It's been an interesting journey since I wrote my first article which turned out to be an editor's pick. So perhaps it is timely for me to do a little round-up of where my research has brought me so far in this very first article of 2013.
In the search for a better performing portfolio, I wrote about how the mean-variance optimization process could be used if the data that was used in the process was normal or near-normal in the statistical sense of the term.
When analyzing portfolios that were distinctly non-normal, I discussed about fat tails and non-normal distributions. I deem these as interesting academic exercises but lacking efficacy. My reasoning for this is that normality allows for a more practical approach to analyzing the market.
The slim tails of a normal distribution still account for the possibility of rare events happening. Probability is a long-term or asymptotic concept. Like the person who can win a lottery on his first bet, a rare event can occur even when the probability of it happening is small. In other words, a small probability does not mean zero probability.
Stock data is often non-stationary and this results in what looks like a fat tail. It is not a fat tail that causes non-stationarity. It is a symptom. In dealing with such symptoms, I prefer to treat them as a mixture of normal distributions.
More recently, I introduced the subject of my research that enabled the use of a mean-variance optimizer applied to a universe of both normal and non-normal stocks. When analyzed as a mixture of normal distributions, a mean-variance optimization process can be used, albeit with some refinements.
It's this hybrid strategy that I will now refer to as our Developing Optimization and Rebalancing Algorithm or D.O.R.A. for short. It goes without saying (but I will say it anyway) that there is still research to be done but the results so far seem more than encouraging.
Where We Are Now
In the illustrations that follow, we use starting portfolio values of $100 so it is easy to get a quick appreciation of percentage growth. Taxes, commissions and the use of a risk-free proxy (unless implicitly included as in case 1 below) are not included in the calculations. Price data has been sourced from Yahoo Finance on a dividend-adjusted basis. The results are true-tests, obtained by going back in time to use only the data available as at each review point, calculating the weights, then going forward to compare the performance between the re-engineered (golden), equal-weights (green) and optimized buy and hold (gray) portfolios. The re-engineered portfolio is the portfolio that has been subject to D.O.R.A. The portfolios are assumed to be 100% invested throughout. C.A.G.R. denotes the Compounded Annualized Growth Rate and A.D.C.R. is the mean Annualized Daily Compound Rate. The V Ratio measures the standard deviation of the Annualized Daily Compound Rates divided by the A.D.C.R.
Since the indices are intrinsically "naively" diversified, we would expect the performance of the optimized buy and hold portfolio to be the best performer. The figure shows that the re-engineered portfolio and the optimized buy-and-hold perform very closely. But the re-engineered portfolio avoided the dip in mid-2008 unlike the equal-weights and optimized buy and hold portfolios which fell in tandem.
2. Securities for long term holding
The stock universe consists of the following 21 stocks. These are stocks that someone like Warren Buffett might hold (and he has) in his portfolio. They are for the long term and presumably will revert to the mean some time along the way. As such, we would expect the optimized buy and hold portfolio to hold its own against the equal-weights portfolio. The figure shows that it indeed has but notice the re-engineered portfolio still appears to do slightly better than both.
American Express Company (AXP), ConocoPhillips (COP), Costco Wholesale Corp (COST), Exxon Mobil Corp(XOM), General Electric Company(GE), GlaxoSmithKline (GSK), Ingersoll Rand (IR), Johnson & Johnson(JNJ), Kraft Foods Inc (KFT), M&T Bank Corp (MTB), Moody's Corp (MCO), Procter & Gamble Co (PG), Sanofi American Depositary (SNY), The Bank of NY Mellon Corp (BK), The Coca Cola Company (KO), The Washington Post Company (WPO), Torchmark Corp (TMK), US Bancorp (USB), United Parcel Service UPS), Wal-Mart Stores Inc (WMT), Wells Fargo & Company (WFC)
3. Securities for shorter-term trading
Finally, let's take a look at a high volatility portfolio consisting of the stocks below. Since they are high volatility and presumably unstable in the sense that they might not revert to their means, we would expect the optimized buy and hold to not do any better than the equal-weights portfolio over the long term.
As shown in the figure below, this is the case. But what is striking is the fact that the re-engineered portfolio had a compounded annualized growth rate of almost 119% during this period i.e. any amount invested in the re-engineered portfolio on 31st Oct 2008 would have grown 24.87 times by 8th Dec 2012!
The compounded growth of any portfolio depends on the day it starts and the day it ends so this high performance could be unique to that period. While the high return in this instance may look great, what we are aiming for is a re-engineered portfolio that consistently beats the equal weights portfolio.
In many runs on different start days with different holding periods, I am glad to report that the re-engineered portfolio has not lost to the equal-weights portfolio and in most cases beats it significantly.
Stocks in the High-Volatility Model Portfolio (stocks in Italics are sourced from the OxStones Investment Club: Alumina Ltd (AWC), Aluminum Corp Of China Ltd (ACH), Arch Coal (ACI), Archer Daniels Midland Company (ADM), Best Buy Co (BBY), CEMEX, S.A.B. de C.V. (CX), CNH Global NV (CNH), Cameco Corp (CCJ), Central European Dist Corp (CEDC), Central European Media Ent Ltd (CETV), China Life Insurance Co. Ltd (LFC), Coca Cola, Coeur d'Alene Mines Corp (CDE), Corning (GLW), DRDGOLD Ltd (DRD), Fibria Celulose SA (FBR), France Telecom (FTE), GOL Linhas Areas Inteligentes SA (GOL), Harmony Gold Mining Co. Ltd (HMY), Humana Inc (HUM), Impala Platinum Holdings Ltd (OTCQX:IMPUY), Kinross Gold Corp (KGC), McDonald's Corp (MCD), Net 1 Ueps Technologies (UEPS), Newmont Mining Corp (NEM), Nokia Corp (NOK), Oi SA (OIBR), Potash Corp of Saskatchewan (POT), Owens-Illinois (OI), Petroleo Brazileiro (PBR), Pilgrim's Pride Corp (PPC), Repsol Ypf SA (OTCQX:REPYY), Telefonica SA (TEF), Teva Pharmaceutical Ind Ltd (TEVA), Total SA (TOT), Universal Corporation (UVV), Veolia Environnement SA (VE), Wal-Mart Stores, Western Refining Inc. (WNR), Yahoo! (YHOO)
I am not an investment adviser but 9 years as head of the actuarial division in a publicly listed reinsurance company has taught me a thing or two about the vagaries of chance and possible ways to tame it.
Research continues on how to further improve return while taming volatility as it is the taming of chance or volatility that produces the results that we have gotten so far.
The portfolio risks and returns that I have illustrated in this article are conservative results. Other output, no matter how exciting, are discarded if they cannot be validated using the principles behind the model.
In the next article, I will show you an enhanced portfolio the model has produced that performs at a higher rate with minimal downside. In the meantime, readers who wish to track the details of the portfolio above can do so at this website.