Carhart four-factor model
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In portfolio management, the Carhart four-factor model is an extra factor
addition in the Fama–French three-factor model, proposed by Mark
Carhart. The Fama-French model, developed in the 1990, argued most
stock market returns are explained by three factors: risk, price (value
stocks tending to outperform) and company size (smaller company stocks
tending to outperform). Carhart added a momentum factor for asset pricing
of stocks. The Four Factor Model is also known in the industry as the
Monthly Momentum Factor (MOM).[1][2] Momentum is the speed or velocity
of price changes in a stock, security, or tradable instrument.[3]
Development
The Monthly Momentum Factor(MOM) can be calculated by subtracting
the equal weighted average of the lowest performing firms from the equal
weighed average of the highest performing firms, lagged one month
(Carhart, 1997). A stock would be considered to show momentum if its
prior 12-month average of returns is positive, or greater. Similar to the
three factor model, momentum factor is defined by self-financing portfolio
of (long positive momentum)+(short negative momentum). Momentum
strategies continue to be popular in financial markets. Financial analysts
often incorporate the 52-week price high/low in their Buy/Sell
recommendations.[4]
The four factor model is commonly used as an active management and
mutual fund evaluation model.
Three commonly used methods to adjust a mutual fund's returns for risk
are:
1. The market model:
The intercept in this model is referred to as the "Jensen's alpha".
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2. The Fama–French three-factor model:
The intercept in this model is referred to as the "three-factor alpha".
3. The Carhart four-factor model:
The intercept in this model is referred to as the "four-factor alpha".
is the monthly return to the asset of concern in excess of the
monthly t-bill rate. We typically use these three models to adjust for risk. In
each case, we regress the excess returns of the asset on an intercept (the
alpha) and some factors on the right hand side of the equation that attempt
to control for market-wide risk factors. The right hand side risk factors are:
the monthly return of the CRSP value-weighted index less the risk free rate
(
), monthly premium of the book-to-market factor (
) the
monthly premium of the size factor (
), and the monthly premium on
winners minus losers (
) from Fama-French (1993) and Carhart
(1997).
A fund manager shows forecasting ability when his fund has a positive and
statistically significant alpha.
SMB is a zero-investment portfolio that is long on small capitalization (cap)
stocks and short on big cap stocks. Similarly, HML is a zero-investment
portfolio that is long on high book-to-market (B/M) stocks and short on low
B/M stocks, and UMD is a zero-cost portfolio that is long previous 12month return winners and short previous 12-month loser stocks.
See also
References
1. ^ Carhart, M. M. (1997). "On Persistence in Mutual Fund
Performance". The Journal of Finance. 52 (1): 57–82.
doi:10.1111/j.1540-6261.1997.tb03808.x. JSTOR 2329556.
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2. ^ Hezbi, Hashem; Salehi, Allahkaram (22 September 2016).
"Comparison of Explanatory Power of Carhart Four-Factor Model and
Fama-French Five-Factor Model in Prediction of Expected Stock
Returns". Financial Engineering and Portfolio Management. pp. 137–
152.
3. ^ Staff, Investopedia. "Momentum Indicates Stock Price Strength".
Investopedia. Retrieved 2021-02-28.
4. ^ Low, R.K.Y.; Tan, E. (2016). "The Role of Analysts' Forecasts in the
Momentum Effect" (PDF). International Review of Financial Analysis.
48: 67–84. doi:10.1016/j.irfa.2016.09.007.
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