March 2013
Intermediate to advanced
608 pages
17h 23m
English
book
Investment Risk and Uncertainty: Advanced Risk Awareness Techniques for the Intelligent Investor
by Steven P. Greiner
Content preview from Investment Risk and Uncertainty: Advanced Risk Awareness Techniques for the Intelligent Investor
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.
CHAPTER 14
Portfolio Optimization
Every portfolio manager faces the challenge of building portfolios that achieve an optimal trade-off between risk and return. Harry Markowitz1 was the first to develop a mathematical framework to solve this problem in the 1950s. The Markowitz model, as it is known in the literature, considers the first two moments of the asset returns, namely the mean and the variance, to measure the return and the risk of the portfolio, respectively. The model is known as Markowitz’s MVO (mean-variance optimization) in the financial world.
Let the weight of an asset in a portfolio be the proportion of the total funds invested in this asset. The portfolio return is modeled as a linear function of the weights, representing the portfolio’s expected return; and the portfolio risk is modeled as a quadratic function in the weights, representing the variance of the portfolio. The trade-off between risk and return is obtained by solving a simple quadratic program (QP) of the form:
(14.1) 
where α is the vector of expected returns, Q is the covariance matrix of returns, and λ > 0 is the portfolio manager’s risk aversion parameter that represents the investor’s preference as how to trade-off risk and return. The solution to the QP determines the asset weights in an efficient portfolio—the portfolio with the minimum risk ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Read now
Unlock full access
More than 5,000 organizations count on O’Reilly
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.Julian F.
I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.