In Search Of The Ultimate Efficient Portfolio Part 2

by: Maurice Chia

In Part 1 of this article I concluded by asking if we could find an even more efficient portfolio by adding more stocks to the universe. In this article, I have added the following stocks to those in the appendix to make a total of 187 securities. For good measure, I have added a list of ETFs to the universe as well.

Is there a point to all this madness?

Indeed there is. First, I would like to see the effect of increasing the number of securities in the universe in terms of its risk/return characteristics. Recall that doing an optimization process looks at the 3 variables of risk (volatility), return, and correlation simultaneously. In other words, you are not looking at just the best returns, or just the lowest volatilities or even just the ones with best Sharpe ratios.

Secondly, I have added ETFs to the universe to illustrate the fact that you can find a better portfolio than by simply combining a risk free asset with an ETF or a group of ETFs. While ETFs do have their advantages in terms of tax and transaction costs, the investor who has the time to do so can discover some gems by going through an optimization process.

The securities that I have added below include a random sampling of favorites from investment gurus Warren, Icahn, and Pickens among others, as well as, some ETFs:

America Movi SA de CV (AMX), American Express Co (AXP), Amylin Pharmaceuticals (AMLN), Apache Corp (APA), BP plc (BP), The Bank of New York Mellon Corp (BK), Brinker International (EAT), Canadian Natural Resources Ltd (CNQ), Chesapeake Energy Corp (CHK), The Coca Cola Co (KO), Commercial Metals Co (CMC), ConocoPhillips (COP), Costco Wholesale Corp (COST), DIRECTV (DTV), DaVita (DVA), Dawson Geophysical Co (DWSN), Dynegy (DYN), EOG Resources (EOG), Enzon Pharmaceuticals (OTCQX:ENZN), Fomento Economico Mexicano SAB De CV (FMX), Forest Laboratories (FRX), Gannett Co (GCI), GlaxoSmithKline (GSK), HDFC Bank Ltd (HDB), Halliburton Co (HAL), Hess Corp (HES), Ingersoll-Rand plc (IR), Johnson & Johnson (JNJ), Kraft Foods (KFT), Lions Gate Entertainment Corp (LGF), M&T Bank Corp (MTB), MasterCard (MA), McMoRan Exploration Co (MMR), Mentor Graphics Corp (MENT), Moody's Corp (MCO), Motorola Solutions (MSI), Murphy Oil Corp (MUR), National Oilwell Varco (NOV), New York Community Bancorp (NYB), News Corp (NWS), Noble Corp (NE), Oshkosh Corp (OSK), Petroleo Brasileiro SA (PBR), Plains Exploration & Production Co (PXP), Procter & Gamble Co (PG), SPDR S&P MidCap 400 Trust ETF (MDY), sanofi-aventis (SNY), Service Corporation International (SCI), Suncor Energy (SU), Taiwan Semiconductor Manufacturing Co ltd (TSM), Take-Two Interactive Software (TTWO), Clorox Corp (CLX), The Hain Celestial Group (HAIN), Torchmark Corp (TMK), U.S. Bancorp (USB), USG Corp (USG), United Microelectronics Corp (UMC), United Parcel Service (UPS), Vanguard Emerging Markets Stock ETF (VWO), Wal-Mart Stores (WMT), Washington Post Co (WPO), Weatherford International ltd (WFT), Wells Fargo & Co (WFC), iShares FTSE China 25 Index ETF (FXI), iShares S&P Latin America 40 Index ETF (ILF), iShares MSCI Brazil Index ETF (EWZ), iShares MSCI EAFE Index ETF (EFA), iShares MSCI Mexico Index ETF (EWW), iShares MSCI South Africa Index ETF (EZA), iShares MSCI South Korea Index ETF (EWY), iShares MSCI Taiwan Index ETF (EWT), iShares S&P 500 Index (IVV)

Efficient Portfolio Results

The efficient frontier for the universe of 187 securities is shown in the graph below. Note that the data is taken from inception or 3650 days whichever is applicable.

The optimal portfolio produced from this universe with a long term average return equivalent to the one produced in my previous article with 117 stocks is as follows. The underlined stocks are from among the securities that have been added to the new universe:

Amylin Pharmaceuticals 3.0%, RF Micro Devices 0.5%, Yahoo! 2.0%, Chesapeake Energy Corp 4.5%, Duke Realty Corp 2.0%, EMC Corp 7.2%, Intuitive Surgical 3.2% Alliance Resource Partners 31.1%, Amgen 4.8%, Coach 3.2%, Davita 0.5%, MasterCard 6.2%, MicroSoft Corp 3.3%, Quest Diagnostics 1.2%, Southern Copper Corp 5.3%, Southern Co 21.9%.

Compare this with the optimal portfolio from the previous article with 117 stocks in its universe:

RF Micro Devices 1.6%, Yahoo! 0.8%, Citrix Systems 0.1%, Duke Realty Corp 2.5%, EMC Corp 8.4%, Intuitive Surgical 8.4%, Alliance Resource Partners 29.1%, Altera Corp 0.6%, Amgen 7.2%, Coach 7.7%, Microsoft Corp 3.3%, Quest Diagnostics 7.0%, Southern Copper Corp 4.4%, Southern Co 18.5%

Portfolio volatility from the universe with 187 securities was about 1.2 percentage points less than the portfolio from a universe of 117 securities.

A Proxy is a Proxy is a Proxy

What about combining an ETF with the risk-free asset?

Adherents of Modern Portfolio Theory [MPT] will say that the ultimate efficient frontier is the straight line that you draw from a risk-free asset to the tangent portfolio.

As illustrated in the graph below, iShares Barclays 1-3 year Treasury Bond ETF [SHY] is our risk free proxy. If you find that drawing a line from the risk-free asset to the tangent portfolio roughly coincides with the efficient frontier that has been constructed (red dots), it is because SHY has already been included in the mean-variance computations.

In MPT, the tangent portfolio is supposed to be the market portfolio. Advocates of an all ETF portfolio might be tempted to suggest that the S&P 500 or a similar index (in the graph, the ETFs are denoted by the little white 'e' symbols) could be a proxy for the market portfolio.

But try trying a line mentally from SHY to the iShares S&P 500 Index ETF [IVV] and you will find it is far below our constructed efficient frontier. Why is this case?

The reason is the market portfolio by definition must be all-encompassing. In other words, it must contain every available investment that money can flow to. While an ETF could come in handy as a diversified portfolio for investors who have little time to perform their own analysis, it is far from the makings of the theoretical market portfolio...and possibly far from being efficient.

In my next article, I will examine this further using the Guggenheim Russell Top 50 ETF. And in a separate article, I will examine the workings of a long-short optimized strategy and how it can be used to further improve the risk/return characteristics of any optimized portfolio.


The following 117 stocks formed the asset universe and were chosen at random:

AK Steel Holding Corp (AKS), Abbott Laboratories (ABT), Advanced Micro Devices (AMD), Air Products and Chemicals (APD), Albemarie Corp (ALB), Allegheny Technologies (ATI), Alliance Resource Partners (ARLP), Altera Corp (ALTR), Altria Group (MO), American Electric Power Co (AEP), Amgen (AMGN), Apple (AAPL), Ashland (ASH), Automatic Data Processing (ADP), Baker Hughes (BHI), iShares Barclays 1-3 year Treasury Bond ETF (SHY), Brinker International , CA (CA), CSX Corp (CSX), Capital One Financial Corp (COF), Celestica (CLS), Chevron Corp (CVX), Citrix Systems (CTXS), Coach (COH), Comerica (CMA), Consolidated Edison (ED), Cooper Industries (CBE), Corning (GLW), Crane Company (CR), Crown Castle International Corp (CCI), D.R. Horton (DHI), Dominion Resources (D), Dover Corp (DOV), Duke Realty Corp (DRE), E.I.du Pont de Nemours and Co (DD), EMC Corp (EMC), E*TRADE Financial Corp (ETFC), Eastman Chemical Co (EMN), Exelon Corp (EXC), Fifth Third Bancorp (FITB), First Horizon National Corp (FHN), Flextronics International Ltd (FLEX), Ford Motor Co (F), General Dynamics Corp (GD), General Electric Co (GE), Harley-Davidson (HOG), Honeywell International (HON), Hub Group (HUBG), Hudson City Bancorp (HCBK), Intel Corporation (INTC), International Business Machines Corp (IBM), International Game Technology (IGT), Intuitive Surgical (ISRG), Jacobs Engineering Group (JEC), Kansas City Southern (KSU), KeyCorp (KEY), Kimberly-Clark Corp (KMB), LM Ericsson Telephone Co (ERIC), LSI Corp (LSI), Lam Research Corp (LRCX), Legg Mason (LM), MeadWestvaco Corp (MWV), MicroSoft Corp (MSFT), New York Community Bancorp , NextEra Energy (NEE), Norfolk Southern Corp (NSC), Novartis AG (NVS), Occidental Petroleum Corp (OXY), Owens Illinois (OI), Parametric Technology Corp (PMTC), Parker Hannifin Corp (PH), Peabody Energy Corp (BTU), Polaris Industries (PII), Polycom (PLCM), Popular (BPOP), Praxair (PX), Quest Diagnostics (DGX), RF Micro Devices (RFMD), Rpc (RES), Regions Financial Corp (RF), Robert Half International (RHI), Rockwell Automation (ROK), SAP AG (SAP), STMicroelectronics NV (STM), Schlumberger Ltd (SLB), Southern Copper Corp (SCCO), St. Jude Medical (STJ), Stanley Black & Decker (SWK), Starbucks Corp (SBUX), Steel Dynamics (STLD), Stryker Corp (SYK), Suntrust Banks (STI), Sunoco Logistics Partners L.P. (SXL), Susquehanna Bancshares (SUSQ), Symantec Corp (SYMC), Synovus Financial Corp (SNV), T Rowe Price Group (TROW), TCF Financial Corp (TCB), Teradyne (TER), Texas Instruments (TXN), Textron (TXT), The Boeing Co (BA), Chubb Corp (CB), Southern Co (SO), Timken Co (TKR), The Travelers Companies (TRV), Total System Services (TSS), United Rentals (URI), United Technologies Corp (UTX), Verizon Communications (VZ), WW Grainger (GWW), Western Digital Corp (WDC), Woodward (WWD), Xerox Corp (XRX), Yahoo! (YHOO), Zions Bancorporation (ZION), iGATE Corp (IGTE)

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

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