Selecting Low-Cost Funds to Replicate the Carhart Four Factors

Summary

The document frames a practical fund-selection problem: find one ETF or mutual fund for each of the market, size, value, and momentum factors, with the goal of tracking the Carhart four-factor returns cheaply. It proposes evaluating a candidate fund by regressing its returns on the corresponding factor return. For a value fund, for example, the desired exposure has a high coefficient of determination and a factor loading near one, while the intercept and residual capture other performance and tracking differences.

This is a screening criterion rather than a completed investment analysis. The document names no candidate funds, reports no regression results, and does not discuss estimation periods, fees, turnover, liquidity, benchmark construction, or whether a single fund can isolate each factor. Those choices would materially affect how well a fund tracks a factor and how robust the comparison is out of sample.

Key ideas

• A four-fund portfolio could seek separate exposure to market, size, value, and momentum factors.
• Regression can assess whether a candidate fund tracks its intended factor.
• A high R-squared and a loading near one are proposed as desirable tracking properties.
• The document offers a selection framework but no fund recommendations or empirical results.
• Fees, benchmark definitions, sample period, and unintended exposures remain unexamined.

Tags

# What ETFs and mutual funds track the Carhart 4 factors best? I.e. how to replicate these factors cheaply?


# What ETFs and mutual funds track the Carhart 4 factors best? I.e. how to replicate these factors cheaply?












I am looking for a portfolio of ETFs and mutual funds that tracks market, size, value and momentum factors.

One ETF/mutual fund per factor. So say that I want an ETF that tracks the value factor (let's call the return on that ETF $r^{value}_t$), what I am looking for is for an asset whose regression:

$r^{value} = \alpha_{value} + \beta^{value} HML^{Cahart} + \epsilon_t^{value}$

It should have a high $R^2$ and a $\beta^{value}$ close to 1.

Any suggestions of such ETFs/mutual funds?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.