*This course is accredited by IIROC, FPSC and The Institute for Advanced Financial Education. Please see Accreditation Details for more information.*

**Course Summary:** The authors address flaws in the traditional application of Modern Portfolio Theory related to Strategic Asset Allocation (SAA). Estimates of parameters for portfolio optimization based on long-term observed average values are shown to be inferior to alternative estimates based on observations over much shorter time frames. An Adaptive Asset Allocation portfolio assembly framework is then proposed to coherently integrate portfolio parameters in a way that delivers substantially improved performance relative to SAA over the testing horizon.

## Introduction

Practitioners, academics, and the media have derided Modern Portfolio Theory (MPT) over much of its history, but the grumbling has become outright disgust over the past ten years. This is largely because the dominant application of the theory, Strategic Asset Allocation, has delivered poor performance and high volatility since the millennial technology crash, and the traditional assumptions of MPT under the Efficient Markets Hypothesis offer no explanation or hope for a different outcome in the future.

Strategic Asset Allocation probably deserves the negative press it receives, but the mathematical identity described by Harry Markowitz in his 1967 paper is beyond reproach.

Modern Portfolio Theory requires three parameters to create optimal portfolios from two or more assets:

- Expected returns
- Expected volatility
- Expected correlation

The trouble with Strategic Asset Allocation is that it applies MPT *using long-term averages* of these parameters to create optimal portfolios. Unfortunately for SAA adherents, long-term averages turn out to be poor estimates of returns, volatility and correlation over the 5, 10 or even 20-year horizons that are meaningful for most investors.

This course will highlight the flaws inherent in the use of long-term averages as estimates for portfolio optimization for each of the three parameters, and offer methods of generating more meaningful estimates using simple measurements of nearer-term observations.

*Garbage In: Garbage Out (GIGO)* The Flaw of Averages

### GIGO: Returns

The magnitude of errors in long-term return assumptions cannot be overstated. Consider the following chart, which shows the range of real returns to U.S. stocks over rolling 20-year periods from 1871 through 2009. While 20 years or so approximates a typical retirement investment horizon, it exceeds, by multiples, the average psychological horizon of most investors, which is much closer to 3 or 4 years (Dalbar, 2012).

### Chart 1: Rolling real total returns to the S&P 500, 1871-2010

Note that, even over horizons as long as 20 years, annualized real returns to stocks range from -0.22% immediately prior to the Great Depression crash, to 13.61% during the 20 years subsequent to the 1982 low.

This amount of variability in returns means the difference between living on food stamps after 10 years of retirement and leaving a deca-million dollar legacy for heirs. For endowments, this means the difference between persistently missing funding obligations and a growing surplus. In other words, constructing portfolios through the use of long-term average return estimates is analogous to a game of Russian Roulette, where luck alone decides your fate.

While many investors behave as though there is no alternative to long-term averages for return forecasting, and allocate based on these static assumptions via an SAA framework, a large proportion of investors and institutions do bias portfolios tactically in an effort to generate better returns. Overwhelmingly, these investors apply a long-term value approach to provide a better estimate than long-term averages, such as that proposed by Sharpe (2009). Typically, these methods bias portfolios toward equities as equities fall in price (get cheaper), and reduce exposure as equities become expensive.

### Chart 2: Return factor estimates over various horizons

Data source: Darwin Funds

As shown in the diagram above, however, there are alternatives to long-term value for biasing return estimates. At the extremely short-term horizon, from intra-day to several days, high frequency traders take advantage of myriad factors related to correlation, trend and mean-reversion to generate return estimates. The incredible track records of firms like GETCO and Renaissance Technologies offer abundant evidence of the efficacy of these types of very short-term estimates.

Unfortunately, anomalies at these horizons are fleeting, non-structural and subject to extreme levels of arbitrage. As a result, this end of the estimate horizon has become a virtual arms race where all but the most well-funded and technologically adept investors will eventually die off.

Moving out the investment horizon from daily to monthly, another factor begins to exert a powerful influence: momentum. In the same way physical objects keep moving in the same direction until friction intervenes, security prices tend to continue moving in the same direction for several weeks subsequent to any observation period. In other words, at the start of any period, securities that have outperformed over the recent past will tend to continue outperforming over the near future.

The first formal analysis of this phenomenon was conducted on individual U.S. stocks by Jagadeesh and Titman (1993). Carhart (1997) subsequently asserted that momentum should be included as a fourth risk factor to compliment the longstanding Fama and French 3-factor model. Since then, a mountain of evidence has identified this factor in virtually every conceivable asset, including residential real estate (EconomPicData, 2012), art (Mei & Moses, 2010), and asset classes themselves (Asness, 2008 and Faber, 2009)

The following chart demonstrates the tendency for assets that rank in the top half of a group of 10 global asset classes based on 6-month momentum to persist within the top half of performers over the following month. On average, the probability that a top half 6-month performer will deliver returns in the top half over the subsequent month is 54% versus 46% for a bottom-half performer using a sample period from January 1995 to the 2012. On average, the top 3 assets have a 55.8% chance of ending in the top half of assets by returns the next month, while the bottom 3 end up in the top half just 45.1% of the time.

### Chart 3: Probability that top *n* ranked assets by 6 month momentum will perform in the top half the following month

Data source: Darwin Funds

This may seem like a relatively small edge at first glance. However, the 55.8% win rate for top 3 assets translates to an information coefficient of 0.116. Grinold’s Fundamental Law of Active Management allows us to use this number to estimate an Information Ratio for this simple strategy. For example, if we make three bets each month (36 bets per year) to hold the top 3 assets, this would yield an Information Ratio of 0.116 * SQRT(36) = 0.70 vs. the equal weight portfolio of all 10 assets. Why would we neglect this evidence in favor of long-term average returns for portfolio construction?

DOUG.SHAW.9

ADAPTIVE ASSET ALLOCATION: A PRIMER: I FOUND THE QUESTIONS DID NOT RELATE TO THE MATERIAL IN THE ARTICLE. NO INFO ON “EQUAL WEIGHTING, OR ON AAA PORTFOLIO. I WOULD SUGGEST SOME ONE CHECK THE QUESTIONS IF THEY RELATE TO THE ARTICLE PRIOR TO PUBLISHING THEM.DOUG SHAW

Saturday, December 6 @ 4:59 pm //////

DEAN.DISPALATRO.1

Hi Doug,

Please note this course consists of 4 pages. See the bottom of each page for links to each.

Tuesday, December 9 @ 9:58 am