Dfa - Dimensional Fund Advisors

Fama and French’s three factor model attempts to explain the variation of stock prices through a multifactor model that includes a size factor and BE/ME factor in addition to the beta risk factor. Fama-French model essentially extended the CAPM (which breaks up cause of variation of stock price into systematic risk which is non-diversifiable and idiosyncratic risk which is diversifiable) by introducing these two additional factors. Fama and French find that stocks with high beta didn’t have consistently higher returns than stocks with low beta and this indicates that beta was not a useful measure under their model. Their model is based on research findings that sensitivity of movements of the size and BE/ME factor constituted risk, and

The extracted data used includes monthly returns from January 1972 to July 2011. The assets are selected so that the portfolio contains the largest, most liquid, and most tradable assets. The choice of such a variety of assets across several markets was used in order to generate a large cross sectional dispersion in average return. It helped to reveal new factor exposure and define a general framework of the correlated value and momentum effects in various asset classes.

“The Benefits of diversification are clear. Portfolio theory has played a crucial role in explaining the relationship between risk and return where more than one investment is held. It also enables us to identify optimal and efficient portfolios.”

CAPM is a model that describes the relationship between risk and expected return, and the formula itself measures the expected return of the portfolio. Mathematically, when beta is higher, meaning the portfolio has more systematic risk (in comparison to the market portfolio), the formula yields a higher expected return for the portfolio (since it is multiplied by the risk premium and is added to the risk free interest rate). This makes sense because the portfolio needs to

DFA’s founders believed in two principals (outside of efficient markets): the value of sound academic research, and the ability of skilled traders to contribute to a fund’s profits even when the investment was inherently passive. By working closely with the academic world, DFA is able to exploit opportunities generated from academic research before others are able to; this creates opportunities for short and long-term excess return. Also, working in stocks that other mutual funds do not participate (micro, small-cap) allows DFA to exploit opportunities in otherwise illiquid stocks. By having a large presence in this market, the company is able to take advantage of trading opportunities with counterparts (liquidity discounts from block purchases).

Thus, this block-trading strategy combined with adverse selection avoidance allowed the DFA to beat the market and thus the benchmark by about 200 basis points over the 20 year period. And as a result became the benchmark for these types of portfolios.

In the years since 2000, a few investors have determined that their small cap portfolio outperformed their shares held in larger companies in terms of ROI (return on investment). The total dollar price earned was lesser; nevertheless the benefit percentage was

Using CAPM to provide the calculation for the equity, this presents both positive and negative effects.

CAPM results can be compared to the best expected rate of return that investor can possibly earn in other investments with similar risks, which is the cost of capital. Under the CAPM, the market portfolio is a well-diversified, efficient portfolio representing the non-diversifiable risk in the economy. Therefore, investments have similar risk if they have the same sensitivity to market risk, as measured by their beta with the market portfolio.

Investors hold diversified portfolios : One of the assumptions of CAPM model is that investors are holding only portfolios which are subjected to systematic risk , the unsystematic risk can be ignored , therefore the unsystematic risk has been ignored (Lakonishok & Shapiro , 1986)

To reduce a firm’s specific risk or residual risk a portfolio should have negative covariance or rather it should have no variance at all, for large portfolios however calculating variance requires greater and sophisticated computing power. As such, Index models greatly decrease the computations needed to calculate the optimum portfolio. The use of such Index models also eliminates illogical or rather absurd results. The Single Index model (SIM) and the Capital Asset Pricing Model (CAPM) are such models used to calculate the optimum portfolio.

Using time series regression on the monthly returns we have estimated the beta coefficient for each stock. Using the market model of CAPM i.e., regressing each stock’s monthly returns against the market index (Nifty100) we have estimated individual stock beta’s.

DFA’s passive investment approach means that it is able to add value by tapping on some of the world’s leading economists to bring their latest academic research into practice. This approach is not for every investor as there are both sides to this strategy:

As indicated by the case study S&P 500 index was use as a measure of the total return for the stock market. Our standard deviation of the total return was used as a one measure of the risk of an individual stock. Also betas for individual stocks are determined by simple linear regression. The variables were: total return for the stock as the dependent variable and independent variable is the total return for the stock. Since the descriptive statistics were a lot, only the necessary data was selected (below table.)

Generally, researchers are interested in studying factors that can be applied to predict asset prices. Relied on Markowitz (1952)’s earlier work on diversification and modern portfolio model, it is known that idiosyncratic risk can be diversified away and only systematic risk matters to investors. Treynor (1961), Sharpe (1964) and Lintner (1965) independently contributed to the CAPM to explain the relationship between the systematic risk factor and securities returns. This emphasize the importance of systematic risk for investors to estimate asset price in order to earn excess return on market.