Buffett: low volatility anomaly master

A recent paper by Frazzini (et al) at AQR uncovers the driver behind Warren Buffett’s returns:

we find that the alpha become statistically insignificant when controlling for exposures to Betting-Against-Beta and quality factors. We estimate that Berkshire’s average leverage is about 1.6-to-1 and that it relies on unusually low-cost and stable sources of financing. Berkshire’s returns can thus largely be explained by the use of leverage combined with a focus on cheap, safe, quality stocks.

In other words, low beta investing with leverage.  The previous post showed a low beta quintile portfolio turning $1 in 1974 to $100 in 2007 [CAR 14%].

Berkshire Hathaway returns $1500 over the same period [CAR 24%], which matches Frazzini’s estimated leverage [24/14.5 = 1.6].  There is a significant reduction in rate of return from 1998.  However, a strategy based on Buffett’s style appears to retain effectiveness over the entire period (outside recessions), consistent with a low beta strategy.

Figure 3:


This strategy is outside the reach of the individual investor due to the size of the portfolio and frequent rebalancing.  But could the strategy be approximated using a low beta fund?  Access to low cost financing for leverage is the key.  Buffett’s borrowing costs are legendary: the free float from his insurance business.  Unfortunately for the privateer, interest is likely to consume much of the 10% per annum generated by gearing.

An alternative is to find a fund or manager aligned with this strategy.  For example, AQR has a low volatility fund AUEIX:


SPLV is the largest fund in this category at $4B assets and 2.7% yield.

Robeco offers enhanced low volatility funds and has several billion under management also:


None of these funds employs leverage though.


Low beta anomaly: long history and recessions

I am researching whether low beta investing has benefited from recent conditions, such as the interest rate bear market since 1982 which could favor higher yielding equities such as utilities found in low beta screens (especially in today’s low yield environment).

I found this Cliff Asness paper showing that low beta outperformance is NOT an industry bet:


We show that a betting against beta (BAB) strategy has delivered positive returns both as an industry-neutral bet within each industry and as a pure bet across industries. In fact, the industry-neutral BAB strategy has performed stronger than the BAB strategy that only bets across industries and it has delivered positive returns in each of 49 U.S. industries and in 61 of 70 global industries.

This draws me towards USMV over SPLV due to greater diversification across industries:


Next, I overlaid a 40 year history of a low beta portfolio with RecessionAlert‘s robust recession model.


Chart D, page 3

blog figs

It can be seen that high beta stocks decline rapidly during recessions.  Low beta stocks fare much better but there may be some value in holding cash during recessions.

The next post describes how an enormous fortune was built using a low beta strategy combined with leverage.

Is there a mean reversion anomaly?

There has been a fair amount of online discussion regarding mean reversion, typically focussed on the S&P500 or SPY ETF.

Michael Stokes shows that short term mean reversion is a recent phenomena and may actually now be inoperative:


David Varadi of the famous indicator DV2, presents 10 year backtests with impressive statistics.  The time period coincides with that shown by Stokes above.


Larry Connors has a simple mean reversion system showing good performance stretching back to the 80s.  The rules are as follows:

  • Price must be above its 200-day moving average.
  • Buy on close when cumulative RSI(2) is below 5.
  • Exit when price closes above the 5-day moving average.

See http://systemtradersuccess.com/connors-rsi-update-for-2013/ for an equity curve and more discussion.

Sanz Prophet has a very nice implementation of an adaptive strategy which transitions from trend following to mean reversion around 2000-2003 and appears to be currently switching back.  This is a good illustration of the limited set of circumstances when short term mean reversion is found in the S&P500.


Engineering a mean reverting instrument

This is a popular strategy which looks for well correlated instruments and takes opposite positions when a pretermined drift has occured (e.g. 2 standard deviations), expecting “reversion to the mean”.  Also known as pairs trading and beyond the scope of this article.  Note that very closely aligned instruments are available such as IVV and SPY (which both track the S&P500), or an ETF versus a basket of its underlying stocks.  These are (or were?) fertile hunting grounds for hedge funds, until the inefficiencies are aritraged away.

Final thoughts

My view is that index mean reversion is not a pervasive enough anomaly to build a long term outperforming investment strategy.  Other disadvantages include: (often) a high number of trades (higher taxes and commissions) and limited academic literature on methods (e.g. published on ssrn.com).

Free lunches

Liquid financial instruments are normally correctly valued.  There are some situations when this does not apply; these are called anomalies e.g. momentum, post-earnings-announcement-drift etc.  To beat the broad market returns consistently, a strategy must be based around this type of situation.  These anomalies are grounded in a structural market behavior which prevents the inefficiency from being arbitraged.

Here are two examples of commonly discussed strategies not based on a reliable behavior:

1) Indicator readings e.g Buy RSI < 30, Sell RSI > 70

These are very appealing to the beginner backtester due to the ease of coding and likelihood that a combination of optimized parameters (out of millions) will generally look good over a specific test period.

If the market rewarded one indicator value over another, sophisticated players would soon take advantage and thereby cause it to disappear.

2) Options strategies e.g. iron condor

There are many on-line services purporting to sell profitable strategies combining various options types.  The problem is that each option is accurately priced based on current volatility and underlying price.  An iron condor profits when underlying price stays in a range.  This allows the sold options to expire worthless.  Are buyers generously donating free money?  Alas no, the trade gives a 90% chance of profit with a 10% reward to risk ratio (i.e. zero expectancy!).

How about the mythical ‘adjustments’ which reposition legs during extreme market moves.  If the overall strategy is profitable then the adjustments are solely responsible and should be traded alone (thus saving commissions).  Inefficiencies are more likely to be found during extreme moves than regular times. [If readers have more data on this, please let me know].

Selling puts on breakouts (Sanz Prophet)

Here are a few histogram plots in response to a post on Sanz Prophet’s blog:


The plots show SPY returns after buying VIX lows (similar to buying SPY breakouts) then selling on expiry (Opex).  Only one trade loses more than 6%, confirming Sanz’s comment regarding tail frequency.  Buying VIX highs are shown for comparison.

The tighter distribution makes perfect sense: VIX is a 1 month forward volatility forecast (evidently a very good one).  Therefore 1 month SPY returns are expected to cluster tightly after VIX lows.  Options prices include forecasted volatility, thereby ensuring efficiency (no free lunches – see next post).

Buy SPY on VIX 20 day low, sell at opex (average trade 16 days):


Buy SPY on VIX 20 day high, sell at opex (average trade 16 days):



XIV is an ETN which targets the inverse daily return of VIX by shorting VIX futures.
As the monthly options cycle progresses, at the end of each business day the fund gradually transitions from the first month future to second month future.  Normally (80% of the time), the longer contract is higher priced therefore selling (shorting) high and buying low.  This is known as positive “roll yield” or “term” structural advantage.

This excellent chart from Trading Volatility shows the relationship:

blog figs

Volatility tends to decrease during stock market rallies, reducing VIX and increasing XIV.

An alternative viewpoint is that the high returns result from the volatility risk premium (highly recommended) i.e. the risk of an explosion in volatility while holding XIV.  Theoretically, XIV can go to zero overnight if VIX triples (approximately).  The trade-off is ~100% per annum returns from 2004-2007 and 2009-2013.

One idea is to hold most of the portfolio in low beta funds (total return ~20% outside recessions) with, say, 10% allocated to a XIV “roll yield” and/or “breadth based” strategy.  This could boost total annual returns by 10% (to 30%) with a small chance of XIV going to zero (probably during a recession but could be any time).

XIV allocation should be tax sheltered due to higher transaction frequency and sized so that the zero case is not catastrophic.

Momentum Investing: Instrument selection is critical

Money management and following a proven market anomaly are also critical.  But the subject of this post is instrument selection.

The Fama-French data shows annualized return from 1926-2000 was:

Small Value Stocks 14.9%
Large Value Stocks 12.9%
Large Growth Stocks 10.8%
Small Growth Stocks 9.9%

Vanguard offers VISVX or VBR to participate in small value outperformance.

More recently, in the previous two bullish periods, 2003 to 2007 and 2009 to 2013:

  2003-2007   2009-2013
  CAR% Sharpe Max DD   CAR% Sharpe Max DD
SPY 14 2.0 7   25 2.0 16
VISVX 17 2.6 7   38 2.3 14
FLSTX 23 2.8 10   40 2.1 21
Low-beta 17 2.3 7   20 3.0 8
XIV 93 35   82 2.3 28
TNA         126 2.5 39

Notice how small value performs well and could possibly be used as an all-weather instrument choice for the intermediate term strategies discussed on this blog.  One risk of selecting sector ETFs is their narrowness and therefore possibility of under-performance in a specific market period.  One could make a case that bargain hunters buy value in a declining market, providing some support (this may drive the performance Fama-French found).

More on XIV in the next post: higher risk and higher reward with an inbuilt structural advantage 80% of the time.  A portion of equity could be allocated to XIV to boost returns, with the balance in low-beta (for example).

A weekly 2 year correlation table is shown below.  Notice in the second column how closely small value (VISVX) has tracked FLSTX which is one of the highest performing unleveraged funds.

FLSTX 1 0.897 0.982 0.899 0.772 0.792
FDXAX 0.984 0.932 0.994 0.835 0.726 0.82
VISVX 0.982 0.945 1 0.834 0.703 0.846
FEIRX 0.946 0.985 0.97 0.823 0.559 0.921
xiv 0.899 0.733 0.834 1 0.771 0.71
spy 0.897 1 0.945 0.733 0.462 0.938
FATEX 0.86 0.818 0.862 0.708 0.735 0.656
IYR 0.847 0.965 0.898 0.719 0.401 0.967
IYE 0.833 0.664 0.818 0.714 0.85 0.489
Beta-Low-US 0.791 0.937 0.845 0.705 0.315 1