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In the field of finance, Modern Portfolio Theory is a good theory. I say this because while there are many enhancements to this theory, none have managed to replace it. Stemming from this theory is the Capital Asset Pricing Model (CAPM) that says for a given risk free rate there is only one optimal portfolio-- the market portfolio, which can be combined with cash to achieve the lowest level of risk for any possible return.

The market portfolio in theory is the weighted sum of every asset in the market. It should include every single possible available asset, including real estate, precious metals, stamp collections, jewelry, and anything with any worth and is optimized. The CAPM model defines a line (called the Capital Asset Line) that joins the risk free asset to the optimized market portfolio as a tangent that rests on a bullet-shaped frontier that encompasses the market portfolio.

Theory to Practice

In my previous article, I looked at an all-ETF portfolio. The risk return chart for this portfolio is displayed below. In this portfolio every ETF is negatively correlated to at least one other ETF within this universe of investments.

Click to enlarge

Practice Note 1: While CAPM wants us to invest a proportion of our wealth in a market portfolio of risky assets that is optimized with the remainder in cash, identifying a market portfolio that is all-encompassing is difficult-- if not impossible. The key word here is "optimized". In practice, we can optimize any universe of investments that we are comfortable with.

Practice Note 2: The second point to note is that CAPM wants us to join a risk free asset to the market portfolio. In practice, the risk-free rate does not exist because even the safest investments carry a very small amount of risk. Thus, the interest rate on a three-month U.S. Treasury bill is often used as the risk-free proxy.

Practice Note 3: Having a risk-free proxy as part of the mean-variance efficient frontier calculations precludes the need to draw the Capital Asset Line. This is a tautological equivalence that greatly simplifies the application of the efficient frontier to the practice of efficient portfolio construction.

The equivalence between CAPM and the mean-variance efficient frontier is a mathematical fact with no assumptions needed. The logic is straight-forward:

The mean-variance formula calculates the efficient frontier for any given universe of securities. Every portfolio in this frontier is optimal. In other words, there is no portfolio within this universe that has a higher historical expected return for a given volatility or a lower volatility for a given expected return.

But a line from the risk-free asset to the tangent optimal portfolio of risky assets would contain a mix of cash and risky assets that are above the efficient frontier and therefore "more" optimal.

Since the mean-variance calculation by definition must always yield the "most" efficient portfolio, including the risk-free proxy in its calculation is equivalent to drawing a line from the risk-free asset to a tangent portfolio that contains only risky assets. In the chart above, SHY is our risk-free proxy that has been included in the efficiency calculations.

Seeking an optimized stock portfolio

For those of us who are primarily interested in stocks, how can we apply the same analysis as we did with the all-ETF portfolio? Let's push the envelope on this and analyze the 50 stocks below that have appeared in recent SA Alerts:

Abbott Laboratories (NYSE:ABT), Advanced Micro Devices (NYSE:AMD), Air Products and Chemicals (NYSE:APD), Altria Group (NYSE:MO), American Electric Power Co (NYSE:AEP), Amgen (NASDAQ:AMGN), Apple (NASDAQ:AAPL), Ashland (NYSE:ASH), Automatic Data Processing (NASDAQ:ADP), Baker Hughes (NYSE:BHI), CA (NASDAQ:CA), CSX Corp (NYSE:CSX), Chevron Corp (NYSE:CVX), Consolidated Edison (NYSE:ED), Cooper Industries (CBE), Corning (NYSE:GLW), Crane Co (NYSE:CR), Dominion Resources (NYSE:D), Dover Corp (NYSE:DOV), E.I.du Pont de Nemours & Co (NYSE:DD), Exelon Corp (NYSE:EXC), Ford Motor Co (NYSE:F), General Dynamics Corp (NYSE:GD), General Electric Co (NYSE:GE), Honeywell International (NYSE:HON), Intel Corp (NASDAQ:INTC), International Business Machines Corp (NYSE:IBM), Kimberly- Clark Corp (NYSE:KMB), MeadWestvaco Corp (NYSE:MWV), Microsoft Corp (NASDAQ:MSFT), NextEra Energy (NYSE:NEE), Norfolk Southern Corp (NYSE:NSC), Occidental Petroleum Corp (NYSE:OXY), Parker Hannifin Corp (NYSE:PH), Rockwell Automation (NYSE:ROK), Schlumberger Ltd (NYSE:SLB), Stanley Black & Decker (NYSE:SWK), Teradyne (NYSE:TER), Texas Instruments (NASDAQ:TXN), Textron (NYSE:TXT), The Boeing Co (NYSE:BA), Chubb Corp (NYSE:CB), Southern Co (NYSE:SO), Timken Co (NYSE:TKR), The Travelers Companies (NYSE:TRV), United Technologies Corp (NYSE:UTX), Verizon Communications (NYSE:VZ), W.W. Grainger (NYSE:GWW), Western Digital Corp (NASDAQ:WDC), Xerox Corp (XRX).

The graph below shows the 50 stocks with historical mean return on the y-axis and volatility on the x axis. iShares Barclays 1-3 Year Treasury Bond ETF (NYSEARCA:SHY) is the risk-free proxy and correlations have been taken over the period July 31, 2003 to January 27, 2012.

Click to enlarge

7 Profiles

In the all-ETF portfolio, we had 7 profiles to serve as an illustration of how you could construct your portfolio in relation to your tolerance for volatility. The constraints on low, medium, high risk ETFs in the all-ETF portfolio notwithstanding, it appears you can achieve a more efficient portfolio with a subset of the 50 stocks above, especially in the high end of the volatility spectrum.

Historical Return Volatility (all-ETF) Volatility (Stocks)
Profile 1 5% 1.75% 2.09%
Profile 2 10% 4.93% 4.28%
Profile 3 15% 8.63% 6.97%
Profile 4 20% 13.6% 9.75%
Profile 5 25% 22.98% 12.77%
Profile 6 28% 31.47% 15.24%
Profile 7 30% 36.51% 17.11%

The corresponding portfolio mixes are as follows:

Profile 1: Amgen (0.5%), Microsoft Corp (0.4%), Western Digital Corp (0.7%), Rockwell Automation (0.7%), Southern Co (2.8%), Timken Co (0.6%), iShares Barclays 1-3 Year Treasury Bond ETF (89.5%), Dominion Resources (0.8%), NextEra Energy (2.2%), Occidental Petroleum Corp (0.5%), W.W. Grainger (1.4%)

Profile 2: Amgen (0.8%), Apple (1.2%), Microsoft Corp (1.5%), Western Digital Corp (1.7%), Intel Corp (0.2%), Rockwell Automation (0.3%), Southern Co (9.3%), iShares Barclays 1-3 Year Treasury Bond ETF (64.3%), Dominion Resources (4.3%), NextEra Energy (5.8%), Norfolk Southern Corp (0.3%), Occidental Petroleum Corp (2.1%), Parker Hannifin Corp (1.1%), The Travelers Companies (3.2%), W.W. Grainger (4.0%)

Profile 3: Amgen (1.0%), Apple (2.5%), Corning (0.1%), Microsoft Corp (2.4%), Western Digital Corp (2.6%), Intel Corp (0.6%), Southern Co (15.7%), Air Products and Chemicals (1.0%), iShares Barclays 1-3 Year Treasury Bond ETF (39.1%), Dominion Resources (7.8%), NextEra Energy (8.7%), Norfolk Southern Corp (0.7%), Occidental Petroleum Corp (3.6%), Parker Hannifin Corp (2.1%), The Travelers Companies (5.8%), W.W. Grainger (6.2%)

Profile 4: Amgen (1.3%), Apple (3.7%), Corning (0.1%), General Dynamics Corp (0.1%), Microsoft Corp (3.4%), Western Digital Corp (3.5%), Intel Corp (0.9%), Southern Co (22.1%), Air Products and Chemicals (2.4%), iShares Barclays 1-3 Year Treasury Bond ETF (13.9%), Dominion Resources (11.3%), NextEra Energy (11.4%), Norfolk Southern Corp (0.9%), Occidental Petroleum Corp (5.1%), Parker Hannifin Corp (2.9%), The Travelers Companies (8.6%), W.W. Grainger (8.5%)

Profile 5: Amgen (1.9%), Apple (7.1%), Corning (0.1%), General Dynamics Corp (1.5%), Microsoft Corp (5.7%), Western Digital Corp (5.2%), Intel Corp (0.9%), Southern Co (30.6%), Dominion Resources (15.2%), NextEra Energy (10.3%), Norfolk Southern Corp (1.5%), Occidental Petroleum Corp (2.0%), Parker Hannifin Corp (3.1%), The Travelers Companies (10.0%), W.W. Grainger (4.9%)

Profile 6: Amgen (2.4%), Apple (10.3%), Corning (0.1%), General Dynamics Corp (4.0%), Microsoft Corp (7.9%), Western Digital Corp (6.6%), MO (2.9%), Intel Corp (1.0%), Southern Co (36.2%), Dominion Resources (16.9%), NextEra Energy (3.2%), Parker Hannifin Corp (0.7%), The Travelers Companies (7.7%)

Profile 7: Amgen (3.1%), Apple (11.6%), Corning (0.6%), General Dynamics Corp (5.9%), Microsoft Corp (9.0%), Western Digital Corp (6.9%), Altria Group (6.6%), Intel Corp (2.4%), Southern Co (39.4%), Dominion Resources (13.9%), The Travelers Companies (0.6%)

Keep It Simple

The Markowitz frontier makes use of historical prices and the sum of company, industry, and economic factors such as inflation, growth, currency fluctuations, technological change etc. gets "factored" into the price. While there is an oft-quoted disclaimer that "past performance is not necessarily indicative of future performance", history does contain useful information.

The disconnect between the use of historical returns and future investment performance disappears when one accepts that in the mean-variance calculation, we are not forecasting in the usual sense of the word but simply accepting a possible return to the historical mean at some time in the future. In other words, we are not trying to determine next month's or next week's stock price. But there is a more essential reason for assuming normality.

In the limit, the variance for a stable, non-normal distribution does not exist. In other words, without normality, there is no variance and without variance there is no CAPM, no Modern Portfolio Theory, and no Efficient Frontier. Having established an optimized portfolio, deviations from the assumption of normality can and should be addressed as part of the re-balancing process.

I think it was Kurt Lewin, the Polish-American psychologist known for his work in the field of social, organizational, and applied psychology who once said that there was nothing more practical than a good theory.

Source: Portfolio Optimization: Bridging The Gap Between Theory And Practice