## Statistical Value vs Economic Value

On Tuesday, on the verge of a big gap up by the S&P 500, we came across this study which showed there is value for traders in fading gap ups. We crunched the numbers ourselves and came to the conclusion that shorting stock market gap ups is profitable in a statistically significant way, yet totally useless. Here are the numbers under 2 scenarios, using SPY data since inception in 1993:

1 – Short every gap up. Cover either when the gap is filled or if not, at the close.

% Profitable: 74

Avg Gain: 3bps

Count: 2530

Std: 66bps

t 2.6

2 – Short every gap up. Cover either when the gap is half filled or if not, at the close:

% Profitable: 85

Avg Gain: 3bps

Count: 2530

Std: 49bps

t 2.6

The data is robust and significant. But 3bps in profits is useless, as it would all be eaten up by commissions and slippage. That doesn’t mean there is not something useful about this data, just that basic stats on fading gaps is the start of the search for a good trade, not the end.

## S&P 500 vs R2K

Yesterday, we noticed that the Russell 2000 ETF had a strong up day while the S&P 500 barely scratched out a gain. Recently we’ve been noticing that the small cap index might be leading the overall market, so we ran a basic test: whenever the IWM closes up over 1% while the SPY closes up less than .5% (or down), buy the IWM at the close and hold for the next 2 days.

Going back to January of 2009, we found 19 occurrences. The average return of the Russ was a loss of 1.2% with a Standard Deviation of 3%. The results are not all that significant statistically, but the tendency seems towards mean reversion.

But then we looked at the equity curve of this trade over the years:

As you can see, for a while the system was great for catching breakouts, before it became great for mean reversion. To us, that means there is really nothing here and we can’t say we know anything by observing how the R2k behaves compared to the S&P on any given day. But this is a great example of how even quantitative testing is as much art as it is science. How does one treat a pattern that flip flops? How far back do you test? Is it curve fitting if you add another variable to try to smooth it out?

These are all important questions for any quant to ask, and the answer is as much about personal style and preference as it is about math and statistics.

## Rebalancing Frequency

In an attempt to improve the Long Stock and Levered Bond strategy, we decided to sample different rebalancing periods. As the chart below demonstrates, there is almost no difference between a quarterly or monthly rebalancing. The quarterly rebalancing has a slightly better performance, which is a bonus as it means less slipage and commissions paid as well.

## On Stocks and Bonds

In our last post we discussed the benefits of a simple long stock portfolio with a levered bond position, and how the combined portfolio had lower drawdowns than just being long stocks. Deciding to look further under the hood, we were curious what the exact stock/bond return breakdown was during months where stocks fell by more than 2 standard deviations, going back to 1987.

As it turns out, the S&P return component totally dominates the overall portfolio performance, apparently because stocks are a lot more volatile than bonds. Another way to visualize this is to look at the 12 month rolling correlation between the “just stocks” portfolio and the “stocks + levered bonds” portfolio.

All of this begs the question: why a mix of stocks and bonds in the first place? The whole idea of the combined portfolio, often in a 60/40 allocation, is one of the most common practices on Wall Street. But does it necessarily make sense? There are several ways to approach this question, and as a starting point we’d like to offer the following chart of the rolling 12 month correlation between the S&P 500 and US Treasuries.

## Hedging Equities with a Levered Bond Position

In Steve Drobny’s excellent book “Invisible Hands: Top Hedge Fund Traders on Bubbles, Crashes, and Real Money”, Jim Leitner mentions the possibility of using a levered bond position as a hedge for an equity-oriented portfolio.

Unlike a protective put buying strategy or a long position in Vix futures, bonds have positive carry. The best way to test the merits of a hedging strategy is to compare the individual performances of the market, the hedge, and the combined entity. So we tested the following scenarios:

- 100% Allocation to S&P 500
- 100% Allocation to US Treasury Bond futures (returns don’t include t-bills)
- 100% Allocation to S&P 500 cash and 100% to US Treasury Bond futures rebalanced monthly

Here’s a plot of the returns for each portfolio from 1987 to present.

Here is the statistical breakdown of the results:

(Data source: St Louis Fed FRED Database, Robert Shiller)