Alpha-Beta Test Run Results

We have estimated the alpha-beta values for 51 mutual funds for 1-year (brown), 3-year (green), and 5-year (blue) ending 9/30/2006. Our estimated values are consistent with the published values at Morningstar, Yahoo, and Google. However, there were some values which were not the same as the published values due to different reference indexes other than S&P 500 were used for the published data. In our calculations, we use VFINX returns as the market returns. We believe this is a much better market index than the theoretical S&P 500 index.

We made three observations about this test run. First, our calculation methodology must be consistent with the methodology used by Morningstar since our estimated values for alpha and beta are consistent with the published values at Morningstar web site. We also checked our values with the published values at Google Finance. We have discovered the same consistency. So we believe that our data source and calculation methods are reliable.

Secondly, the 51- funds used in our test run have a wide range of alpha-beta values. The beta values range from 0.25 to 3.00 while alpha values range from -14 to +41. We believe these ranges cover a wide spectrum of data. So the alpha-beta values are not concentrated closely to its origin (alpha = 0 and beta = 1). There is a great possibility for someone to select overly under-valued or over-valued funds among the funds. We believe there is greater potential if all mutual funds are considered for this project.

Thirdly, the values of alpha and beta are not very stable over different time periods. The “best” funds (low beta with high alpha) are changing places among themselves. This may be the reason why some sector rotation funds can outperform the overall market for an extended period of time. This characteristic may be a good treasure place for swing traders to harvest the change tides of sectors or styles.

Our next project is to study the time series characteristics of alpha and beta value for a few selected funds.

David Swensen Asset Allocation Model

David Swensen is the Chief Investment Officer of Yale Endowment. Here are his investment recommendations for himself and others.

For investors unable to compete effectively in active management, Swensen recommended a generally passive approach of indexed funds with the following allocations:

• 30% domestic equities
• 15% foreign equities
• 05% emerging markets
• 20% real estate
• 15% traditional bonds
• 15% Treasury Inflation-Protected Securities (TIPS)

For those investors, investing should be boring—like watching grass growing. If they try to engage in active management on a casual basis, "they are bound to fail," he said. Swensen’s pioneering approach to alternative investing has contributed handsomely to Yale’s 20 years of 16 percent annualized returns. Yale’s current asset allocation is the following:

• 14% domestic equities
• 14% international equities
• 05% fixed income
• 25% absolute return
• 25% real estate
• 17% private equity

The 25% absolute return and the 17% private equity may not be available to average investors. However, the ETF markets are very creative now. New ETF funds are introduced every month. One may be able to find these alternative investment vehicles in the coming years.

Bill Schultheis Asset Allocation Model

PAUL B. FARRELL wrote an article about Bill Schultheis. He quoted Bill: "Wall Street's most common way is to diversify with stocks by industry sector; technology, health care, transportation, financials, energy and so forth. The result is a portfolio of primarily large-cap stocks that will, in the long run, move almost identical to the S&P 500 index."

Bill Schultheis is a strong advocate of modern portfolio theory: "A more prudent way to diversify is to identify the dimensions of the market that move dissimilar to the S&P 500 in the short run, and build a portfolio accordingly." And that means a decidedly different kind of asset allocation. Instead of focusing on industry sectors, the focus is shifted to include all stock categories including small-caps and international. Here's the simple asset allocation from Bill Schultheis using just seven Vanguard index funds:

(40%) Bond Market Index;
(10%) Standard & Poor's 500;
(10%) Large-Cap Value Index;
(10%) Small-Cap Index;
(10%) Small-Cap Value Index;
(10%) International Stock Index;
(10%) REIT Index.

At surface this allocation model looks simple, but it is one of the best asset allocation models out there. Removing or adding one fund to this model would make the portfolio worse off.

This model has one weakness. Without any sector funds in this portfolio would make this model a little bit weak in a sector driven market such as the technology bull market of the 1990s or the recent energy sector bull market in the recent years. However, by adding 10 sector funds to this portfolio would make the number of funds more than doubled. Then this would not be a simple asset allocation model.

On Price Quantity and Value

When I go grocery shopping, I have to deal with two things. One of them is Quantity. Another one of them is price. When economists talk about GDP, they have to deal with quantity and price. When rich people buy or sell gold, they have to know the quantity and price of gold. When investors buy stocks, they have to know the number of shares and the share price. In general, there is a fixed relationship between price, quantity, and value.

V = P * Q

Where V is value, Q is quantity, and P is price per unit of quantity.

The same equation is applicable in the cases of grocery shopping, GDP calculation, gold trading, and stock investing. However, there are some subtle characteristics about the quantity and price. Today I am going to explore this subtlety.

In the case of grocery shopping, the total quantity of food one family can consume over a specific period, say during a year, can be fairly stable. However, the total cost of the food consumption can vary widely depending one the price of food. The rate of change for the total quantity of food can be much smaller than the rate of change of price over the same period of time.

In the case of GDP estimation, since the total quantity of domestic products is impossible to determine accurately. So the Gross Domestic Product is usually just a total value number. Price change is determined independently. The change of quantity of domestic products is smaller than the change of price. So the economists call this extra-change in price as inflation.

In the case of gold trading, the total quantity of gold in the world changes less than 2% on an annual basis while the change of gold price can be as high as 100% per year. Gold price gyration over the past several years is an excellent example of the price change.

In trading stocks, the total outstanding shares of a company changes very little every year while the price movements of many stocks usually over 100% every year. One can almost find some stocks with daily price change over 50%.

From the above example, I can easily conclude that the price change over time is much faster than the quantity change over the same time. If this assumption is indeed true, then one can make some further conclusions.

Since the real values of grocery, gross domestic products, gold, and stocks are associated with quantity only, any extra-change in price will never last a very long time. The extra-change will reverse toward it real value. Investment gurus such as Warren Buffett call this real value as intrinsic value for stocks. Since the intrinsic value for any company would not change as rapidly as its stock price, so the over-price or under-price of stocks will reverse to its intrinsic value eventually.

Since the real value or intrinsic value is much less volatile than the price movements, one can win continuously if he can spot the differentials between the price and value. This is why investors always stress that one has to buy low and sell high.

Sample Funds to Study Alpha-Beta Matrix

By today, Zhen has completed the first part of data preparation calculations. Now we need to test some real mutual fund data in order to derive our understandings of the scope of Alpha-Beta Matrix. First, let’s study the equity style funds and sector funds first. Stlyle and Sector funds are used often to construct diversified portfolios.

We are going to select 27 style funds, 18 sectors funds, and 5 real estate funds in our first test. Three funds are selected for each style and two funds are chosen for each sector. We use five real estate funds in this test. So we have a total of 50 sample funds, or about 1% of the mutual fund universe.

Some of the factors considered in selecting funds are fund size versus fund family, index versus actively managed fund, and management fees. Based on these factors, we selected the following 27 style funds in nine styles.

(1) Large cap growth
a. FCNTX – Fidelity Contra fund
b. JANSX – Janus Fund
c. VIGRX –Vanguard Growth Index
(2) Large cap blend
a. VFINX –Vanguard 500 Index
b. FMAGX – Fidelity Magellan Fund
c. JSVAX – Janus Contrarian Fund
(3) Large cap value
a. DODGX – Dodge & Cox Stock
b. FEQIX – Fidelity Equity Income Fund
c. VWNDX – Vanguard Winsor
(4) Mid-cap growth
a. RPMGX – T. Rowe Price Mid-cap Growth
b. FDEGX – Fidelity Aggressive Growth
c. JAENX – Janus Enterprise
(5) Mid-cap blend
a. FLPSX – Fidelity Low Price Stock Fund
b. VSEQX – Vanguard Strategic Equity
c. VIMSX – Vanguard Mid-cap Index
(6) Mid-cap value
a. FDVLX – Fidelity Value Fund
b. JMCVX – Janus Mid-cap Value
c. VASVX – Vanguard Selected Value
(7) Small cap growth
a. BGRFX – Baron Growth
b. JAVTX – Janus Venture
c. VISGX – Vanguard Small Growth Index
(8) Small cap blend
a. NAESX – Vanguard Small Cap Index
b. FSLCX – Fidelity Small Cap Stock
c. DISSX – Dreyfus Small Cap Index
(9) Small cap value
a. RYTRX – Royce Total Return
b. VISVX – Vanguard Small Cap Value
c. JSCVX – Janus Small Cap Value

We have selected 18 sector funds in nine sectors.

(1) Consumer goods
a. FDFAX – Fidelity Select Consumer Staples
b. ICLEX – Icon Leisure & Consumer Staples
(2) Consumer Services
a. FSCPX – Fidelity Select Consumer Discretionary
b. ICCCX – Icon Consumer Discretionary
(3) Energy
a. FSENX – Fidelity Select Energy
b. VGENX – Vanguard Energy
(4) Financial
a. FIDSX – Fidelity Select Financials
b. FSFSX – AIM Financials
(5) Health care
a. FSPHX – Fidelity Select Health Care
b. VGHCX – Vanguard Health Care
(6) Industrial
a. FCYIX – Fidelity Select Industrials
b. ICTRX – Icon Industrials
(7) Materials
a. FSAGX – Fidelity Select Gold
b. VGPMX – Vanguard Precious Metals
(8) Technology
a. FSPTX – Fidelity Select Technology
b. JAGTX – Janus Global Technology
(9) Utilities
a. FIUIX – Fidelity Utilities
b. BULIX – American Century Utilities

The Five Real Estate Funds selected are listed below.

(1) FRESX – Fidelity Real Estate Fund
(2) VGSIX – Vanguard REIT Index
(3) CSRSX – Cohen & Steers Realty Shares
(4) REACX – American Century Real Estate
(5) AIGYX – Alpine Realty Income & Growth

Base Periods for Calculating Returns

Daily Data is usually available for stocks or mutual funds. Stock data is available in five columns: Open, High, Low, Close, and Adjusted Close at Yahoo Finance. Mutual fund data is available for daily close and adjusted daily close.

Weekly data is available on the first trading date of the week. Monthly Data is available on the first trading date of each month.

Daily Return is calculated based on the daily data.

Weekly Return has two ways. One is based on consecutive 5 trading days. This is used to calculate long-term time series (several years). Another one is based on the calendar week from Monday through Friday. This is used to calculate short-term time series (usually less than one year).

Monthly Return is calculated for each Calendar month, such as January, February, etc.

Quarterly Return is calculated for each Calendar quarter, such as 1st Quarter, 2nd Quarter, etc.

Annual Return is based on the Calendar year, such as 2001, 2002, 2003, etc.

YTD (year-to-date) return is calculated as the total return up to the current date of concern. The rate is not annualized usually.