Wednesday, January 05, 2005

Portfolio optimization made doable or at least more doable

Brandt, Santa Clara, and Valkanov have an interesting working paper that should help investors create optimal portfolios.

I will let them explain their paper:
"We propose a simple new approach to equity portfolio optimization based on firm
characteristics. We parameterize the weight invested in each stock as a function of the firm's characteristics, with the implicit assumption that these characteristics fully capture all aspects of the joint distribution of returns that are relevant for forming optimal portfolios. We then estimate the coefficients of the portfolio policy by maximizing the utility that would have been obtained by the investor from implementing the policy over the sample period."

In English? They develop a model that can be used to find optimal portfolio weights of assets based on the asset's characteristics. Moreover, the model is flexible enough to be altered to fit a variety of utility functions.

While some of us may question how "simple" the method is (the authors repeatedly claim it is simple), the paper really is much more practically applicable than many of the quantitative models based on the Markowitz optimal portfolio approach and it tends to based on firm characteristics (such as size and book to value ratios) that are readily available.

Again in the authors' words:
The most important aspect of our parameterization is that the coefficients are constant across assets and through time. Constant coefficients across assets implies that the portfolio policy only cares about the characteristics of the stocks, not about the stocks themselves. The implicit assumption is that the characteristics fully capture all aspects of the joint distribution of returns that are relevant for forming optimal portfolios. Constant coefficients through time means that the coefficients that maximize the investor's conditional expected utility at a given date are the same for all dates and therefore also maximize the investor's unconditional expected utility.

In the later sections of the paper, the authors relax many of the restrictive assumptions they used initially (for example they allow for the possibility of coefficients changing with the economy) and even create a real portfolio based on their model. Their model portfolio dramatically outperforms other market models.
The optimal portfolio has a volatility slightly larger than that of the market portfolio, 19% versus 16%, but has an average return of 24.4% as opposed to 12.0%. This translates into a certainty equivalent gain of 10%.
So what does their so-called optimal portfolio look like? Given what we know about anomalies and apparent inefficiencies (for example: value anomaly and size anomaly and momentum investing), it should not be surprising that the optimal portfolio had more small stocks and more value stocks.
"The market portfolio has a bias towards very large firms (due to value weighting) and firms with below average book-to-market ratios (growth), while it is neutral with respect to momentum. In contrast, the optimized portfolio has a slight bias toward small firms and much stronger biases toward high book-to-market ratio (value) firms and past winners."

The paper is available from the UCLA working paper site.

1 comment:

stockexpert said...

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3 Steps To Profitable Stock Picking

Stock picking is a very complicated process and investors have different approaches. However, it is wise to follow general steps to minimize the risk of the investments. This article will outline these basic steps for picking high performance stocks.

Step 1. Decide on the time frame and the general strategy of the investment. This step is very important because it will dictate the type of stocks you buy.

Suppose you decide to be a long term investor, you would want to find stocks that have sustainable competitive advantages along with stable growth. The key for finding these stocks is by looking at the historical performance of each stock over the past decades and do a simple business S.W.O.T. (Strength-weakness-opportunity-threat) analysis on the company.

If you decide to be a short term investor, you would like to adhere to one of the following strategies:

a. Momentum Trading. This strategy is to look for stocks that increase in both price and volume over the recent past. Most technical analyses support this trading strategy. My advice on this strategy is to look for stocks that have demonstrated stable and smooth rises in their prices. The idea is that when the stocks are not volatile, you can simply ride the up-trend until the trend breaks.

b. Contrarian Strategy. This strategy is to look for over-reactions in the stock market. Researches show that stock market is not always efficient, which means prices do not always accurately represent the values of the stocks. When a company announces a bad news, people panic and price often drops below the stock's fair value. To decide whether a stock over-reacted to a news, you should look at the possibility of recovery from the impact of the bad news. For example, if the stock drops 20% after the company loses a legal case that has no permanent damage to the business's brand and product, you can be confident that the market over-reacted. My advice on this strategy is to find a list of stocks that have recent drops in prices, analyze the potential for a reversal (through candlestick analysis). If the stocks demonstrate candlestick reversal patterns, I will go through the recent news to analyze the causes of the recent price drops to determine the existence of over-sold opportunities.

Step 2. Conduct researches that give you a selection of stocks that is consistent to your investment time frame and strategy. There are numerous stock screeners on the web that can help you find stocks according to your needs.

Step 3. Once you have a list of stocks to buy, you would need to diversify them in a way that gives the greatest reward/risk ratio (The Sharpe Ratio). One way to do this is conduct a Markowitz analysis for your portfolio. The analysis is from the Modern Portfolio Theory and will give you the proportions of money you should allocate to each stock. This step is crucial because diversification is one of the free-lunches in the investment world.

These three steps should get you started in your quest to consistently make money in the stock market. They will deepen your knowledge about the financial markets, and would provide a sense of confidence that helps you to make better trading decisions.

About the Author: Zheng Fang is the creator of Advance Stock Pattern Scanner of and the owner of several stock picking blogs:

1. Optimal Portfolio
2. Candlestick Stock Picks
3. Cup and Handle Stock Picks
4. Technical Analysis