Math 134A
Fixed Income
Lecture 1
Professor Jeff Ludwig
Jeff’s Background
MIT undergraduate degree in aeronautics and astronauticsMIT Masters and PhD in electrical engineering and computer sciencePhD Thesis: Low Power Digital Filtering Using Approximate Signal Processing
Color portrait of Professor Jeff Ludwig: a smiling man with short gray hair wearing a dark button-up shirt.
Career on Wall Street in quantitative trading
Credit Suisse Proprietary Index Arbitrage Trader
PIMCO Portfolio Manager and Head of Equity Derivatives
Millennium Partners Hedge Fund Portfolio Manager
Most recently Director of Jump Labs
R&D for Jump Trading, a high frequency trading firm
Focus on long term collaborations with academia
Joined UCI Department of Mathematics in 2018
Jeff’s Background
What is quantitative trading?
The use of computers and mathematics to earn profits by electronically trading liquid securities in the global financial markets Accomplished by small teams that compete against each other and harmonize:
Financial Markets experts
Mathematics superstars
Programming whizzes
Meteoric rise in number of people and dollars involved: $100B to $3T in past 20 years
What is quantitative trading?
The Dream: pure information processing transforms mathematical models into moneyThe Reality: all models have a half-life, markets are non-stationary, incessant innovation and adaptation essential to successAn ecosystem for creative innovation in research and production is required for survival
What is high frequency trading?
Quantitative Trading on Steroids: speed & smarts60 exchanges around the world connected with cutting-edge telecommunications networksMove information around the planet at or near what the laws of physics permitHardware and software pushed to achieve speed of light and Shannon limits, HPC for algorithms1 T packets of market information per day, based on 1000 feeds and 1B packets/feed/day
Book cover of Flash Boys: A Wall Street Revolt by Michael Lewis, on a red background with a small black bull silhouette in the center.
A Revolution in Finance
Modern portfolio theory (MPT) was born with a 14-page paper published in 1952Its creation and evolution spawned 10 Nobel Prizes from 1990 to 2013A brilliant and innovative collaboration between mathematicians, engineers, and economistsOur common mission in Math 134A
Master Modern Portfolio Theory
Outline for Today
Overview of course and final grade determination
Introduction to Investments and Investment Science
Course Overview
1. Introduction to Investment Science
PART I. DETERMINISTIC CASH FLOWS 2. The Basic Theory of Interest 3. Fixed Income Securities 4. The Term Structure of Interest Rates 5. Applied Interest Rate AnalysisPART II. SINGLE-PERIOD RANDOM CASH FLOWS 6. Mean-Variance Portfolio Theory 7. The Capital Asset Pricing Model 8. Other Pricing Models
Course Overview
1. Introduction to Investment Science
PART I. DETERMINISTIC CASH FLOWS 2. The Basic Theory of Interest 3. Fixed Income Securities 4. The Term Structure of Interest Rates 5. Applied Interest Rate AnalysisPART II. SINGLE-PERIOD RANDOM CASH FLOWS 6. Mean-Variance Portfolio Theory 7. The Capital Asset Pricing Model 8. Other Pricing Models
Course Overview
1. Introduction to Investment Science
PART I. DETERMINISTIC CASH FLOWS 2. The Basic Theory of Interest 3. Fixed Income Securities 4. The Term Structure of Interest Rates 5. Applied Interest Rate AnalysisPART II. SINGLE-PERIOD RANDOM CASH FLOWS 6. Mean-Variance Portfolio Theory 7. The Capital Asset Pricing Model 8. Other Pricing Models
Course Overview
1. Introduction to Investment Science
PART I. DETERMINISTIC CASH FLOWS 2. The Basic Theory of Interest 3. Fixed Income Securities 4. The Term Structure of Interest Rates 5. Applied Interest Rate AnalysisPART II. SINGLE-PERIOD RANDOM CASH FLOWS 6. Mean-Variance Portfolio Theory 7. The Capital Asset Pricing Model 8. Other Pricing Models
Course Overview
1. Introduction to Investment Science
PART I. DETERMINISTIC CASH FLOWS 2. The Basic Theory of Interest 3. Fixed Income Securities 4. The Term Structure of Interest Rates 5. Applied Interest Rate AnalysisPART II. SINGLE-PERIOD RANDOM CASH FLOWS 6. Mean-Variance Portfolio Theory 7. The Capital Asset Pricing Model 8. Other Pricing Models
Course Overview
1. Introduction to Investment Science
PART I. DETERMINISTIC CASH FLOWS 2. The Basic Theory of Interest 3. Fixed Income Securities 4. The Term Structure of Interest Rates 5. Applied Interest Rate AnalysisPART II. SINGLE-PERIOD RANDOM CASH FLOWS 6. Mean-Variance Portfolio Theory 7. The Capital Asset Pricing Model 8. Other Pricing Models
We will cover textbook chapters 1 through 8
Final Grade Determination
Homework 10%Quizzes 20% Midterm 30%Final Exam 40%The final letter grade is based on a curve that reflects how your performance compares to other students in the class
Math 134A Course Website
Lectures are posted on the course website
Homeworks are posted on the course website
Course syllabus is posted on the course website
Quizzes will be given via the course website
Exams will be given via the course website
Errata in textbook is on the course website
UCI Math Finance Club
https://www.linkedin.com/groups/13695883/
Connect students with finance industry experts
Foster passions for mathematical finance
Support each other’s studies and job searches
Organized to serve students and run by studentsQuarterly quantitative trading competitions
Annual Midwest Trading Competition
Introduction to Investments
Investment is the current commitment of resources in order to achieve later benefitsOr more broadly, we may consider flows of expenditures and receipts comprising
a stream of cash flows
How do we tailor the streams of cash flows to meet our objectives?
Cash Flow Stream (-1, 1, 2, 4, 3, 2.5)Stem plot titled Cash Flow Stream. Horizontal axis labeled Time from 0 to 7. Vertical axis labeled Dollars from negative 2 to 5. Stems: at time 1 dollars equal negative 1; at time 2 dollars equal 1; at time 3 dollars equal 2; at time 4 dollars equal 4; at time 5 dollars equal 3; at time 6 dollars equal 2.5.
Investment Science Investment Science is the application of scientific tools to investments There is also an art to investment ``Systematic procedures and objective tests serve to strengthen the analyst’s judgment, not to replace it.’’ David Durand, MIT
Important Concepts in Investments
The comparison principle
Arbitrage
Dynamics and Equilibrium
Risk Aversion
Typical Investment Problems
Pricing
Hedging
Risk Assessment and Management
Risk Aversion
Nonsatiation Property
Mean-Variance Optimization
Pure Investment
Portfolio Selection: where to invest available capital
Corporate Finance: decision making under uncertainty
Investment Science: Goals and Benefits
Goal: optimally combine stocks, bonds, and other investment products into portfolios with desirable propertiesBenefit: this process enhances total productivity and prosperity globally by converting projects that in isolation may be too risky into members of attractive combinations
A Sample Problem
Suppose $100 were invested in the year 2000 at 3.3% annual interest, compounded yearly. Approximately how much would that investment be worth at the end of 2020? V2001 = $100 * (1 + 0.033) V2002 = V2001 * (1 + 0.033) = $100 * (1 + 0.033) 2V2020 = $100 * (1 + 0.033) 20 V2020 = $191
U.S.A. Stock Market Average Annual Return: 10%Line chart of the U.S.A. stock market index. A tooltip at the left edge reads 124.88 on September 5, 1980. Horizontal axis shows years 1986, 1996, 2006, 2016. Vertical axis shows index values from 0 to 4000. The green line trends upward overall, with notable dips around 2000-2002 and 2008-2009, reaching above 3000 by the late 2010s.
Summary of Today
Investment is defined as the current commitment of resources in order to achieve later benefitsInvestment Science is the application of scientific tools to investments
Cash flow streams may be deterministic or random
Our goal is to master Modern Portfolio Theory (MPT), an elegant foundation for the analysis of investments with random cash flow streams
Black-and-white photograph of a man in a white shirt and striped tie gesturing in front of a chalkboard covered with mathematical notation including subscripted variables l1, l2, and a boxed V1.
A great opportunity to discuss class material or anything else you may be thinking aboutI welcome stimulating discussion and questions within or beyond Math 134A
Hope to you see you there!
An Invitation to Office Hours