The Volatility Effect
Introduction
The volatility effect arose from empirical evidence from Blitz (see paper in link above) that stocks with low volatility earn high risk-adjusted returns. In fact, they find that these risk-adjusted returns are higher than the market. This work completely violates the notion set forth by traditional CAPM theory, which states that in order for an investor to be compensated with higher returns, he must assume more risk. This is astounding. They go on to prove that the volatility effect is itself a factor uncorrelated with the other factors (size, value, momentum, beta), and can prove to be an attractive investment strategy. In this post, I aim to replicate Blitz’s methodology and obtain similar results.
Data and Methodology
Data
Blitz analyzes end-of-month returns from December 1985 to January 2006 on data from FTSE World Developed index (global large-cap). To simulate size and value, they get fundamental data from Compustat, Worldscope, and Thomson Reuters. Since I don’t have access to any of these data sources, I must try to replicate the results using free providers (Yahoo). For size and value factors, I can use the Fama-French data. They turn their returns into log-returns in order to make them additive over time. Log-returns were used in all of their results.
Methodology
At the end of every month, Blitz constructs equally weighted decile portfolios by ranking stocks on the past 3-year volatility of weekly returns. To obtain the value, momentum, and size factors (suggested by Fama-French), they also create decile portfolios ranked on book-to-market ratio (value), past 12-month minus 1-month total return (momentum), and free float market value (size). Portfolios are rebalanced monthly and transaction costs are ignored.
For performance evaluation, they calculate monthly returns and look at the average, standard deviation, and Sharpe ratio. In order to disentangle the volatility premium from other factors, they perform both a factor regression ex-post and a double-sorting methodology ex-ante. The double sorting methodology first sorts constituents on one factor, then on the volatility factor. It then samples equally from each of the first factor’s bucket and gets the top decile/lowest decile from the second bucket.
My Data/Methodology
Since I don’t have access to any of the data sources that Blitz has, I must use free resources. I will obtain all of my returns data from Yahoo. I will get daily price data and convert it into log-returns to make them additive. I then convert it to weekly data in order to obtain 3-year weekly volatility. I will also obtain monthly data for evaluating performance. Since I don’t have access to fundamental data, I will use the Fama-French factors to simulate SMB, HML, UMD, the market, and the risk free rate. Since we know the FF factors come from NYSE, AMEX, and NASDAQ firms, we can only sample the US volatility puzzle. I use as many stocks as I can that come from these exchanges that have price data on Yahoo within the sample period. The same methodology is used.
In our sliding window of 3 years, we first divide each year into months. Then in each month, we represent a week as 5 days. If the last week is not 5 days, we add the remaining days of returns to the previous week. So we should have monthly log-returns data set and a monthly 3-year sliding window weekly volatility set.
My Results
Unfortunately, I wasn’t able to replicate the results set forth by Blitz. I will attribute this error to my lack of consistent data. There are some interesting things we can see in my results that we can analyze.
The graph above depicts the value of $1 over log returns over the sample period. The green line indicates the lowest-volatility decile equal weighted portfolio. You can see a consistent, smooth, increase in value, even during the dot-com crash! This supports Blitz’s argument that there exists a low-volatility risk premium. The red line shows the tenth decile portfolio, the ones with the highest volatility. And the blue line is the Long/Short portfolio.
Lowest Volatility Decile Statistics
Sharpe Ratio of D1: 0.340132633384
Mean Return of D1: 0.911%
Standard Deviation of D1: 2.68%
T value: 5.28027842055
Highest Volatility Decile Statistics
Sharpe Ratio of D10: 0.0473750254652
Mean Return of D10: 0.44%
Standard Deviation of D10: 9.32%
T value: 0.735458171561
Market Statistics
Sharpe Ratio of market: 0.102076588569
Mean Return of market: 9.03%
Standard Deviation of market: 8.853%
T value: 1.80303204058
These statistics indicate that we may have been able to capture the low-volatility premium, but the high volatility decile isn’t significant. This would explain the reason for our Long/Short under-performance compared with Blitz’s results. We actually see a mean monthly return of 1% with very little volatility for the low-decile portfolio, so that’s kind of exciting. And we can also see a pattern where low volatility stocks outperform the high volatility stocks (which contradicts CAPM).
Further Information
Blitz goes on to show that this low volatility premium exists in other regions across the world. He also demonstrates how this factor is unrelated to any of the others specified by Fama French (SMB, HML, UMD). I was able to replicate this graph (though not as strongly):
My biggest argument for why this occurs derives from behavioral finance. The classic lottery ticket problem explains that investors are very much irrational: someone will more often than not play in the market and buy stocks with high volatility in hopes of big returns, even though you can obtain a much safer (albeit less chance of massive return) through low-volatility stocks.
Factor Investing