Match Factor Exposure

This tool allows you to match the factor exposures or performance of the given asset or portfolio using a combination of assets from the given list. The tool finds the combination of the given assets that most closely clones the factor exposures of the target asset or portfolio based on the selected time period and factor model. The closest match based on past performance is also displayed for comparison purposes.

Target Portfolio
Ticker	Name	Allocation
VTSMX	Vanguard Total Stock Mkt Idx Inv	62.00%
DFSVX	DFA US Small Cap Value I	38.00%
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Regression
Factor	Loading	t-stat	p-value
Market (Rm-Rf)	1.03	61.249	0.000
Size (SMB)	0.41	23.890	0.000
Value (HML)	0.13	5.224	0.000
Profitability (RMW)	0.06	2.257	0.028
Investment (CMA)	0.03	1.099	0.276
Alpha (α)	1.03bps	0.201	0.841
Annualized Alpha (α)	0.12%

Factor Exposure Clone
Ticker	Name	Allocation
VTSMX	Vanguard Total Stock Mkt Idx Inv	60.25%
IJS	iShares S&P Small-Cap 600 Value ETF	39.75%
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Factor Exposure Clone Regression
Factor	Loading	t-stat	p-value
Market (Rm-Rf)	1.06	53.363	0.000
Size (SMB)	0.37	18.312	0.000
Value (HML)	0.12	4.045	0.000
Profitability (RMW)	0.14	4.687	0.000
Investment (CMA)	-0.03	-1.024	0.310
Alpha (α)	-15.99bps	-2.630	0.011
Annualized Alpha (α)	-1.92%

Returns Based Clone
Ticker	Name	Allocation
VTSMX	Vanguard Total Stock Mkt Idx Inv	57.53%
IJS	iShares S&P Small-Cap 600 Value ETF	42.47%
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Returns Based Clone Regression
Factor	Loading	t-stat	p-value
Market (Rm-Rf)	1.07	50.455	0.000
Size (SMB)	0.39	18.389	0.000
Value (HML)	0.13	4.031	0.000
Profitability (RMW)	0.15	4.713	0.000
Investment (CMA)	-0.03	-1.020	0.312
Alpha (α)	-17.04bps	-2.637	0.011
Annualized Alpha (α)	-2.04%

Match Summary

Match summary
Name	Description	Rm-Rf	SMB	HML	RMW	CMA	Alpha	Annual Alpha	R²	F-stat	Returns Regression R²
Target Portfolio	VTSMX=62.00%, DFSVX=38.00%	1.03	0.41	0.13	0.06	0.03	0.01%	0.12%	99.5%	1,983.36	-
Factor Exposure Clone	VTSMX=60.25%, IJS=39.75%	1.06	0.37	0.12	0.14	-0.03	-0.16%	-1.92%	99.2%	1,369.43	98.9%
Returns Based Clone	VTSMX=57.53%, IJS=42.47%	1.07	0.39	0.13	0.15	-0.03	-0.17%	-2.04%	99.1%	1,223.77	98.9%

Portfolio Performance

Portfolio performance statistics
Name	Description	Initial Balance	Final Balance	Compound Monthly Return	CAGR	Stdev	Best Year	Worst Year	Max. Drawdown	Sharpe Ratio	Sortino Ratio
Target Portfolio	VTSMX=62.00%, DFSVX=38.00%	$10,000	$14,945	0.67%	8.37%	16.04%	41.53%	-16.42%	-26.08%	0.45	0.66
Factor Exposure Clone	VTSMX=60.25%, IJS=39.75%	$10,000	$13,314	0.48%	5.89%	15.79%	34.73%	-18.04%	-28.97%	0.31	0.43
Returns Based Clone	VTSMX=57.53%, IJS=42.47%	$10,000	$13,483	0.50%	6.16%	15.87%	34.95%	-17.85%	-28.39%	0.32	0.45

Notes on results:

Past performance is no guarantee of future results, which may vary. All use is subject to terms of service.
Investing involves risk, including possible loss of principal. The value of the investments and the income derived from them may fluctuate over time.
All portfolio returns presented are hypothetical and backtested. Hypothetical returns do not reflect trading costs, transaction fees, or taxes.
Portfolio optimization determines target weights for portfolio assets based on mathematical models that can use either historical or forecasted data as inputs. Optimization results are not guarantees of future performance.
The results are based on information from a variety of sources we consider reliable, but we do not represent that the information is accurate or complete.
The results do not constitute investment advice or recommendation, are provided solely for informational purposes, and are not an offer to buy or sell any securities.
The results are based on the total return of assets and assume that all received dividends and distributions are reinvested.
The Fama-French, AQR, Alpha Architect, q-factor, and fixed income model factor returns are based on the US market
Returns based clone is based on minimizing the sum square of monthly return differences.
Returns regressions are based on multiple linear regression of monthly returns.
The clone portfolios assume monthly rebalancing.
CAGR = Compound Annual Growth Rate
Stdev = Annualized standard deviation of monthly returns
Sharpe and Sortino ratios are calculated and annualized from monthly excess returns over risk free rate (3-month treasury bill)
Stock market correlation is based on the correlation of monthly returns

Factor Analysis Summary

Factor regression results
Name	Ticker	Start Date	End Date	Rm-Rf	SMB	HML	RMW	CMA	Alpha	Annual Alpha	R²
Vanguard Total Stock Mkt Idx Inv	VTSMX	Jan 2001	Dec 2005	0.99	0.01	0.02	-0.00	-0.00	-0.01%	-0.08%	100.0%
DFA US Small Cap Value I	DFSVX	Jan 2001	Dec 2005	1.10	1.06	0.32	0.15	0.07	0.04%	0.46%	97.7%
iShares S&P Small-Cap 600 Value ETF	IJS	Jan 2001	Dec 2005	1.17	0.92	0.27	0.34	-0.06	-0.39%	-4.70%	96.7%

Vanguard Total Stock Mkt Idx Inv

Factor regression results for Vanguard Total Stock Mkt Idx Inv
Factor	Loading	Standard Error	t-stat	p-value
Ticker	VTSMX
Time Period	Jan 2001 - Dec 2005
Coefficient of Determination (R²)	100.0%
Regression F statistic	25,800.85 (p-value = 0.000)
Market (Rm-Rf)	0.99	0.004	223.917	0.000
Size (SMB)	0.01	0.004	1.788	0.079
Value (HML)	0.02	0.007	2.592	0.012
Profitability (RMW)	-0.00	0.006	-0.005	0.996
Investment (CMA)	-0.00	0.006	-0.691	0.493
Alpha (α)	-0.69bps	0.000	-0.511	0.612
Annualized Alpha (α)	-0.08%

DFA US Small Cap Value I

Factor regression results for DFA US Small Cap Value I
Factor	Loading	Standard Error	t-stat	p-value
Ticker	DFSVX
Time Period	Jan 2001 - Dec 2005
Coefficient of Determination (R²)	97.7%
Regression F statistic	468.83 (p-value = 0.000)
Market (Rm-Rf)	1.10	0.042	26.136	0.000
Size (SMB)	1.06	0.042	24.947	0.000
Value (HML)	0.32	0.062	5.075	0.000
Profitability (RMW)	0.15	0.061	2.387	0.021
Investment (CMA)	0.07	0.058	1.281	0.206
Alpha (α)	3.85bps	0.001	0.301	0.765
Annualized Alpha (α)	0.46%

iShares S&P Small-Cap 600 Value ETF

Factor regression results for iShares S&P Small-Cap 600 Value ETF
Factor	Loading	Standard Error	t-stat	p-value
Ticker	IJS
Time Period	Jan 2001 - Dec 2005
Coefficient of Determination (R²)	96.7%
Regression F statistic	313.35 (p-value = 0.000)
Market (Rm-Rf)	1.17	0.048	24.483	0.000
Size (SMB)	0.92	0.048	18.932	0.000
Value (HML)	0.27	0.071	3.874	0.000
Profitability (RMW)	0.34	0.070	4.910	0.000
Investment (CMA)	-0.06	0.067	-0.976	0.333
Alpha (α)	-39.18bps	0.001	-2.683	0.010
Annualized Alpha (α)	-4.70%

Annual returns
Year	Inflation	Target Portfolio		Factor Exposure Clone		Returns Based Clone		Vanguard Total Stock Mkt Idx Inv (VTSMX)	iShares S&P Small-Cap 600 Value ETF (IJS)
Year	Inflation	Return	Balance	Return	Balance	Return	Balance	Vanguard Total Stock Mkt Idx Inv (VTSMX)	iShares S&P Small-Cap 600 Value ETF (IJS)
2001	1.55%	0.88%	$10,088	-2.38%	$9,762	-1.78%	$9,822	-10.97%	11.68%
2002	2.38%	-16.42%	$8,431	-18.04%	$8,000	-17.85%	$8,069	-20.96%	-14.04%
2003	1.88%	41.53%	$11,933	34.73%	$10,779	34.95%	$10,890	31.35%	39.76%
2004	3.26%	17.34%	$14,002	16.50%	$12,557	16.77%	$12,716	12.51%	22.60%
2005	3.42%	6.73%	$14,945	6.03%	$13,314	6.03%	$13,483	5.98%	6.00%

Monthly returns
Year	Month	Target Portfolio Return	Factor Exposure Clone Return	Returns Based Clone Return	Vanguard Total Stock Mkt Idx Inv (VTSMX)	iShares S&P Small-Cap 600 Value ETF (IJS)
2001	1	6.29%	5.43%	5.54%	3.83%	7.86%
2001	2	-6.57%	-7.35%	-7.21%	-9.41%	-4.21%
2001	3	-5.10%	-6.01%	-5.97%	-6.72%	-4.94%
2001	4	7.39%	7.63%	7.59%	8.16%	6.82%
2001	5	2.97%	1.77%	1.82%	1.01%	2.91%
2001	6	0.41%	-0.19%	-0.09%	-1.64%	2.01%
2001	7	-1.68%	-1.12%	-1.08%	-1.71%	-0.22%
2001	8	-4.23%	-4.00%	-3.86%	-6.00%	-0.96%
2001	9	-11.11%	-11.20%	-11.35%	-9.00%	-14.53%
2001	10	3.06%	3.31%	3.36%	2.52%	4.50%
2001	11	7.70%	7.60%	7.60%	7.63%	7.55%
2001	12	3.77%	3.79%	3.93%	1.78%	6.83%
2002	1	-0.18%	0.10%	0.20%	-1.24%	2.14%
2002	2	-1.33%	-1.40%	-1.36%	-2.05%	-0.42%
2002	3	6.46%	6.10%	6.22%	4.38%	8.72%
2002	4	-1.31%	-1.35%	-1.11%	-4.90%	4.03%
2002	5	-1.95%	-2.18%	-2.24%	-1.22%	-3.63%
2002	6	-5.17%	-6.09%	-6.03%	-7.06%	-4.62%
2002	7	-10.90%	-11.10%	-11.31%	-8.02%	-15.78%
2002	8	-0.15%	0.15%	0.13%	0.53%	-0.42%
2002	9	-9.01%	-9.21%	-9.15%	-10.07%	-7.91%
2002	10	5.36%	5.63%	5.50%	7.65%	2.58%
2002	11	7.00%	5.84%	5.82%	6.06%	5.50%
2002	12	-4.81%	-4.44%	-4.37%	-5.57%	-2.74%
2003	1	-2.89%	-3.14%	-3.18%	-2.54%	-4.05%
2003	2	-2.61%	-2.63%	-2.69%	-1.69%	-4.05%
2003	3	0.59%	0.60%	0.56%	1.09%	-0.15%
2003	4	9.10%	8.45%	8.47%	8.21%	8.81%
2003	5	8.24%	7.42%	7.51%	6.11%	9.42%
2003	6	2.28%	2.00%	2.04%	1.43%	2.85%
2003	7	4.14%	3.37%	3.44%	2.36%	4.91%
2003	8	3.43%	3.41%	3.48%	2.39%	4.96%
2003	9	-1.01%	-2.08%	-2.15%	-1.15%	-3.51%
2003	10	7.59%	7.30%	7.38%	6.12%	9.09%
2003	11	2.44%	2.54%	2.62%	1.38%	4.30%
2003	12	4.80%	3.78%	3.73%	4.48%	2.71%
2004	1	3.24%	2.21%	2.20%	2.23%	2.17%
2004	2	1.42%	1.86%	1.89%	1.43%	2.50%
2004	3	-0.31%	0.08%	0.16%	-1.07%	1.82%
2004	4	-2.51%	-2.83%	-2.88%	-2.11%	-3.93%
2004	5	0.98%	1.44%	1.44%	1.35%	1.58%
2004	6	3.84%	3.39%	3.48%	2.09%	5.35%
2004	7	-4.38%	-4.18%	-4.20%	-3.80%	-4.75%
2004	8	-0.37%	0.28%	0.28%	0.31%	0.24%
2004	9	2.95%	2.91%	2.99%	1.74%	4.69%
2004	10	1.40%	1.39%	1.37%	1.68%	0.95%
2004	11	6.71%	6.44%	6.56%	4.68%	9.11%
2004	12	3.63%	2.82%	2.76%	3.63%	1.57%
2005	1	-3.02%	-2.90%	-2.92%	-2.68%	-3.25%
2005	2	2.31%	2.40%	2.42%	2.07%	2.90%
2005	3	-1.82%	-1.99%	-2.01%	-1.75%	-2.36%
2005	4	-4.21%	-3.43%	-3.51%	-2.32%	-5.12%
2005	5	4.86%	4.72%	4.78%	3.77%	6.16%
2005	6	2.09%	2.05%	2.13%	0.81%	3.92%
2005	7	5.25%	4.80%	4.84%	4.11%	5.84%
2005	8	-1.22%	-1.31%	-1.34%	-0.94%	-1.87%
2005	9	0.83%	0.54%	0.51%	0.86%	0.05%
2005	10	-2.27%	-2.48%	-2.52%	-1.86%	-3.41%
2005	11	4.06%	4.34%	4.37%	3.97%	4.91%
2005	12	0.21%	-0.34%	-0.37%	0.14%	-1.06%