: How do small cap stocks perform vs. large cap stocks (like Dow constituents) during bear trends? Does anyone have any good information on how small cap stocks, e.g. < 0M, perform during bear trends and/or recessions

To a certain extent, small cap companies will in general follow the same trends as large cap companies. The extent of this cointegration depends on numerous factors, but a prime reason is the presence of systemic risk, i.e. the risk to the entire market. In simple terms, sthis is the risk that your portfolio will approach asymptotically as you increase its diversification, and it's why hedging is also important.

That being said, small cap businesses will, in general, likely do worse than large cap stocks, for several reasons. This was/is certainly the case in the Great Recession.

Small cap businesses have, on average, higher betas, which is a measure of a company's risk compared to the overall market. This means that small cap companies, on average outperform large cap companies during boom times, but it also means that they suffer more on average during bear times. The debate over whether or not the standard beta is still useful for small cap companies continues, however. Some economists feel that small cap companies are better measured against the Russell 2000 or similar indexes instead of the S&P 500.
Small cap companies may face problems accessing or maintaining access to lines of credit. During the Great Recession, major lenders decreased their lending to small businesses, which might make it harder for them to weather the storm.
On a related point, small businesses might not have as large an asset base to use as collateral for loans in bad times. One notable large cap company that used its asset base to their advantage was Ford, which gave banks partial ownership of its factories during hard times. This a) gave Ford a good amount of cash with which to continue their short-term operations, and b) gave the banks a vested interest in keeping Ford's lines of credit open. Ford struggled, but it never faced the financial problems of GM and Chrysler.
Despite political rhetoric about Main Street vs. Wall Street, small businesses don't receive as much government aid in times of crisis as some large cap companies do. For example, the Small Business Lending Fund, a brilliant but poorly implemented idea in 2010, allocated less than billion to small businesses. (The actual amount loaned was considerably less). Compare that to the amounts loaned out under TARP. Discussions about corporate lobbying power aside, small businesses aren't as crucial to the overall stability of the financial system
Small businesses don't always have the manpower to keep up with changes in regulation. When the Dodd-Frank Act passed, large banks (as an example), could hire more staff to understand it and adapt to it relatively easily; small banks, however, don't always have the resources to invest in such efforts.

There are other reasons, some of which are industry-specific, but these are some of the basic ones.

Graph(s)

If you want visual confirmation that small cap businesses follow a similar trend, here is a graph of the Russell 2000 and S&P 500 indexes:

Here is a similar graph for the Russell 2000 and the Dow Jones Industrial Average.

If you wanted to confirm this technically and control for the numerous complicated factors (overlap between indexes, systemic risk, seasonal adjustment, etc.), just ask and I'll try to run some numbers on it when I have a chance. Keep in mind, too, that looking at a pretty picture is no substitute for rigorous financial econometrics. A basic start would be to look at the correlation between the indexes, which I calculate as 0.9133 and 0.9526, respectively. As you can see, they're pretty close. Once again, however, the reality is more complicated technically, and a sufficiently detailed analysis is beyond my capabilities.

Just a quick side note. These graphs show the logarithm of the values of the indexes, which is a common statistical nuance that is used when comparing time series with radically different magnitudes but similar trends.

Data sources

S&P500 and Russell 2000 data came from Yahoo! Finance, and the Dow Jones Industrial Average data came from Federal Reserve Economic Data (FRED)

Code

Per usual, I try to provide code whenever possible, if I used it. Here is the Stata code I used to generate the graphs above. This code assumes the presence of russell2000.csv and sp500.csv, downloaded from Yahoo! Finance, and DJIA.csv, downloaded from FRED, in the current directory.

clear

// Read Russell 2000 data
insheet using russell2000.csv, comma clear
keep date adjclose
rename adjclose russell2000
lab var russell2000 "Russell 2000 small cap"
save smallcap, replace

// Read S&P 500 data
insheet using sp500.csv, comma clear
keep date adjclose
rename adjclose sp500
lab var sp500 "S&P 500"

// First merge
merge 1:1 date using smallcap
drop if _merge == 1
drop _merge
save smallcap, replace

// Read Dow Jones data
insheet using DJIA.csv, comma clear
rename value djia
lab var djia "Dow Jones Industrial Average"

// Second merge
merge 1:1 date using smallcap
drop if _merge == 1
drop _merge
save smallcap, replace

// Format date
gen newdate = date(date, "YMD")
drop date
rename newdate date
tsset date, daily

// Analysis variables
gen lgRussell = log(russell2000)
gen lgSP = log(sp500)
gen lgDJIA = log(djia)

lab var lgRussel "Russell 2000 small cap"
lab var lgSP "S&P 500"
lab var lgDJIA "Dow Jones Industrial Average"

compress
save smallcap, replace

// Analysis

// Graph 1 - visual confirmation of a similar trend
graph twoway tsline lgRussell lgSP if year(date) > 2000, ///
title("Log of Russell 2000, SP500 index value", size(small)) ///
tlabel(01jan2001 01jan2004 01jan2007 01jan2010 01jan2013, labsize(vsmall)) ///
caption("money.stackexchange.com", size(vsmall) pos(5)) ///
xtitle("Date", size(small)) ///
ytitle("log(index value)", size(small))
graph export graph1_russell_sp500.png, replace

// Graph 2 - another visual confirmation
graph twoway tsline lgRussell lgDJIA if year(date) > 2000, ///
title("Log of Russell 2000, DJIA index value", size(small)) ///
tlabel(01jan2001 01jan2004 01jan2007 01jan2010 01jan2013, labsize(vsmall)) ///
caption("money.stackexchange.com", size(vsmall) pos(5)) ///
xtitle("Date", size(small)) ///
ytitle("log(index value)", size(small))
graph export graph2_russell_djia.png, replace

Further reading

Fidelity published an article on the subject that you might find interesting, and Seeking Alpha has several pieces related to small-cap vs. large-cap returns that might be worth a read too.

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