Science Trader's Blog

Conclusion

2007-11-24T13:45:00.000-08:00

I've waited 2 weeks for your reactions and was happy to receive many, either by e-mail or as a comment here on this site.

This is a short summary of those reactions:
- systems are likely over-optimized and lack adaptability to different market conditions
- more criteria than just the Sharpe ratio are needed to select a system
- longer timeframes (e.g. 3-5 years) are needed to select a system
- subscriber should ask vendor if fundamental analysis is part of the system (not relying on only technical analysis)
- results cannot be generalized to all C2 systems, since analysis was limited to end-of-day stock systems
- recent market conditions were unusual

Here's my own opinion. First, I agree that out of the 100 systems I included, a substantial number could have been suffering from over-optimization. The problem is that it is hard to tell from the Sharpe ratio (and perhaps any other statistic) which system is likely over-optimized and which one isn't. I.e. if you have 100 over-optimized systems some of them will still show reasonable Sharpe ratios when going live (on C2) for a substantial amount of time.

Second, using more selection criteria than just the Sharpe ratio might be a good idea. However, these other criteria would need to have low correlation with the Sharpe ratio and still measure reward/risk in some way. Very difficult to find such criteria... An additional problem is that as we add more criteria we also increase the risk of over-optimizing the selection process.

Third, I agree that the longer the timeframe, the better. Ideally, it should include a period of severe Depression... Practically, we have to work with the data available and this is currently about 4 years, a period when the broader market gained a little less than 50%.

Fourth, having a good understanding of the system's underlying method might be a great selection criterion. The problem is, as a subscriber we can never reliably observe it. While the C2 stats are quite honest, we'll never know for sure about the vendor's underlying method as it depends entirely on what he says instead of on an independent third party's assessment.

Fifth, I also agree that results for future, options, forex, and intraday stock systems might look better or worse than what I showed here for end-of-day stock systems. I'll see if I can replicate the analysis for these other categories. A big problem here is that it is questionable if a subscriber could reproduce the hypothetical trades for some of the scalping system.

Finally, the recent credit crunch has done a lot of damage (not only to C2 systems, but to hedge funds as well). Remember though that the analysis includes many systems that were not affected by the credit crunch at all, e.g. in my first analysis (6 months, split into 2 periods of 3 months), only systems started in 2007 would be affected. But I'll see if I can redo the analysis without including data after May 2007.

One person also mentioned that some systems might have shut down while not closing positions. This could mean that results for the 2nd period look worse (or perhaps better...) than they really are, assuming a subscriber would have closed his positions once the vendor terminated the system. I understand this limitation, but as far as I can see it doesn't apply the majority of the systems in the tables I showed.

As I explained before these results were an important reason for me to suspend trading end-of-day C2 systems. Perhaps I will rerun the analyses a year from now when we'll have longer histories and see if things look more attractive then. To keep myself busy, I started a new C2 system myself: Kauai.

Some more analysis (3)

2007-11-10T21:47:00.000-08:00

We're continuing the previous analysis, but instead of considering 3 and 6 months of history, we're now looking at 9 months:

The first thing we can see is that as the time periods get longer, the Sharpe ratios get smaller. Only one end-of-day stock system was ever launched on C2 with more than 18 months of history, and a Sharpe ratio > 2 for the first 9 months. I won't discuss all the details of the table, as by now I assume readers are familiar with interpreting these results (otherwise: see the previous 2 posts). However, what should be mentioned is the fact that 80% of the top-10 systems for the first 9 months underperformed the S&P 500 during the next 9 months, and in most cases by a substantial amount.

Extending the timeframe further, we get:

Before coming to a conclusion, I'd like to collect some feedback from readers. So what is your interpretation of all this?

Some more analysis (2)

2007-11-08T22:32:00.000-08:00

In my previous post I compared the performance of the highest ranking systems during their first 3 months from inception to their performance during month 4-6. The conclusion of that analysis was that for all but one of the 10 highest ranking systems in the first period, performance during the 2nd period was substantially worse. Still, not taking into account transaction costs and slippage, the average Sharpe ratio of these 10 systems during the second period was slightly better than that of the S&P500 index.

Obviously the choice of 2 periods of 3 months each is arbitrary, and one could argue that 3 months is too short to judge the quality of a system. If that is true, we would expect to see more promising results if we would allow us a longer time period to evaluate a system before subscribing. So, let's look at the performance of 10 end-of-day stock systems with the highest Sharpe ratio's for their first 6 months:

As we can see, "Good NEWS Predictor" is again leading for the first period. However, this time performance during the 2nd period is quite disappointing. "Momentum #3" and "Momentum Breakout" show how bad it can get... We have to be a little cautious though, because I expect that at some point the vendor of Momentum #3 terminated trading the system without closing positions (while the equity curve continuous uncontrolled). In that case subscribers would have halted trading before digesting the full -0.68 Sharpe ratio. Momentum Breakout is quite a tragic case, as subscribers during the 2nd period found there account losing money during a runaway bull market (as indicated by the large negative excess Sharpe ratio).

Also of interest is Trend Plays #1. While it had a very decent Sharpe ratio (and equity curve) for the first period, in fact it underperformed the S&P500 index during that time on a risk-adjusted basis (as indicated by the -0.21 excess Sharpe ratio).

I didn't find these numbers particularly encouraging. Even with half a year of history it is quite a gamble what you'll get as a subscriber during the next 6 months for these systems that all had these attractive equity curves. In a way, it's interesting to look at some current end-of-day systems that will show up in this table half a year from now (i.e. they currently have about half of a year history).

Consider Small Cap Fundamental Value with a Sharpe ratio of 4.3 over 29 weeks:

It would show up right in between Momentun #3 and Good NEWS Predictor. Any guesses about its performance over the next 6 months??? I simply don't know. Perhaps it will do great, perhaps not. So far history suggests it's difficult to judge based on the Sharpe ratio.

Wave Rider (Sharpe ratio 2.2 over 27 weeks) is another system that will be included in the table 6 months from now:

We will continue with longer histories (9 and 12 months) in a few days.

Some more analysis

2007-11-06T22:10:00.000-08:00

One of the reasons that led to my decision to terminate my portfolio was some analysis I did last week. It was motivated by my experiences in practice: in a few cases I had selected a system with great performance statistics, and it subsequently did quite well in my portfolio; but in other cases the performance was quite disappointing, even though at the time I signed up the system looked great.

So I decided to look at all end-of-day stock systems ever listed on C2 and see how often a "good-looking" system (based on the performance shown on C2) would continue to "look-good" in the future.

I further decided to define "looking-good" as: outperforming the S&P500 index based on the Sharpe ratio. With the underlying idea that I might as well put my money into the SPY (S&P 500 ETF) rather than going through all the trouble of trading if I have no reasonable expectation to get a better Sharpe ratio than the S&P500.

I only included systems with more than 10 trades, and started by taking all systems with a track record of more than half a year. Some of these started way back in 2004, others just 6 months ago; in other words they nicely spread out over time.

Next I downloaded the equity history for each system (using the C2 data api) and calculated the Sharpe ratio for the first 3 months after each system started, and then for months 4-6. What I would hope to see was that systems with a high Sharpe ratio in the first 3 months would also have a high Sharpe ratio in the next 3. Because when that is true, I could pick a system with a high Sharpe ratio as soon as it would have 3 months of track record and expect a nice result for the next 3 months when I would trade it myself!

It turns out, there are 75 end-of-day stock systems with more than 6 months of history. The table below shows the 10 systems with the highest Sharpe ratio for the first 3 months after they were launched:

The table shows that of all end-of-day stock systems ever launched on C2, no one had a Sharpe ratio higher than "Good NEWS Predictor" (4.22) for the first 3 months after inception. Trading it for the next 3 months would turn out to be a good choice, as it got an even higher Sharpe ratio (4.62) for that period. Interestingly, it did actually slightly worse during the first 3 months than the S&P500, as shown in the column Excess Sharpe ratio (i.e. the Sharpe ratio of the system minus the S&P500 Sharpe ratio over the same period). Unfortunately, the other 9 systems were less consistent, as they all did worse in the second period in terms of absolute Sharpe ratio and most did worse as well in terms of excess Sharpe ratio.

In fact--and this is where the trouble starts--half of the systems did worse than the S&P500 in the second period. On average they still outperformed the S&P500 Sharpe ratio by 0.51, but it's a difficult choice between getting the index return for sure, or having a 50/50 chance of out/underperforming the index.

The table also shows that when selecting one of these extremely well-performing systems for the first 3 months, there's a 3/10 chance of ending up with a loss in the next 3 months (negative Sharpe ratio).

As I am planning to show in a subsequent post, the 3 month period is actually a "best-case" scenario: The table looks much worse for many other periods (e.g. 4 months).

End of the Portfolio

2007-11-04T17:36:00.000-08:00

As you've probably noticed, my portfolio has not been doing well for almost the entire past 5 months. Despite all my efforts to analyze systems, I have not been able to pick a profitable set of systems. Whereas the S&P500 is almost exactly back to where it was when I started my portfolio, I am sitting on a loss of 13% (excluding the P/L from my various put options to hedge, the loss would be even larger).

The main problems I have encountered can be summarized as follows:
- Technology issues with auto trading (extreme-os)
- Vendor decided to terminate/change system after major losses (Trend Plays #1, Longstoch-ST)

In addition, I was close to signing up for Positive Forex, which completely collapsed shortly thereafter.

Time to move on!

New hedge

2007-10-30T07:01:00.000-07:00

The current put options on the Russell 2000 ETF (IWM) will expire in 2 weeks, so it's time to roll them forward. Therefore I sold (closed) the IWM Nov 72 puts today for $0.16 and bought (opened) the IWM Jan 72 puts for $1.26.

New Portfolio Weights

2007-10-28T00:15:00.000-07:00

Starting this Monday, the optimal portfolio weights (for newly initiated positions) will change. Previous optimal weights were:
Weekend Trader: 32%
Trend Plays #1: 53%
ARS: 68%

Starting next week, the new weights will be:
Weekend Trader: 60%
Trend Plays #1: 49%
ARS: 41%

Since the weights sum to 150%, leverage will be about 1.5:1.

Nice (17%) Profit on WYY

2007-10-27T00:05:00.000-07:00

Today, a limit was hit for a WYY position held by Trend Plays #1. Initiated on 6/4/2007, the trade yielded a nice 17% return.

Why are these distributions useful?

2007-10-25T21:17:00.000-07:00

I ended my previous post with the words "Why is all this useful?", and today I'll try to answer this question.

Remember, I started discussing these distributions because Weekend Trader recently closed two trades with very large returns. Together with a trade with even larger returns (initiated in 2006) they have been responsible for almost half of the entire return (percentage-wise) of the system since its inception.

If you believe that these 3 trades are outliers, luck, the result of randomness etc, it would not make much sense to count on more of those for the future. After all, this is not about gambling but about trading. In that line of thinking, the performance of the system should be judged average at best.

However, if you believe these trades are an inherent part of the system's mechanics (perhaps due to a "let profits run" approach), the system (or vendor) should receive full credit for them, and performance might be judged good or even excellent.

The distributions we fitted can help to get more confidence in either the first ("luck") hypothesis or the second ("credibility") hypothesis, and allow us to determine how likely it is we can expect more of those big home-hitters in the future.

At first sight one might be tempted to conclude that since 3 out of 72 trades each resulted in increases on capital of more than 11%, the probability of this happening is 3/72 or 4.2%. I.e. we would expect every one out of 24 trades to increase equity by more than 11%. The problem with such an estimate is that it is not very precise: By the same calculation, the chance of observing a trade that increases equity by 10% (instead of 11%) is also 3/72, simply because none of the 72 trades so far showed a return between 10 and 11 percent. Similarly, the chance of observing a trade that increases equity with more than 12% (instead of 11%) falls quite abruptly to 1/72. Finally, if we would want to know the chance of a trade increasing equity by more than 17%, it would be zero, as we haven't seen those trades (yet)--but we all know that the chance is unlikely to be zero. Perhaps very small, but unlikely to be exactly zero.

Using distributions allow us to obtain more precise (and smoother) estimates. After fitting a distribution, we can get a precise estimate for whatever return percentage we are interested in, 10.4%, 10.8%, 200%, -30%, anything. It comes at a cost however: If we do a bad job at fitting a distribution, the probability estimate it will give us might be badly off. How badly? Consider the normal (Gaussian) distribution shown in red in the previous two graphs. Clearly it doesn't fit the histogram very well. According to this distribution, the chance of observing a trade that increases equity by more than 11% is only 0.27%! Compare this to the observed probability of 4.2%, and you see that this distribution underestimates the probability by a factor 15!

What do the other 3 fitted distributions have to say about the chance of observing a trade that increases equity by more than 11%?
- Cauchy: 3.7% (or 1 in 27 trades)
- Stable: 1.9% (or 1 in 53 trades)
- Generalized hyperbolic: 2% (or 1 in 48 trades)

These estimates look quite a bit more realistic than the Normal!

What about a trade that would increase equity by more than 20% (note: such a trade hasn't happened yet, so without fitting these distributions we wouldn't have a clue).
- Normal: 5.16e-08 (or 1 in 19,385,163 trades)
- Cauchy: 2% (or 1 in 51 trades)
- Stable: 0.7% (or 1 in 138 trades)
- Generalized hyperbolic: 0.5% (or 1 in 211 trades)

If we believe estimates from the last 3 distributions, such an event would not be that rare (the Normal estimate demonstrates once more how bad it is for fitting heavy-tailed distributions).

Based on these results, I have a hard time believing that these outlier trades are pure luck. I'm leaning more towards the second hypothesis: they're part of the characteristics of the system and should be treated as such. Obviously this doesn't mean it makes it a lot more comfortable to trade the system. It can be quite nerve-wracking to wait for the next big home-hitter... But analyses like these should give some confidence that it's worth waiting.

As you probably noticed, it can make quite a difference which distribution to choose... In subsequent posts I'll discuss how to measure and test how well a particular distribution fits the data, which might make such a choice a little easier.

Weekend Trader Alternative Distributions

2007-10-23T23:26:00.000-07:00

As we saw last week, the normal (Gausssian) distribution doesn't fit the returns per trade of Weekend Trader really well. Therefore I fitted 3 alternative distributions that have been suggested for modeling of financial data:
- Cauchy
- Stable
- Generalized Hyperbolic

I will discuss some of their properties in subsequent posts. Let's first see what they look like:

The y-axis now shows the density (rather than the frequency, shown in the previous post). Not surprisingly, the 3 alternative distributions seem to follow the histogram much closer than the normal (red line) distribution. I obtained the parameters of all distributions through maximum-likelihood estimation (mle), an often used optimization method in statistics.

Why is all this useful, you might ask? Hang on, we'll discuss soon...

Weekend Trader Distribution of Trade Returns

2007-10-15T21:41:00.000-07:00

Today, Weekend Trader closed two positions for a very nice return, both about 46%. Because the system always initiates trades with 25% of equity (4 open positions at any point in time), the two positions combined added 23% to the equity of the system.

Obviously the question is, how often can we expect to celebrate such nice trades? And, what is the chance of even larger profits? And, finally, what are the chances the system will close a trade for a 46% loss.

Over the coming weeks I will attempt to address these questions, by looking into the distribution of the trade returns of some systems, including Weekend Trader. To kick it off, let's look at a histogram of the Weekend Trader returns per trade.

The total number of trades since inception was 72 and most (29) of them yielded between zero and 2% on equity (i.e. between zero and 8% on the trade itself). The small bar at the far right represents a trade with a return of 16.7% on equity (66% on the trade itself) on a position in TFR held during the first half of 2006. The next bar (counting from the right) represents the two recently closed trades I described earlier.

The average of the return on equity (i.e. the expected return in statistics lingo) is 1.15% and the standard deviation is 3.54%. As a comparison, I plotted the normal distribution with this mean and standard deviation (red line). Visual inspection shows that the Weekend Trader returns are not normally distributed, as the peak is higher and the tails are heavier. This is confirmed by the 3rd and 4th moments of the distribution, i.e. the returns have a skewness of 1.85 and kurtosis of 5.29, while both are zero for the normal distribution.

Why is it important to note that the returns are not normally (Gaussian) distributed? Well, if they were, we could predict the probability and size of extreme returns quite easily. For example, we could predict that 95% of the returns fall within a range of ~2 standard deviations below and above the mean. However, if the returns are not normally distributed, such predictions can be misleading and (in this case) underestimate the chance of an extreme (positive or negative) return.

What I appreciate a lot in these returns, is that the extreme values all appear on the positive end of the distribution (and of course, I like extremely large returns). On the negative end, the bars of the histogram are all lying below the normal distribution, which is very good.

Rolling Correlations (3)

2007-10-08T21:38:00.000-07:00

Earlier this week, I looked at 100-day rolling correlations between ARS and Weekend Trader, and between ARS and Trend Plays #1. This leaves one more combination for today: the correlation between Weekend Trader and Trend Plays #1:

This looks much more pleasant than the previous two graphs. For the most recent 100 trading days, the correlation between Weekend Trader and Trend Plays #1 is 0.26, which is only half of the correlation (0.52) between ARS and Trend Plays #1 for that same period. The max 100-day correlation between Weekend Trader and Trend Plays #1 is also quite reasonable: 0.37, substantially lower than the max 100-day correlation between Weekend Trader and ARS (0.62).

Rolling Correlations (2)

2007-10-08T21:31:00.000-07:00

Yesterday, I looked at 100-day rolling correlations between ARS and Weekend Trader. Today, I'll show the same for ARS and Trend Plays #1:

The correlation between ARS and Trend Plays #1 for the last 100 trading days is higher (0.52) than the correlation between ARS and Weekend Trader (0.42). The upward trend that started about a year ago is still continuing.

Rolling Correlations

2007-10-07T23:10:00.000-07:00

One of the reasons to trade a portfolio of systems (like I do), is to reduce volatility. This works best if correlations between the systems are as close to zero as possible. It is interesting to track rolling correlations over time, and the figure below shows 100-day rolling correlations between ARS and Weekend Trader (red line), and a 95% confidence interval (blue lines, based on a simple bootstrap with 1,000 replications). See this post for a more detailed explanation.

The figure shows that for the most recent 100 trading days, the correlation between ARS and Weekend Trader was 0.42, down from a recent high at 0.62. I consider these numbers quite high--I'd prefer to have systems correlate less, because otherwise it doesn't matter much (from a volatility perspective) if I would trade only one system rather than multiple systems. So, I'll keep monitoring and hope it'll come down a bit in the next months.

C2 Still Expanding

2007-09-30T15:09:00.000-07:00

Six weeks ago was the last time I checked the number of newly added systems to the C2 universe of systems. It's time for an update:

During the last 30 days, 263 new systems were added. Not bad at all! The record of 365 new systems was set for the period 8/6 - 9/6.

Just for the five-day period from 8/29 - 9/2 as many as 166 new systems were added!
Of course, that is a little odd--so many systems in such a short period of time. So, I started to dig a little a deeper, and guess what? As much as 130 of these were from a single vendor. That must be quite a record. Even more peculiar: So far, none of these systems has made a single trade. Obviously, I'm very curious where this will go...

New Portfolio Weights

2007-09-30T00:22:00.000-07:00

Starting this Monday, the optimal portfolio weights (for newly initiated positions) will change. Previous optimal weights were:
Weekend Trader: 9%
Trend Plays #1: 58%
ARS: 80%

Starting next week, the new weights will be:
Weekend Trader: 32%
Trend Plays #1: 53%
ARS: 68%

Since the weights sum to 153%, leverage will be about 1.5:1.

As a result of its good recent performance, statistics for Weekend Trader have improved substantially. Because it realized its recent gains in a time when ARS and Trend Plays #1 were mostly flat, it is not surprising that the portfolio optimizing algorithm was sensitive to this and let the weight increase substantially, from 9% to 32%.

"Vince Rowe Show" Interview

2007-09-27T10:29:00.000-07:00

Here are the links to my interview on the "Vince Rowe Show" a few days ago. Each segment is about 10 minutes. We discuss C2, selecting systems, auto trading, slippage and many more things. Obviously 10 minutes is too short for a real in-depth discussion, but nonetheless I hope you'll enjoy it.

First segment

Second segment

Weekend Trader Surprise

2007-09-24T21:35:00.001-07:00

As you might have noticed there haven't been that many posts during the last month. Part of the reason is that really not a lot happened to the systems in my portfolio. When I recalculated the weights two weeks ago, they were nearly identical to those I calculated in August. The portfolio P/L was oscillating a bit between -10% and -5%, and that was about it. However, last week I was pleasantly surprised by Weekend Trader soaring 25% to an all-time high.

The event confirms that sticking to a system is important. My experience so far is that profits usually come when you expect them the least.

Even though the system has a history of nearly two years on Collective2, the events of last week had a substantial impact on the statistics. For example, the graph below shows the Sharpe ratio and its BCa-bootstrapped (10,000 replications) 95%-confidence interval on each day, calculated using the data available up to the day of calculation (e.g. the left-most point of the curves is based on the first 100 trading days, the right-most point is based on the entire history of 486 trading days). The last five trading days caused the Sharpe ratio to jump from 0.82 to 1.31, which demonstrates how unstable these statistics can be--even with two years of data.

What we can learn from this is that there really is no point in preferring a system with a Sharpe ratio of 1.2 over one with a Sharpe ratio of 1, if they jump around all the time and have large overlapping confidence intervals. Most likely these differences are too small to be both statistically and practically meaningful. Instead of trying to pick the "best" system, we might be better off trading a larger number of "reasonably good" systems simultaneously.

Science Trader On Air!

2007-09-19T15:00:00.000-07:00

Tomorrow (Thursday) between 12.15pm and 1pm EST, I will be interviewed by host Vince Rowe of the Online Trading Academy Dallas Radio Show. If you're interested you can follow the show by podcast or--if you're living in the Dallas area--on BizRadio 1360am.

New Portfolio Weights

2007-09-07T20:32:00.000-07:00

Starting next week, the optimal portfolio weights (for newly initiated positions) will change slightly. Previous optimal weights were:
Weekend Trader: 13%
Trend Plays #1: 57%
ARS: 78%

Starting next week, the new weights will be:
Weekend Trader: 9%
Trend Plays #1: 58%
ARS: 80%

Since the weights sum to 147%, leverage will be about 1.5:1.

(Part of the reason not to leverage to 2:1, is that some equity needs to be available for the put options that I use to offset against the broader market)

Weekend Trader Backtest

2007-08-25T11:54:00.000-07:00

A while ago, I asked the vendor of Weekend Trader if any backtest data were available. Initially, he send me several graphs. More recently however I received the underlying data, so I could do some more analysis. I think this can be very valuable because we can compare the backtest results with the hypothetical C2 results and see if there's any evidence of massive overoptimization in the backtest (note the emphasis of massive; I think a little overoptimization is unavoidable and not a problem).

The figure below shows the hypothetical equity curve starting on 10/26/1999, which is the beginning of the backtest. After 1,508 trading days, the curve is no longer based on the backtested returns, but instead on the hypothetical C2 returns (starting October 24, 2005); the border between these different periods is marked by the dotted line. I have scaled the equity to an index, starting at 100; and included the S&P500 returns over the same period, also indexed at 100. The y-axis has a log-scale, which means that if the daily return percentage would be constant, the equity curve would follow a straight line.

Visual inspection seems to suggest that until so far the C2 results don't deviate much from the backtest. In fact, the first 250 days of the C2 history look very similar to the last 250 days of the backtest period, in terms of the slope of the curve. I will compare some other aspects (drawdowns, alpha, beta, sharpe etc.) in subsequent posts.

Trend Plays #1 Did it Again

2007-08-23T23:27:00.001-07:00

Again, a Trend Plays #1 trade was closed for a really nice profit today:

TCHC bought 6/22/07 for $11.13, sold today for $14.51 = 30% profit

The profit is actually even larger, because I bought some more on 7/2/07 for $10.77 as a result of a portfolio re-allocation.

(click to enlarge...)

Note the 45% drawdown early may--it's real, not a split!

What Happened to Positive Forex?

2007-08-21T10:41:00.000-07:00

Six weeks ago, I opened a demo account with BulldogFX and subscribed to Positive Forex.

I was very happy with the demo, and pleased to see that the demo auto trade fills matched hypothetical C2 fills almost exactly. However, I was less pleased with the performance of the system itself:

Every now and then systems are blowing up spectacularly on C2, and I'm very worried that I found myself close to subscribing to the system. Because I didn't finish my analysis of the system, I don't know what my final decision would have been...

On a positive note, I have always been very suspicious of forex systems relative to stock systems, because I have seen many forex systems blow up before. That's one of the reasons why I've only traded stock systems in my portfolio so far. Perhaps if there have been a few systems on C2 with stable track records of more than 2 years, I might consider forex again, but in the near future, I'll stick to stocks.

A possible explanation why Positive Forex blew up is that it was generating high returns by ignoring hidden risk (i.e. a collapse of the carry trade). You can find a nice explanation here.

New hedge

2007-08-21T07:34:00.001-07:00

Yesterday, Weekend Trader replaced three of its four positions. It has now reached the target weight of 0.13, as discussed here. Because leverage is lower now, I needed to readjust the hedge. I also found that hedging with the Russell 2000 index tracker ETF (IWM) gives a slightly better fit than hedging with SPY.
Therefore, I sold the SPY Dec 142 puts for $6 (bought last week for $8.30) and bought the IWM Nov 72 put for $2.33.

ARS Excess Sharpe Ratio

2007-08-19T13:49:00.000-07:00

Please find below the 100-day excess Sharpe ratio for ARS. See here for an explanation of the excess Sharpe ratio.

(click to enlarge...)

As the figure shows, ARS outperformed the SPY on a risk-adjusted basis for most of the 100-day rolling windows, although recently it substantially underperformed. Testing for difference between the Sharpe ratio of ARS and the Sharpe ratio of the SPY over the entire history (590 trading days), we find that it's not statistically different from zero, as the 95% confidence interval is [-0.58, 1.81].