Morningstar Advisor - June/July 2010 - 45

published in my 1959 book [Portfolio Selection: Efficient Diversification of Investments]. I never ever assumed that probability distributions were normal. I never justified meanvariance analysis in terms of probability distributions being normal. My basic assumption is that you act under uncertainty to maximize expected utility. In fact, I was a student of Sam’s father, and he convinced me, as well as half the rest of the world, that the way to act under uncertainty is to maximize expected utility using probability beliefs where there weren’t any objective probabilities. So, how do I get off peddling mean-variance analysis when I believe in expected utility? An illustration of what I believe is given in Chapter six of my 1959 book, where I recommend maximizing expected logarithm of one-plus-return if you’re in for the long run. I have a table showing various levels of return, the log utility of that return, and the value of a simple quadratic approximation. Between a 30% or 40% loss and a 40% or 50% gain on the portfolio as a whole, the quadratic approximation is very close to the log utility. So, the expected value of the one has to be close to the expected value of the other, as long as we’re talking about portfolios that rarely lose much more than 30% or 40% or gain much more than 40% or 50%. Of course, the expected value of the quadratic is a function of mean and variance. So, for the nine or 10 securities that I had available for my illustrative mean-variance analysis, I show that not only does the approximation look good in the table, but, in fact, if you knew the mean and variance, you could guess the expected utility quite well. What Levy and I did was to do that same experiment using historical returns on investment companies and a variety of utility functions. We confirmed that if your probability distribution is not too spread out,

Markowitz, Mean Variance Optimization, and Expected Utility
Harry Markowitz’s revolutionary 1952 paper “Portfolio Selection” [Journal of Finance, Vol. 7, Issue 1, pp. 77–91] introduced a now commonplace concept: Investors can construct an “efficient portfolio” by investing in diverse securities combined to maximize expected returns while minimizing expected volatility. Markowitz demonstrated how mean variance optimization can be used to engineer the best combination of securities based on their mean (or expected return), their variance (the square of standard deviation of return), and their correlation with each other. Critics contend that MVO is limited by its simplified use of mean and variance to describe the distribution of an asset’s returns. The result is typically plotted as a classic, symmetrical bell curve, but return distributions don’t always neatly follow that outline. A normal, or bell-curve, distribution may underestimate the likelihood of returns at either extreme. (See “Déjà Vu All Over Again,” Morningstar Advisor, February/March 2009.) However, expected utility theory, which is the foundation of the economics of investing, does not assume that returns follow a bell-curve distribution. According to the theory, an investor ranks alternative portfolios by their “expected utility,” which is the probabilityweighted average of the “utility” of every one of the portfolio’s possible returns. The utility of each return depends on the investor’s attitude toward risk. The important point here is that expected utility can be calculated for a wide range of distributions. There is no presumption that returns follow a normal distribution. It is a simple, elegant approach to taking risk and investors’ risk attitudes into account when assessing alternative portfolios. In fact, the Morningstar Rating for mutual funds (star rating) is based on the expected utility theory. But Markowitz had been “indoctrinated at point-blank range in expected utility theory” by Leonard J. Savage. So why did he base his model of portfolio selection on mean and variance? Markowitz first addressed this question in his landmark 1959 book, Portfolio Selection: Efficient Diversification of Investments, and elaborated on it in a 1979 paper with Haim Levy, “Approximating Expected Utility by a Function of Mean and Variance” [The American Economic Review, Vol. 69, No. 3 (June, 1979), pp. 308–317] These works demonstrate that if the probability distribution of the return on the portfolio as a whole is not too wide, mean and variance can be used to form a good estimate of expected utility even though returns do not follow a normal distribution. Levy and Markowitz further found that the distributions in annual returns of investment companies were not too wide for MVO to be a useful approach to construct portfolios.

and the annual returns on investment companies turn out to be not too spread out, then if you know mean and variance, you can guess expected utility quite well.

Savage: Not at all, that’s just a fluke. I had

heard of Harry and the Markowitz optimization model but had not paid much attention to it. I was not in that line of work. But in 1989, I got a phone call from a guy with a Texas drawl thick enough to cut with a knife. He asked me an interesting question. He said that when oil companies choose portfolios of exploration sites, they sort these sites from best to worst on something like expected net present value. Then, they

‘It’s Jimmie Savage’s Son!’
Kaplan: Sam, as Harry just mentioned, he was a student of your father. Is that how you developed an interest in portfolio theory?

MorningstarAdvisor.com 45


http://www.MorningstarAdvisor.com

Morningstar Advisor - June/July 2010

Table of Contents for the Digital Edition of Morningstar Advisor - June/July 2010

Morningstar Advisor - June/July 2010
Contents
New on MorningstarAdvisor.com
Contributors
Letter From the Editor
What Risks to Bonds Are You Most Concerned About?
The Irrational Lizard Brain
Investment Briefs
The Problem With Financial Plans
Preparing for Turbulance
Different Models, Similar Results
The Game Is Up
Some People Are Bullish on Bonds
Bonds We Like
What Does Harry Markowitz Think?
Escape From the Pack
Four Picks for the Present
Rising Rates Could Affect Equities, Too
The Banking Sector Knocks on Wood
Back to Basics
On the Prowl for Smooth Operators
Mutual Fund Analyst Picks
50 Most Popular ETFs
Undervalued Stocks With Wide Moats
New at Morningstar
R-E-S-P-E-C-T
Morningstar Advisor - June/July 2010 - Morningstar Advisor - June/July 2010
Morningstar Advisor - June/July 2010 - Cover2
Morningstar Advisor - June/July 2010 - 1
Morningstar Advisor - June/July 2010 - 2
Morningstar Advisor - June/July 2010 - Contents
Morningstar Advisor - June/July 2010 - 4
Morningstar Advisor - June/July 2010 - 5
Morningstar Advisor - June/July 2010 - New on MorningstarAdvisor.com
Morningstar Advisor - June/July 2010 - 7
Morningstar Advisor - June/July 2010 - Contributors
Morningstar Advisor - June/July 2010 - Letter From the Editor
Morningstar Advisor - June/July 2010 - What Risks to Bonds Are You Most Concerned About?
Morningstar Advisor - June/July 2010 - 11
Morningstar Advisor - June/July 2010 - 12
Morningstar Advisor - June/July 2010 - 13
Morningstar Advisor - June/July 2010 - The Irrational Lizard Brain
Morningstar Advisor - June/July 2010 - 15
Morningstar Advisor - June/July 2010 - Investment Briefs
Morningstar Advisor - June/July 2010 - 17
Morningstar Advisor - June/July 2010 - The Problem With Financial Plans
Morningstar Advisor - June/July 2010 - 19
Morningstar Advisor - June/July 2010 - 20
Morningstar Advisor - June/July 2010 - Preparing for Turbulance
Morningstar Advisor - June/July 2010 - 22
Morningstar Advisor - June/July 2010 - 23
Morningstar Advisor - June/July 2010 - Different Models, Similar Results
Morningstar Advisor - June/July 2010 - 25
Morningstar Advisor - June/July 2010 - 26
Morningstar Advisor - June/July 2010 - 27
Morningstar Advisor - June/July 2010 - 28
Morningstar Advisor - June/July 2010 - 29
Morningstar Advisor - June/July 2010 - The Game Is Up
Morningstar Advisor - June/July 2010 - 31
Morningstar Advisor - June/July 2010 - 32
Morningstar Advisor - June/July 2010 - 32a
Morningstar Advisor - June/July 2010 - 32b
Morningstar Advisor - June/July 2010 - 32c
Morningstar Advisor - June/July 2010 - 32d
Morningstar Advisor - June/July 2010 - 33
Morningstar Advisor - June/July 2010 - Some People Are Bullish on Bonds
Morningstar Advisor - June/July 2010 - 35
Morningstar Advisor - June/July 2010 - 36
Morningstar Advisor - June/July 2010 - Bonds We Like
Morningstar Advisor - June/July 2010 - 38
Morningstar Advisor - June/July 2010 - 39
Morningstar Advisor - June/July 2010 - 40
Morningstar Advisor - June/July 2010 - 41
Morningstar Advisor - June/July 2010 - 42
Morningstar Advisor - June/July 2010 - What Does Harry Markowitz Think?
Morningstar Advisor - June/July 2010 - 44
Morningstar Advisor - June/July 2010 - 45
Morningstar Advisor - June/July 2010 - 46
Morningstar Advisor - June/July 2010 - 47
Morningstar Advisor - June/July 2010 - 48
Morningstar Advisor - June/July 2010 - 49
Morningstar Advisor - June/July 2010 - 50
Morningstar Advisor - June/July 2010 - 51
Morningstar Advisor - June/July 2010 - Escape From the Pack
Morningstar Advisor - June/July 2010 - 53
Morningstar Advisor - June/July 2010 - 54
Morningstar Advisor - June/July 2010 - 55
Morningstar Advisor - June/July 2010 - 56
Morningstar Advisor - June/July 2010 - Four Picks for the Present
Morningstar Advisor - June/July 2010 - 58
Morningstar Advisor - June/July 2010 - 59
Morningstar Advisor - June/July 2010 - Rising Rates Could Affect Equities, Too
Morningstar Advisor - June/July 2010 - 61
Morningstar Advisor - June/July 2010 - 62
Morningstar Advisor - June/July 2010 - The Banking Sector Knocks on Wood
Morningstar Advisor - June/July 2010 - 64
Morningstar Advisor - June/July 2010 - 65
Morningstar Advisor - June/July 2010 - Back to Basics
Morningstar Advisor - June/July 2010 - 67
Morningstar Advisor - June/July 2010 - On the Prowl for Smooth Operators
Morningstar Advisor - June/July 2010 - 69
Morningstar Advisor - June/July 2010 - Mutual Fund Analyst Picks
Morningstar Advisor - June/July 2010 - 71
Morningstar Advisor - June/July 2010 - 72
Morningstar Advisor - June/July 2010 - 73
Morningstar Advisor - June/July 2010 - 50 Most Popular ETFs
Morningstar Advisor - June/July 2010 - 75
Morningstar Advisor - June/July 2010 - Undervalued Stocks With Wide Moats
Morningstar Advisor - June/July 2010 - 77
Morningstar Advisor - June/July 2010 - 78
Morningstar Advisor - June/July 2010 - New at Morningstar
Morningstar Advisor - June/July 2010 - R-E-S-P-E-C-T
Morningstar Advisor - June/July 2010 - Cover3
Morningstar Advisor - June/July 2010 - Cover4
https://www.nxtbook.com/nxtbooks/morningstar/magazine_2020q3
https://www.nxtbook.com/nxtbooks/morningstar/magazine_2020q2
https://www.nxtbook.com/nxtbooks/morningstar/magazine_2020q1
https://www.nxtbook.com/nxtbooks/morningstar/magazine_2019winter
https://www.nxtbook.com/nxtbooks/morningstar/magazine_2019fall
https://www.nxtbook.com/nxtbooks/morningstar/magazine_2019summer
https://www.nxtbook.com/nxtbooks/morningstar/magazine_2019spring
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20191201
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20181011
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20180809
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20180607
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20180405
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20180203
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20181201
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20171011
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20170809
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20170607
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20170405
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20170203
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20171201
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20161011
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20160809
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20160607
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20160405
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20160203
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20161201
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20151011
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20150809
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20150607
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20150405
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20150203
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20151201
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20141011
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20140809
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20140607
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20140405
https://www.nxtbook.com/nxtbooks/morningstar/magazine_20140203
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20141201
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20131011
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20130809
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20130607
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20130405
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20130203
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20131201
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20121011
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20120809
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20120607
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20120405
https://www.nxtbook.com/nxtbooks/morningstar/investorconference2012
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20120203
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20121201
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20111011
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20110809
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20110607
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20110405
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20110203
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20111201
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20101011
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20100809_lincoln
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20100809
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20100607_lincoln
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20100607
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20100405_lincoln
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20100405
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20100203
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20101201
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20091011
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20090809
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20090607
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20090405
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20090203
https://www.nxtbook.com/nxtbooks/morningstar/advisor_2008fall
https://www.nxtbook.com/nxtbooks/morningstar/advisor_2008summer
https://www.nxtbook.com/nxtbooks/morningstar/advisor_2007spring
https://www.nxtbook.com/nxtbooks/morningstar/advisor_2007fall
https://www.nxtbook.com/nxtbooks/morningstar/advisor_2007summer
https://www.nxtbook.com/nxtbooks/morningstar/advisor_2008spring
https://www.nxtbook.com/nxtbooks/morningstar/advisor_2008catalog
https://www.nxtbook.com/nxtbooks/morningstar/advisor_2008winter
https://www.nxtbookmedia.com