Wayne A. Thorp, CFA is a vice president and senior financial analyst at AAII and editor of Computerized Investing. Follow him on Twitter at @AAII_CI.

Discussion

James from New Mexico posted over 2 years ago:

Very interesting discussion. I'm looking forward to the Fourth Quarter for multi-asset portfolio optimatization. How do you maximize the Sharpe's Ratio?

James from Ohio posted over 2 years ago:

I just finished reading Wayne Thorp's article, "Mean Variance Optimization" in the Third Quarter 2011 issue of Computerized Investing. - - - He did an excellent job presenting the material and in the model development.

I seen this material presented 2-3 other times and every time, the authors, including Wayne, state the investing objective to be "minimize risk. "While this is apparently the popular way to approach portfolio optimization, I think this is entirely the wrong objective. Instead, it should be "maximize return", subject to not exceeding some risk level. - - - Isn't that what most investors really want? Big returns, but they want to sleep at night.

The good news is that Wayne's Solver model solves this problem, too. All you need to do is open the Solver window, specify \$B\$17 in his model as the Target Cell, specify "Max", and change the constraint to "\$B\$18 <= X", where X is any level of risk (standard deviation) you are not willing to exceed.

I did this for X = 16% and the Solver answer is a return of 18.89% with 57.8% of the portfolio allocated to AZO. - - - This is materially better than the return of 13.94% which results when the objective is to "minimize risk". For a small increase in risk (from 13.95%, that's almost 14%, to 16%), an investor's portfolio after a few years will be materially larger. - - - Besides, I'd speculate that only a small portion of the people who read Wayne's and similar articles understand the significance of the difference between a risk of 14% and 16%.

Even without using Solver, you can scroll Wayne's values for AZO in Table 2 and determine what maximum level of risk you are willing to accept and determine if the returns are worth it in your mind. A common expression for such a heuristic optimization method is "look for the sweet spot."

Here's another take on this. Investors should not blindly focus on only risk. I can live with very high risk (standard deviation) in my returns, if the returns are sufficiently high enough to warrant the risk. In Wayne's DUK / AZO example, I could have been very comfortable putting 100% of my money in AZO since the returns were so much higher than other options and I wouldn't have lost money in any year. - - - Granted, the focus of Wayne's article was not on how to pick stocks, but, hopefully, this reasserts my earlier point that "minimizing risk" is the wrong objective.

Finally, early in the article, Wayne states, "Prudent investors choose to invest across several assets (to diversify) in hopes that gains in some assets will offset losses in others." I have heard/read this statement more than a couple times over the last few years. I feel this is a view/approach with extremely low expectations. If you adhere to it, I don't think over the long run that an investor could come close to the long term buy and hold strategy of investing in an S&P 500 index fund, which, historically, has produced average annual returns on the order of 7%-9% (not considering dividends, fees, or tax impact). - - - No doubt some readers will feel that I am mincing words or taking the wording too literally with my objections to these statements. That all that needs to be done is to add the words "more than" before the word "offset". To that extent, I agree. However, I never hear/read the words "more than" in such statements and I am concerned that, mentally, too many investors have set their expectations too low as a consequence. - - - This issue is even more exacerbated with the advice that is sometimes given: "Invest in stocks that are inversely correlated." Well, in a 2-stock portfolio that adheres to that advice, one could go up 25% and the other would go down 25%, resulting in a 0% gain. - - - What's the point of that?

Other opinions and better ideas are welcomed.

Bill from New Jersey posted over 2 years ago:

I tried but was unable to duplicate the Solver portion of the article in my own Excel worksheet. It would be incredibly helpful if the examples were provided as downloadable Excel worksheet files.

Ron from Colorado posted over 2 years ago:

There is a simple way to calculate mean and variance without calculating covariances. Simply calculate the total return for your portfolio (of as many weighted items as you want) for each time period. Then use the AVG and VAR functions on the results. It can be shown mathematically that the mean and variance calulated this way are the same as using covariances (and much easier). You can still use SOLVER to optimize weights to maximum mean return with fixed variance or vice versa. I would be happy to send a spreadsheet to anyone interested for noncommercial purposes.
nordron@umich.edu

Fernando from Florida posted over 2 years ago:

I think Wayne makes it clear under the sub-heading Mean Variance Optimization that the minimum variance portfolio is the beginning of the efficient frontier, which he further defines as including the collection of portfolios which offer higher return with less risk or the same return with less risk. This is only the beginning of further work to come in the next quarter.

David from California posted over 2 years ago:

In order to get the Solver portion to work properly I believe you have to set cell B16 to =B14+B15.
Also to get the Expected Return at the end you need to set B17 to =B14*B9+B15*C9.

Jerry Kirkman from Arizona posted 11 months ago:

Thanks David

Good job finishing the article with the rest of the formulas.