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Monte Carlo

Constructing Portfolios: It's all about the Factors

Wednesday, 20, July, 2011

By: Jay Franklin  |   July 20, 2011

Many studies have shown that the long-term performance of a portfolio is explained by its structure (or asset allocation). The most important aspect of the structure is the breakdown between higher risk assets such as equities and real estate investment trusts and lower risk assets such as bonds and cash.

On the equity side, IFA constructs its portfolios based on the three-factor asset pricing model that Fama and French introduced in 1993. The Fama/French three-factor model says the expected return of a broadly diversified stock portfolio in excess of a risk-free rate is a function of that portfolio’s sensitivity or exposure to three common risk factors: (1) a market factor, as measured by the excess return of a broad equity market portfolio relative to a risk-free rate; (2) a size factor, as measured by the difference between the returns of a portfolio of small stocks and the returns of a portfolio of large stocks; and (3) a value factor, as measured by the difference between the returns of a portfolio of high book-to-market (or value) stocks and the returns of a portfolio of low book-to-market (or growth) stocks. The underlying premise of this model is that small cap and value stocks are riskier than large cap and growth stocks and thus carry higher expected returns.

Given a time series of monthly returns of any diversified portfolio, the exposure to the three factors can be calculated via regression, and an expected future return may be estimated. For any well-diversified US Equity portfolio, exposure to the three risk factors and expenses explains over 95% of the returns.

For any desired risk exposure, investors have a myriad of ways to arrive there. As we will demonstrate below, portfolios that appear to be very different from each other can have virtually the same long-term returns due to similarity of risk factor exposure. Below are the three portfolios that were evaluated:

Portfolio #1 Portfolio #2 Portfolio #3
CRSP Deciles 1-10 (Total US Stock Market) 100%
CRSP Deciles 1-2 (US Large Cap Stocks) 85%
CRSP Deciles 9-10 (US Micro Cap Stocks) 15%
Fama/French Large Growth Index 55%
Fama/French Large Value Index 30%
Fama/French Small Growth Index 10%
Fama/French Small Value Index 5%
Size Coefficient -0.02 0.00 0.02
Value Coefficient -0.02 -0.01 -0.01

Note that portfolio #1 simply represents the total US stock market, and portfolios #2 and #3 seek to replicate this exposure using well-defined subsets of the market. Below is a table showing the monthly returns of each of these portfolios:

January, 1990 to May, 2011 (21 years and 5 months)

Monthly Average Return Standard Deviation
Portfolio #1 0.83% 4.46%
Portfolio #2 0.84% 4.42%
Portfolio #3 0.81% 4.52%
CRSP Deciles 1-10 (Market) 0.83% 4.46%
CRSP Deciles 1-2 (Large) 0.79% 4.33%
CRSP Deciles 9-10 (Micro) 1.16% 6.36%
F/F Large Growth 0.78% 4.54%
F/F Large Value 0.79% 4.89%
F/F Small Growth 0.83% 7.07%
F/F Small Value 1.26% 6.45%

As expected, the returns of the three portfolios are closely clustered together because these portfolios all have a similar exposure to risk. Of course, the returns from month-to-month or year-to-year can be quite different due to random variations (i.e., noise). These differences are captured in the “error term” of the equation of the 3-factor model. The table below shows just how different the monthly and annual returns of these portfolios can be:

Portfolio #2 Portfolio #3
Monthly Returns
Maximum over Portfolio #1 2.61% 3.44%
Maximum under Portfolio #1 -1.43% -1.86%
Rolling 12-Month Returns
Maximum over Portfolio #1 3.09% 11.08%
Maximum under Portfolio #1 -2.56% -5.26%

Since the error term has an expected value of zero, its impact diminishes over time, and for a sufficiently long period (20 years or more) it becomes relatively negligible.

One important application of factor-based portfolio construction is the design and maintenance of tax-managed mutual funds. IFA currently utilizes five such funds in taxable accounts.  These funds seek to minimize taxable distributions by deferring realized gains, harvesting losses, and avoiding companies with very high dividend yields. Simultaneously, each fund targets a particular risk exposure in a passive manner which means there is no attempt to identify “under-valued” companies or to forecast economic/market trends as a basis for placing trades.

An additional application is the construction of passively managed socially and environmentally responsible mutual funds. These funds can target a specific risk exposure while maintaining filters that exclude or underweight companies that do not meet the desired criteria.

The Fama/French 3-factor model creates a framework for investors that helps them target factor exposures rather than arbitrary benchmarks, and it allows them to distinguish between systematic expected returns and random noise. Most importantly, a good understanding of it gives investors the perspective to stay disciplined, especially during times when performance differs from expectations.




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