A week ago, we posted an article that presented simulation performances of low-volatility strategies. The results illustrated that low-volatility portfolios do have higher returns and lower risks than high-volatility portfolios.

The point of this research piece is to identify if the low volatility anomaly is different than the value investing anomaly.

To test our hypothesis, we look at the performance of volatility-based strategies **within** Value and Growth stocks:

- Test the Low-Volatility Factor among Value Stocks;
- Test the Low-Volatility Factor among Growth Stocks;

**Our Methodology**

We construct low-vol and high-vol portfolios among Values and Growth stocks.

Similar to our previous simulation posts, low-vol portfolios are constructed based on Beta (we also look at IVOL, or idiosyncratic volatility, as a robustness test. The results are very similar).

Our value/growth portfolios are constructed based on EBIT/TEV rankings.

Here are the 2 value portfolios:

*To test the Low-Volatility Factor Among Value Stocks:*

**high EBIT Low BETA:**low vol value stocks**high EBIT high BETA:**high vol value stocks

Here are the 2 growth portfolios:

*To test Low-Volatility Factor Among Growth Stocks: *

**low EBIT Low BETA:**low vol growth stocks**low EBIT high BETA:**high vol growth stocks

### Simulation Background

First, we break stocks into 5 valuation quintiles from 1963 to 2013 based on EBIT/TEV rankings.

- For example, if there are 10,000 stocks, stocks 1-2000 go in the first quintile (Value); stocks 8,001-10,000 go in the fifth qintile (Growth).

Next, we rank stocks on BETA (or IVOL) into 5 buckets (quintiles) within the EBIT/TEV deciles.

- For example, if we have 2,000 stocks in the top EBIT/TEV quintile, we’d break those 2,000 stocks into 5 buckets of 400 stocks based on BETA rankings.

Finally, we do 1,000 simulations of random 30 stocks portfolios drawn from either the “High EBIT Low BETA” portfolio or the “High EBIT High BETA” portfolio.

Again, image we have a monkey (named Mr. Random) throwing 30 darts, every month during the 50 year period, to establish in each month separate 30 stock portfolios. Once Mr. Random has thrown his 30 darts in each month, we will have 600 separate monthly portfolios (12 months*50 years) and will have made 18,000 (30 stocks*600 months) individual stock picks. This represents one simulation. We will do 1000 such simulations for the “High EBIT Low BETA” bucket and another 1000 simulations for the “High EBIT High BETA” bucket.

Each simulated strategy represents the returns a low vol value investor or a high vol value investor would achieve over the full time period.

We calculate compound annual growth rates (CAGR), standard deviation, and maximum drawdown, and compile the results in the charts below.

### What Do the Value Returns Look Like?

Low vol value and high vol value stocks generate similar CAGRs, with a slight edge for low vol value. On the whole, **the evidence suggests that low volatility value stocks are primarily driven by their value exposure**, but there is a small edge to low vol stocks. (Click here to compare with beta factor effect among all stocks).

### How About the Risks?

The standard deviations of low vol value portfolios are much smaller than high vol value portfolios. On a risk-adjusted basis, low volatility does seem to add marginal value to a strict value strategy.

As for maximum drawdowns, the evidence is in line with standard deviations: low vol value performs much better than high vol value.

### What Do the Growth Returns Look Like?

We conduct a similar simulation process as the one outlined above. The only difference is that we test the beta factor among Growth stocks.

Similar to value stocks, among growth stocks, there isn’t a huge difference between low vol and high vol stocks, suggesting that price is the determining factor for returns, not volatility measures.

Controlling for growth characteristics, low volatility growth definitely has lower risk than the high volatility growth portfolio. Maximum drawdowns tell a similar story as the standard deviations–low vol growth beats high vol growth.**Conclusions:**

A large part of the performance associated with low volatility stocks is clearly being driven by exposures to value; however, there does appear to be some marginal benefit to investing in low volatility stocks. In the grand scheme of anomalies, I’d give value and momentum a gold medal, and low volatility would get a bronze–not bad!

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Chris ScottOctober 14, 2014 at 11:16 amWes, A few questions:

Did you include smaller cap stocks than with the previous studies? Seems like you would need more stocks in your universe to keep the buckets from getting too small with the two way sort.

Does using idiosyncratic volatility with value show anything different in the results?

Have you looked at combining volatility and momentum? I would expect that including low beta would hurt momentum returns, but would reduce drawdowns.

Wesley Gray, PhDOctober 14, 2014 at 4:08 pmnope. same thing in all the studies–mid/large caps only.

ivol is about the same.

Nope. Doing value/vol first. Results to follow

Chris ScottOctober 14, 2014 at 5:46 pmOk, so in 1963 you’d only have ~1000 stocks in your universe give or take depending on where you set your breakpoint. A decile would be 100 stocks and a quintile within the decile would be 20 stocks, which wouldn’t be enough to form a 30 stock portfolio. Am I missing something on how you constructed the portfolios?

Interesting stuff – looking forward to the next post in this series.

Wesley Gray, PhDOctober 14, 2014 at 6:19 pmyes, with 1k stocks, you’d go to 100, and then pick 30 randomly. If you did another split, you go from 100 —> 20, which wouldn’t hit the min 30 so the port would only end up being 20.

In the early years this sometimes happens, but once you are in the 80’s you get 40-50 stocks

Wesley Gray, PhDOctober 14, 2014 at 8:11 pmChris,

scratch all of that. For these double splits on value/vol we actually do quintile slices. So if you have 1k stocks, you go to 200 stock buckets, which go to 100 stock buckets. Sorry about the confusion. Updated in the posts. Regardless of how you cut it, the intuition is the exact same.

Chris ScottOctober 14, 2014 at 10:26 pmGot it – all makes sense now. Thanks Wes.

Michael MilburnOctober 14, 2014 at 10:25 pmThanks for sharing your research Wes. These type posts are excellent and are much appreciated.

Based on your consistent results I’m beginning to wonder if high

volatility might be lumped into the behavioral bias similar to lotteries

where we are tempted to make a bad bet if upside is significant /

asymetrical.

Like Chris Scott mentions below, I’m also interested to see volatility results compared to momentum if you post on those as it seems like momentum has alot of high volatility stocks. On its face It seems like there should be some regime where volatility is rewarded, but you’re showing that’s usually not the case.

Again, thanks for sharing these empirical results.

Michael MilburnNovember 2, 2014 at 5:40 amWes, Are you using the absolute value of beta so that a stock w/ -1.6 beta and a stock w/ +1.6 beta are the same volatility? thanks,

Wesley Gray, PhDNovember 2, 2014 at 9:56 amHi Michael,

No, just beta.

Curious, why would one want to use absolute value of beta?

Michael MilburnNovember 2, 2014 at 5:11 pmI guess I could be wrong, but was thinking a stock with a -1.6 beta would be just as volatile as a stock with +1.6 beta, just in opposite directions. So would negative beta stocks have the lowest volatility in scenario above? thanks,

I’m looking into this and trying to understand how it’s put together, and I’m trying to understand why I can’t see low volatility benefits in stuff I’ve been working on. I’ve been using average pct change in daily stock price as measure of volatility without regard for whether it’s moving up or down – just how “wiggly” it is compared to other stocks. There’s probably lots of things I could be doing wrong. thanks again,

(I’m also putting together a scoring system based on volatility, value, size, momentum, quality, liquidity, F-score…. maybe something else, not sure, and beta was a piece of data I was working with, and I started writing the calc for volatility based on beta and wasn’t sure how to code it).

Wesley Gray, PhDNovember 2, 2014 at 6:55 pmHey Michael,

There is a distinction between beta and volatility. Beta is formally the covariance of the asset and the mkt relative to the markets volatility; volatility is just the std dev of returns. There is also a term called idiosyncratic volatility, which is the volatility of the residuals from a regression of the asset on the market.

volatilty and idiosyncratic volatility can only be positive. Higher is worse.

Beta is a different beast entirely. Positive is “bad” negative is actually really “good.” In general, assets with negative betas are considered awesome risk-management assets–they go up when the markets blows up. People typically pay a large premium for assets like this (e.g., flood insurance).

Michael MilburnNovember 3, 2014 at 3:52 amThanks Wes, I did some comparisons and I think what I’m using as a measure of volatility (daily avg % price chg) is only loosely correlated with Beta, and often-times surprisingly contrary to beta. I need to think more about what volatility is – but it’s pretty clear the reason I’m seeing different results around volatility is because how I’m measuring it doesn’t have much to do w/ Beta.

MattJuly 18, 2015 at 12:41 pmHello Wes – I read this article with keen interest, as well as the 4-part series that is noted as a summation of your book “Quantitative Value” (which I ordered yesterday, by the way – looking forward to it!).

I’m wondering – and perhaps this will be answered in the book – have you adjusted your approach since the initial criteria noted in that 4-part series to include volatility as a variable when performing your screens? My understanding is that your process is roughly summarized as such: 1) Cut down to companies with market cap of $1.4B+, remove financials, REITs, utilities, 2) Remove “worst” 5% of companies based on each of three measures – potential accounting manipulation, financial distress, accrual manipulation, 3) Rank resultant set into deciles by earnings yield, 4) analyze and rank resultant decile set by quality factors, including a variation of F_Score, along with measures of Gross margin stability/growth, ROC, and ROA, then buy the top 50% with an annual rebalance.

With that said, is volatility now part of the mix above? If so, are you using Beta as the measure (though it is not technically a measure of volatility)? It appears so, since the results of your testing noted in this post indicate “high/low” ebit in combination with “high/low” beta.

And finally, related to some comments below – you mention the notion of negative beta being “good” (your quotes are duly noted), but it seems to me that if you selected company stocks based on the lowest betas, and that set included a large number of negative betas, you would have massive drawdowns during market upturns/bull markets…I just can’t wrap my head around the concept of a negative beta being a “good” thing and it seems that some other measure of volatility would be better, where a simple “higher is worse” assumption can be made.

I think I’m just having a difficult time wrapping my head around the negative beta idea, though to a much greater extent than Michael Milburn was, and when I started running my own analyses, I did the same thing he did, i.e. – use absolute value of beta…sorry if this question is a bit obtuse…I’m just now learning about the application of these techniques – it’s been a long time since my quantitative analysis and econometrics classes as an undergrad econ major!