Risk Analytics and Portfolio Theory - Finance Theory, MIT Lecture 13-14

15.401




15.401 Finance Theory
MIT Sloan MBA Program



Andrew W. Lo
Harris & Harris Group Professor, MIT Sloan School

Lecture 13–14: Risk Analytics and Portfolio Theory


© 2007–2008 by Andrew W. Lo

, Critical Concepts 15.401

ƒ Motivation
ƒ Measuring Risk and Reward
ƒ Mean-Variance Analysis
ƒ The Efficient Frontier
ƒ The Tangency Portfolio

Readings:
ƒ Brealey, Myers, and Allen Chapters 7 and 8.1




© 2007–2008 by Andrew W. Lo Slide 2
Lectures 13–14: Risk Analytics and
Portfolio Theory

, Motivation 15.401

What Is A Portfolio and Why Is It Useful?
ƒ A portfolio is simply a specific combination of securities, usually
defined by portfolio weights that sum to 1:




ƒ Portfolio weights can sum to 0 (dollar-neutral portfolios), and weights
can be positive (long positions) or negative (short positions).
ƒ Assumption: Portfolio weights summarize all relevant information.




© 2007–2008 by Andrew W. Lo Slide 3
Lectures 13–14: Risk Analytics and
Portfolio Theory

, Motivation 15.401

Example:
ƒ Your investment account of $100,000 consists of three stocks: 200
shares of stock A, 1,000 shares of stock B, and 750 shares of stock C.
Your portfolio is summarized by the following weights:

Dollar Portfolio
Asset Shares Price/Share Investment Weight
A 200 $50 $10,000 10%
B 1,000 $60 $60,000 60%
C 750 $40 $30,000 30%
Total $100,000 100%




© 2007–2008 by Andrew W. Lo Slide 4
Lectures 13–14: Risk Analytics and
Portfolio Theory