### A Few Extra Points Part II

September 16, 2011
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**Board:** Macro Economics

**Author: ** yodaorange

Last week I posted about setting realistic investment goals and suggested using long-term market timing to improve performance. Specifically I discussed lowering your allocation to equities when expected returns are low and vice-versa. The target was to achieve an extra 2% to 6% annual portfolio return over long periods, i.e. decades. Research by Ed Easterling/Crestmont, Robert Shiller, Andrew Smithers and others suggest long term market timing can add extra “alpha” to the portfolio returns.

The next logical question is: “Yes, market timing is fine and good but what are some other methods of generating extra portfolio returns?”

Originally this post was going to be about one published technique to hopefully generate extra returns in a systematic manner. After reviewing the post it read like “Men are from Venus, women are from Mars” and might not have been productive at this point in time. What I thought was missing was an understanding of the history and understanding of “alpha” and overall portfolio management/measurement. Some METARites probably know everything in this post and could have written it themselves. If so, my apologies for wasting your time. This post is written for the METARites that are not as familiar with the history and what implications it has for portfolio management. To keep this post under 100 pages and not require a degree in math/statistics to understand, I have simplified many points. For those anal folks like me that want to see the gory details, I have provided links to all of the papers.

The first seminal event in portfolio management was when William Sharpe published “"Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk” in 1964. The model that Shape proposed was latter called Capital Asset Pricing Model aka CAPM. It was and is widely used as the starting point to make financial decisions in many different industries, not just stock portfolio choices. Sharpe was an operations research professor at the University of Washington when he first submitted the paper for publication in 1962 to the Journal of Finance. It was rejected as being “irrelevant.” Sharpe had to wait until the editorial staff changed over before the paper was accepted. There is an interesting “pioneers are the ones with arrows in their backs” aspect to this rejection. Sharpe ended up winning the 1990 Nobel Prize in economics for this single paper! He shared the prize with Harry Markowitz and Merton Miller.

Link to Nobel Prize announcement.

Sharpe’s paper was written from the perspective of making future investment choices. It is an entirely theoretical paper. There is no discussion of how the model works “ex-post” i.e. after the fact. Nor is there any mention of whether the model applies to individual assets like a single stock or a group of stocks (portfolio). There are several assumptions that I am not going to present here. The model is:

Expected return = Risk free interest rate + Beta *(Market return-risk free interest rate)

Where:

1) Risk free interest rate is generally considered to be the yield on short term US treasuries

2) Market return is generally considered to be the SP 500 for US equity investments

The main point to take away from CAPM is the concept of Beta. There is a mathematical definition of Beta which I will not show. Under conditions we are interested in, Beta is ~ how much the asset price changes divided by the market return price change. I think this is the widely understood view of what Beta is. Beta is also called “systematic risk” implying that the asset movement directly correlates to the underlying market movement. For example a Beta of 1.1 means the asset price moves up at 1.10X or 10% greater than the market moves. Sharpe has a discussion about non-systematic risk, which I am also not going to cover. This formula is the basis for “high risk correlates to high reward and vice versa.” While the model does not perfectly fit individual assets, it has stood the test of time and is valuable for an understanding of risk/reward. Note that there is no mention of “alpha” in the CAPM model.

Link to original Sharpe CAPM paper.

BOTTOM LINE 1: is that if you knew nothing other than the CAPM model, you could combine the concept with market timing I outlined last week. Instead of altering the portfolio allocation to equities, you could use higher Beta funds/ETF’s when high market returns are projected. THIS IS NOT A SUGGESTION THAT YOU PLAY RUSSIAN ROULETTE WITH YOUR PORTFOLIO AND BUY THE 2X AND 3X LEVERAGED ETF’S. But going to an ETF with a Beta of 1.1 to 1.3X is reasonable IMO. Just remember to NOT get addicted to the higher Beta ETF’s and have the discipline to switch to lower Beta ones when the predicted market return is low. Note that lowering the allocation to equities has essentially the same effect, as lowering the Beta of the specific ETF you are using. (Slight simplification here.)

After Sharpe published the CAPM model, the question was did it work in the real world? The next seminal paper is “The Performance of Mutual Funds in the Period 1945-1964” by Michael Jensen. The paper was an outgrowth of his Economics PHD at the University of Chicago. Later on, he was a professor at the Harvard Business School. Jensen started with the CAPM model and modified it to make ex-post (after the fact) measurements of actual portfolios, in this case mutual funds. Jensen introduces the concept of “alpha” and in many places, it is still referred to as “Jensen’s alpha.”

Expected return = Risk free interest rate + Beta *(Market return-risk free interest rate) +

Alpha + error term

Where:

1) Risk free interest rate is generally considered to be the yield on short term US treasuries

2) Market return is generally considered to be the SP 500 for US equity investments

3) Alpha is “the average incremental rate of return on the portfolio per unit time which is due solely to the manager’s ability to forecast future security prices.”

4) Error term in simple terms is used to make the model fit the measured data better.

Jensen uses this model to fit the measured results for 115 mutual funds over 20 years. His model fits pretty well after the fact. Beta’s range from .219 to 1.405 with a median of .848. Alpha’s range from -8.0% to +5.8% with a median of -1.1%, most likely due to fund expenses. To my knowledge this is the first paper that showed actively managed mutual funds underperform in a systematic and consistent way. Calling John Bogle!

The key points for METARites are that you can accurately model alpha and beta for portfolios of equities. Beta’s are probably more persistent than alphas. I.e., a high risk, high volatility portfolio is likely to remain high. The converse is also true. For the first time, we see that achieving positive alpha is NOT easy. John Bogle and the indexers definitely have a strong case against active managers. And it has been that way since at least 1945! Pretty amazing IMO that the active fund managers have been able to keep the public investing all of these years.

Link to Jensen paper.

The final seminal paper is “The Cross-Section of Expected Stock Returns” by Eugene Fama and Ken French published in 1992. This paper introduces the “Fama French three factor model” for the first time. Long story short, Fama/French add an additional two parameters to the CAPM model. They show this substantially improves the ability to model portfolio returns. Reported numbers are that the CAPM beta explains about 70% of a portfolios performance. Adding the two additional Fama/French factors improves that to about 90%. The model is:

Expected return = Risk free interest rate + Beta1 *(Market return-risk free interest rate) +

Beta2 * SMB + Beta3 * HML

Where:

1) Risk free interest rate is generally considered to be the yield on short term US treasuries

2) Market return is generally considered to be the SP 500 for US equity investments

3) Beta1 is the same as beta in the CAPM model, the systematic risk

4) SMB is short for “Small minus big” This is the difference between the returns on diversified portfolios of small and big stocks.” Small/big is the market capitalization of the stocks.

5) HML is short for “High minus low” is the difference between the returns on diversified portfolios of high and low book value/price stocks,”

6) All three of the Betas are fitted to the model for each portfolio. They are NOT theoretically derived in advance.

Here are a few selected quotes from the Fama/French paper:

“ . . when the portfolios are formed on size along, we observe the familiar strong negative relation between size and average return. . . Average returns fall from 1.64% per month for the smallest ME portfolio to .90% per month for the largest.”

The more striking evidence is the strong positive relation between average return and book to market equity. Average returns rise from .30% for the lowest BE/ME portfolio to 1.83% for the highest, a different of 1.53% per month.

In fact, if stock prices are rational, BE/ME, the ratio of book value of a stock to the market’s assessment of its value, should be a direct indicator of the relative prospects of firms. For example, we expect that high BE/ME firms have low earnings on assets relative to low BE/ME firms.”

This paper says that small cap stocks tend to outperform large cap stocks and high book value/price tend to outperform low book value/price stocks. The paper looked at several other factors to see if they improve the model fit, but they were discarded in the end. Fama/French settle on these two additional factors as the best ones to add.

Link to Fama/French paper.

Since Fama/French published this paper in 1992, a lot of further research has been done. To the best of my knowledge, I have NOT seen any subsequent papers that substantially claim the Fama/French model is invalid. William Bernstein, the neurologist turned financial researcher did a short paper on how casual investors could determine the three Beta’s for their own portfolios.

Link to William Bernstein.

Ken French regularly updates all of the data you would ever want to see regarding the model. This data allows enterprising folks to evaluate their own portfolios for the three betas used in the model.

BOTTOM LINE 2 is that over long periods of time, you can improve performance by “tilting” your portfolio towards lower market cap and higher book value/price stocks. The key phrase is “over long periods of time” which is generally agreed to be years to decades. Using the Fama/French model is 180 degrees opposite and about a million miles away from ultra short term techniques like high frequency trading. If you are looking for sure fire ways to out perform over 1 minute, 1 hour, 1 day, 1 week, 1 month and 1 year then you can ignore this post. If you are looking for high probability ways to out perform over years to decades, the model is promising.

It would be nice if someone published the Fama/French factors for all mutual funds and/or ETF’s. I am not aware of any source of that data. Morningstar could easily do it, but I suspect it is too complicated for the average, non-METARite investor to comprehend. If you had the Fama/French factors readily available, it would make it easy to compare different ETF’s and choose ones that are appropriate. Lacking the specific model factors, we are left choosing ETF’s and hoping their charter fits them into the optimal model factors. I.e., small market cap and/or “value” ETF’s.

Obviously there is a lot more that can and needs to be said on selecting these ETF’s. I wanted to set the background so that everyone would have a common starting point as we discuss specific portfolio strategies/investments. One other important point is that it is possible to achieve the extra few percent of gain WITHOUT having a positive alpha. Stated differently, you do not have to rely on some hot shot manager du jour to make better stock selections. You can rely on some statistically proven techniques to “tilt” your portfolio for the few extra percent. This is good because it seems that every time we deify a fund manager like Bill Miller for example, they go out and fall back to earth.

On any approach we take for selecting investments using either CAPM or Jensen’s alpha or Fama/French, we are assuming persistence of these factors. So a high beta fund based on historical data is assumed to be a high beta fund going forward, etc. Clearly, if the world gets turned upside down, this may not be true. Even more clearly is that an actively managed portfolio can change its colors over time. A portfolio manager could easily make enough changes to materially impact the model parameters.

My apologies for the length of this post. Congratulations if you made it this far. Next week I plan to post more details on the path of seeking a few extra few percent of return. There are several more points/approaches that I think are pertinent on this path. Next week’s post will have more actionable investment choices for METARites.

Thanks,

Yodaorange