions: The above link will bring you to a video lecture
about how to use inflation statistics in the United States.

Watching this video should take approximately 5 minutes.

displayed on the webpage above.
``````

`````` Instructions: The above link will bring you to a video lecture
about why some inflation may be a sign of a healthy economy.

Watching this video should take approximately 5 minutes.

displayed on the webpage above.
``````

3.1.3 Mathematical Techniques   - Assessment: Math for Life: Ian Morrison’s Sample Chapter, “Time is Money” Link: Math for Life: Ian Morrison’s Sample Chapter, “Time is Money” (PDF)

`````` Instructions: Please go to the webpage and locate the “Contents”
button toward the bottom of the page and click on it.  Then click on
“Inflation” under section 1.5.  This is an Adobe Acrobat file that
Adobe’s website.  Complete questions 1.5.7, 1.5.8, and 1.5.9 on
pages 8–10 in section 1.5, “Inflation.”

Completing this assessment should take approximately 30 minutes.

Solutions: Answers are available after each problem.

displayed on the webpage above.
``````

Instructions: The above link will bring you to a video lecture about how to calculate real returns from one year to the next.

Watching this video should take approximately 5 minutes.

• Assessment: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 4” Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 4” (PDF)

Completing this assessment should take approximately 1 hour and 15 minutes.

Solutions: Answers are in the endnotes beginning on page 232.

3.2 Risk   - Lecture: YouTube: Yale University, Department of Economics: John Geanakoplos’ “14: Quantifying Uncertainty and Risk” Link: YouTube: Yale University, Department of Economics: John Geanakoplos’ “14: Quantifying Uncertainty and Risk” (YouTube)

`````` Also Available in:
[Flash, HTML, MP3 or
QuickTime](http://oyc.yale.edu/economics/econ-251/lecture-14)
[iTunes
U](http://itunes.apple.com/us/itunes-u/financial-theory-video/id428500350)

Instructions: Watch the entire lecture.

Watching this lecture should take approximately 1 hour and 15
minutes.

displayed on the webpage above.
``````
• Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 5: Optimization and Risk” Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 5: Optimization and Risk” (PDF)

Reading this chapter should take approximately 30 minutes.

• Assessment: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 5 Problems” Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 5 Problems” (PDF)

Completing this assessment should take approximately 120 minutes.

Solutions: Answers are in the endnotes beginning on page 233.

• Assessment: The College of William & Mary: Robert Archibald’s Econ304: Intermediate Macro Theory: “Problem Set 3” Link: The College of William & Mary: Robert Archibald’s Econ304: Intermediate Macro Theory: “Problem Set 3” (HTML)

Instructions: Please click on the link and complete questions 1 through 6 of Problem Set 3.

Completing this assessment should take approximately 1 hour.

Solutions: Answers are available under “Problem Set 3 – Expectations, Present Values – Answers” (HTML).

3.3 Arbitrage   - Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 6: Transition: Arbitrage” Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 6: Transition: Arbitrage” (PDF)

`````` Instructions: Read pages 67–72.

Reading this chapter should take approximately 20 minutes.

attributed to Yoram Bauman, and the original version can be found
[here](http://www.smallparty.org/yoram/quantum/).
``````
• Lecture: YouTube: Yale University, Department of Economics: John Geanakoplos’ “09: Yield Curve Arbitrage” Link: YouTube: Yale University, Department of Economics: John Geanakoplos’ “09: Yield Curve Arbitrage” (YouTube)

Also Available in:
Flash, HTML, MP3 or QuickTime
iTunes U

Instructions: Watch the entire lecture.

Watching this lecture should take approximately 1 hour and 15 minutes.

• Assessment: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 6 Problems” Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 6 Problems” (PDF)

Completing this assessment should take approximately 45 minutes.

Solutions: Answers are in the endnotes beginning on page 234.

• Assessment: New York University Stern School of Business: Lasse Heje Pedersen’s “Foundations for Financial Markets” Link: New York University Stern School of Business: Lasse Heje Pedersen’s “Foundations for Financial Markets” (PDF)

Completing this assessment should take approximately 45 minutes.