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The same ingredients placed before a novice cook and a master chef can result in two very different dishes.  Why is this the case? I would suggest it is because the master chef has blended the ingredients using his expert knowledge of how the ingredients react with each other in the amounts that they are allocated so as to produce a dish that has been “optimized” in terms of flavor and appearance.

Prior to Markowitz’s modern portfolio theory which he published in 1952 in the Journal of Finance, investors focused on assessing the risks and rewards of individual securities in constructing their portfolios. Standard investment advice was to identify those securities that offered the best opportunities for gain with the least risk and then construct a portfolio from these. Following this advice, an investor might conclude that technology stocks all offered good risk-reward characteristics and compile a portfolio entirely from these.

Intuitively, this would be foolish and Markowitz formalized this intuition. Detailing a mathematics of diversification in the form of an efficient frontier, he proposed that investors focus on selecting portfolios based on their overall risk-reward characteristics instead of merely compiling portfolios from securities that individually have attractive risk-reward characteristics. In a nutshell, investors should select portfolios — not individual securities.

Thirty eight years later, Harry Markowitz together with Merton Miller and William Sharpe shared a Nobel Prize for what has become a broad theory for portfolio selection.

The rationale is straightforward. If individual securities provide a return that is subject to the vagaries of chance, then a group of securities that are positively correlated will respond in the same way to the luck of the draw. Ensuring that a portfolio consist of securities that have low or negative correlation to one another provides a way to diversify away volatility. This reduced volatility in turn leads to a lower likelihood of loss in any given year which according to Dr. Craig Israelsen of Brigham Young University is of extreme importance in a retirement withdrawal portfolio.

But if such a method of portfolio construction is of such ground breaking importance, why is not pervasive within the investment planning industry? When was the last time you recalled your adviser checking to see if a security or fund he or she recommended fitted nicely with your existing portfolio?

Sensible Excitement

Firstly,  a long term strategy employing an optimized portfolio does not have the excitement of a casino. $100 on an even money bet in roulette in a European casino yields an expected outcome of -$1.35. In spite of this, punters are willing to risk their money for the excitement of a possible big win.

According to an influential study conducted by money managers Gary Brinson, Brian Singer and consultant Gil BeeBower over a ten year period from 1974 to 1983, dubbed the Brinson Study, stock selection and market timing do not matter nearly as much as how you mix the building blocks of your investment portfolio. Asset allocation accounts for more than 90% of the variance of the returns on your investment, as the Study revealed, with the specific stocks you choose and market timing accounting for the rest.

You see the Brinson Study had a more interesting result than the fact that asset allocation explained over 90% of investment return.  The Study showed that market timing and stock picking actually decreased portfolio return by 1.1%.  Effectively, you actively allocate to the detriment of your portfolio performance. Could this be the reason Warren Buffett says: “Lethargy, bordering on sloth, remains the cornerstone of our investment style. The correct holding period for the stock market is forever”.

Active trading, stock-picking, and market timing have a similar air of big-win excitement for the investor… and is lucrative in terms of commissions for the not-so-independent adviser.

The second reason may simply be that there is a general lack of understanding of how to determine the Markowitz efficient frontier.

Many optimization tools exist that simplify the otherwise onerous number of calculations you will have to do by hand or excel. The 3 types of data that drive these tools are the rate of return of each security, its standard deviation or volatility, and the correlations among each pair of securities in the portfolio.

While deriving the efficient frontier is a robust and mathematically well-defined procedure, the efficacy of the results from your optimization exercise are a function of your understanding of the assumptions and the way you handle deviations from the assumptions which underlie the Markowitz efficient frontier model.

Do you use a forecasted rate of return or a historical return? If you use a historical return, how far back do you go? Do the correlations among each pair of securities change over time? If so, how do you account for this? When and how often should you re-balance your optimized portfolio? How do you detect a drift in the historical mean and how should this be handled?

Despite these challenges, a model that can optimize your portfolio risk return profile can be an indispensable tool in your arsenal as an adviser or investor…when used sensibly.

Show me the money

Why talk about money when the whole discussion thus far has been about reducing portfolio risk?

In order to answer this question, we took 10 securities American Express, ConocoPhillips, Johnson & Johnson, Kraft Foods, Procter & Gamble, The Coca Cola Company, USBanCorp, Walmart Stores, Wells Fargo & Wesco Financial and pushed them through our optimizer. The individual security data were taken from inception with the common data running from Jun 2002 to April 2011.

In figure 1 on the right, the red bars chart the annual dollar value of a portfolio consisting of equal amounts invested in each of the 10 securities above starting in March 2004 (a randomly chosen start date) . The optimizer was tasked to provide an efficient portfolio mix with the same expected return as the equal-mix portfolio (using data as-at 2004) but with reduced volatility. The dollar growth in the resultant optimized portfolio is denoted by the blue bars.

It can be observed that the optimized portfolio beat the equal-mix portfolio in all of the 7 years since March 2004 (itself a randomly chosen start date). Not shown is the fact that in all the trials in rolling months subsequent to March 2004, the optimized portfolio also beat all the equal-mix portfolios that were generated.

In figure 2, the red bars denote a random portfolio consisting of the 10 securities above. Again, the optimizer was tasked to provide an efficient portfolio mix with the same expected return as the random portfolio (using data as-at 2004) but with reduced volatility.

Once again, the optimized portfolio beat the random portfolio in all of the 7 years since January 2004 (itself a randomly chosen start date). Not shown is the fact that in all the trials in rolling months subsequent to January 2004, the optimized portfolio beat any random portfolio that was generated.

It should be of interest to the reader that in the exercise above, the efficient allocation was calculated only once at the beginning in 2004. With no re-balancing done in subsequent years, the portfolio still survived the recession of 2008.

Why did the optimized portfolio outperform in terms of returns when reduced volatility was the main objective?

Consider a 5-year investment that promises a 10% annual return.  If you lose 30% of your capital at the end of the first year, you will need about 24% return every year for the next 4 years to achieve what you had originally hoped to achieve in a 5-year time frame. So when you have two portfolios with the same expected return, the one with lower volatility can outperform the portfolio with higher volatility simply because it is harder to recoup your intended position when a large loss occurs compounded into the future. In other words, take care of the downside and the upside will take care of itself.

Risotto anyone?