Slice and dice

From Bogleheads

Slice and dice refers to dividing allocations within a given unitary asset class, such as stocks. Adding additional asset classes to a portfolio (bonds[1], gold, commodities) is asset allocation, not slicing and dicing. Slice and dice portfolios are essentially diversified portfolios that seek to outpace the broad market index by systematically overweighting various sectors.[2]

In its simplest form, the idea is to garner excess returns by holding a portfolio that:[2][3]

a) splits the market portfolio among sub-asset classes that are deemed likely to deliver superior returns;
b) holds higher weightings of size and value sub-asset classes that have lower correlations with the market; and
c) periodically rebalances each sub-asset class to its original weight.

This is in contrast to total stock market investing, which approximates the entire market as a single asset class.

The theoretical justification for slice and dice rests on the benefits of what is often called "diversification." However, in this context the word is used with a specific technical meaning. It refers to asset classes with low correlation coefficients. The benefit comes from the fact that a mixture of assets with low correlation will have better risk-adjusted returns than either of them taken by itself. A well-known example is that even though international stocks are riskier than domestic stocks, adding a moderate amount of international stocks to domestic stocks actually reduces the risk of the domestic stocks--slightly.[4]


Slice and dice has its roots in the research of Fama and French in the 1992 paper, "The Cross Section of Expected Stock Returns", which introduced the three factor model. By the mid and latter part of the nineties, investment advisors and some individuals began postulating, and then implementing portfolios that were based on the market, size, and value factors, in comparison to holding a "market cap" US stock index portfolio, such as the S&P 500 or a Total Market index.[5]

Originally, the portfolio most widely used for theoretical discussion was the 4X25 slice and dice, based on the "four corners" (quadrants) of the Fama / French three factor world: large growth, large value, small growth, and small value. These quadrants are created by splitting the stocks as follows: [6]

  • Split vertically: "Large" constitutes size deciles one through five of the CRSP (Center for Research in Security Prices) database[7], and "Small," deciles six through ten.
  • Split horizontally: "Value" and "Growth" are defined as the bottom and top 30% of stocks sorted by price/book.

Advisors and portfolio theorists arguing slice and dice (including Bernstein, Swedroe, Troutner, among many) considered market cap indexes to be dominated by growth stocks and were used as the growth proxies in slice and dice portfolios.

As an example, a four quadrant slice and dice portfolio consisting of S&P indexes (available in the late nineties/early 2000's) would have consisted of the following:

  • S&P 500 (25%)
  • S&P 500 Value (25%)
  • S&P 600 (25%)
  • S&P 600 Value (25%)

This 4x25 allocation is the scheme used for analysis by Bogle in his "Telltale Chart" address to the Bogleheads reunion in 2002 (Morningstar Investment Forum at that time).[2]

Over time, this original 4x25 allocation scheme was not strictly adhered to in practice in order to allow for more value tilted allocations and allocations more closely tied to an individual's risk profile. The discussion tab (above) contains a brief summary of slice and dice portfolios from several bogleheads authors, starting from 1999.

The 4x25 allocation template is evident in some of the "expert" lazy portfolios. The following three portfolios all show fealty to the 4x25 metric, although one shows an increased value tilt.


As previously stated, slice and dice breaks the total stock market into four segments defined as large growth, large value, small growth and small value stocks. Similar to the equity style boxes, the vertical segments (large / small) are based on the decile rankings by the Chicago Center for Research in Security Prices (CRSP) which breaks down the market into 10 slices containing equal numbers of companies.[7] To determine whether they are "growth" or "value" (horizontal segments), companies are divided according to their risk or volatility levels.[8]

Slice and dice is based on the approach that small cap stocks and value stocks are associated with risk premiums. Weighting a portfolio in favor of small cap stocks and value stocks increases its volatility and therefore return over time.[9]

Those advocating the total stock market approach emphasize tax efficiency, simplicity, and the advantages of owning the total market.[10]

For example, a "total market" investor might be satisfied with a two-fund portfolio that approximates the entire market; Total Stock Market Index and Total Bond Market Index.

A slice and dice investor would use more than one stock fund, such as William Schulteis's "Coffeehouse Portfolio", in which the stock allocation is made up of six equal "slices:" Small-Cap Value Index, REIT Index, Total International Stock Index, Index (S&P) 500, Value Index, and Small-Cap Index.[4]

Slice and dice is more complex than a "total market" approach, as slice and dice portfolios require more attention and more frequent rebalancing than simpler portfolios. The debate boils down to how large the benefit is, whether it is possible to prove unequivocally that there really is a benefit, and, even if so, whether it is worth the effort.[4]


The definitions stated previously have evolved over time to include additional asset classes, such as commodities or non-investment-grade ("high-yield") bonds. The definition of "asset class" is flexible and varies from authority to authority.[4]

Slicing is used to divide an asset class or portfolio in one dimension.[11]

  • A sliced portfolio: Stocks, Bonds, Cash

Slice and dice divides an asset in two or more dimensions.

  • A diced portfolio: Stocks (Domestic and Foreign); Bonds (Domestic and Foreign); Cash (CDs denominated in US and other currencies).

Stocks are divided into two dimensions in a manner similar to the equity style boxes. The vertical slice segregates the asset into value and growth, the horizontal dice (2nd cut) segregates the asset into size (market cap).

International stocks can be divided according to regions. For splitting allocations along regional axes see: Slice and Dice International. International stocks can also be sliced and diced along the four quadrants of the Fama/French three factor model using exchange traded funds. Ishares offers developed market funds based on MSCI international indexes which provide for large blend, large value, small blend and small value splits.

On the bond side, investors can slice and dice a bond portfolio into different "term" and "credit" exposures relative to a total bond index (or hold them in the same percentages, but still hold them separately to better control their allocation to each dimension).[12] (Refer to the fixed income style boxes, which slice vertically as "credit risk" and dice horizontally as "term" or duration.)

What slice and dice is not: If you slice the total world market into pieces and hold each piece in the proportion it represents of the total world market, then you still hold the total world market. There is no tilt and no slice.[13]


Tilting is sometimes associated with slice and dice, as both approaches overweight small cap and/or value stocks compared to the total stock market.[14] However, tilting and slice and dice are completely different concepts.

Tilting does require allocation according to a slice and dice model. However, tilting addresses the question of what the allocation across asset classes is, while slice and dice only specifies that the asset classes are managed explicitly and are fixed.

Tilting means a preference for some asset classes or for some factor loading that is different from the total market of whatever asset population one is working in, usually US equities.[15] Multifactor (multi-factor) investing uses this approach.

Bogle's own view

An interesting, nuanced, and skeptical view is provided by John C. Bogle in "The Telltale Chart," based on a 2002 speech, and included in his 2010 book Don't Count On It! The tenor of the essay is that many popular investment approaches that are often believed to have superior performance, only do so for a while before succumbing to "reversion to the mean" (RTM). His examples include small-cap stocks, value stocks, and "slice and dice" portfolios. (It is commendable that he updated all the charts to 2009 for inclusion in the book, even though many of the assets and portfolios he charts did well recently, undercutting his point).

See also


  1. A bond is not a unitary asset class, since the segments of the bond market: treasuries, corporates, municipals, asset-backed, mortgage securities, inflation indexed securities, zero coupon, are all discrete. However, this restriction has been dropped over time (refer to the "Usage" section which follows).
  2. 2.0 2.1 2.2 The Telltale Chart
  3. Paraphrased from the original text, as suggested by Barry Barnitz. See the discussion tab above.
  4. 4.0 4.1 4.2 4.3 What is "Slice and Dice"?, direct link to post.
  5. This section is based on an email from Barry Barnitz.
  6. The Cross-Section of Expected Stock Returns: A Tenth Anniversary Reflection, by William J. Bernstein
  7. 7.0 7.1 CRSP Cap-Based Portfolio Indices
    1. Ranks all NYSE companies by market capitalization and divides them into ten equally populated portfolios.
    2. Amex and NASDAQ stocks are then placed into the deciles determined by the NYSE breakpoints, based on market capitalization
    3. The series of 10 indices are identified as CRSP 1 through CRSP 10, where CRSP 10 has the largest population and smallest market-capitalization.
    4. CRSP portfolios 1-2 represent large cap stocks, portfolios 3-5 represent mid-caps, portfolios 6-8 represent small caps, and portfolios 9-10 represent micro-caps.
    5. The portfolios are rebalanced quarterly and total return, capital appreciation return, and income return are calculated on a monthly basis.
    About CRSP: The Chicago Center for Research in Security Prices (CRSP), part of the University of Chicago’s Booth School of Business, maintains a database which provide a strong foundation for economic forecasting, stock market research, and financial analyses to academic institutions, investment banks, brokerage firms, corporations, banks, and government agencies. Eighty percent of academic research in stock market and investment analysis uses CRSP data as a source due to the completeness and accuracy of the information.
  8. Slice and Dice Primer
  9. In Defense of "Slice and Dice", from Index Funds Advisors
  10. Dreman Criticizes Fama/French, direct link to post (Fama Paper)
  11. What is "Slice and Dice"?, direct link to post
  12. By email from SmallHi.
  13. What is "Slice and Dice"?, direct link to post
  14. What is "Slice and Dice"?, direct link to post.
  15. What is "Slice and Dice"?, direct link to post.

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