The Hedge Fund strategy that wasn't?

One of Crossing Wall St's more recent posts refers to an older post regarding the returns to trading when the previous day was a large or small return. They conclude that big days lead to more big days in either direction. In order to avoid any biases, I looked at the average daily return and standard deviation each day and created a strategy to buy if it is more than one standard deviation positive and sell if it is more than one negative. I used a ten year lead up and began the strategy in 1960 without including the returns of dividends (12178 observations). I also looked at portfolios using the same strategies for two standard deviation envelopes. For the 1 up and 1 down portfolios, the return (of just the days invested, ignoring risk-free returns) is 53.9% (15.5% standard deviation, 1728 observations) and 26.06% (20% standard deviation, 1817 observations), respectively. For the 2 up and 2 down portfolios, the returns are 82.4% (18.75 standard deviation, 462 observations) and 18.04% (27.5% standard deviation, 501 observations). Also note that these are annualized figures and on average they might make only 35 trades a year.

All things considered, they look like strong strategies. It makes more sense to combine the long strategies since their returns historically are the strongest. My combined strategy was to be long above the 1 standard deviation and use 100% leverage when above the 2 standard deviation. the returns are 79.05% with 23% stdev over 1728 observations.

Just on the basis of my recent trading, I felt that these returns looked too good to be true (granted they are only investing some 15% of the total observations). I hadn't seen this many big days together in the past 5 months or so. So I decided to look at the rolling 10 year cumulative returns to confirm how it has performed historically and how that would appear relative to today.
The chart above plots just that. Particularly back in the 70s the market trended very well. Furthermore the returns to the strategy were strong from the 80s to the 90s. However, the strategy seems to have lost its edge in recent years. The ten year cumulative return most recently was only 17.7%. I'm sure this is greater than the markets return ex-dividend, but my point is that just because a strategy worked in the past, doesn't mean that it will continue. For example, waiting to start the strategy until 1985 cuts the average return from about 70% to 36% with only 500 fewer observations. What is also interesting is that the sign of the minus 1 and minus 2 standard deviation strategy has flipped since 2000. They are buy signals and not sell signals. 13% return (23% stdev) for the down 1 standard deviation if you buy and 50% return (27.7% stdev) for the 2 standard deviation. The up 2 standard deviation strategy still has worked since 2000 (though with dramatically lower returns, 22% with 21% standard deviation), but the 1 standard deviation strategy has not.

The returns to the strategy appear to be stronger if you use 10 year rolling averages and standard deviations for the entry points, but the success of the strategy follows the same trend. For example, this strategy (the one graphed above) since 2000 returned 8% annualized with 28% standard deviation compared to essentially flat with 27% standard deviation the way originally calculated.

Stops

I was directed to IBDIndex through Quantifiable Edges. The more recent posts are also interesting, but this older post on stops is fascinating. Essentially, he tests using an 8% trailing stop and then if you have gained 17% on a trade, he uses a 25% trailing stop. It seems to be pretty successful when trading stocks and would be worth it to check out. In part 2, he gives the results on a robust backtest.

TAA update

I probably will not be posting that often for the next three weeks or so. I have the level 2 C.F.A. coming up and I have got to hit the books.

Anyway, unless there is a correction, May will show a signal to invest in equities according to the TAA model. I was interested in the returns in time periods when the previous signal was to not invest and the following month closed above the 200 day moving average. By comparison, the excess monthly TAA return is 5.16% historically with a 6.94% standard deviation (12% normally) and5.8% excess return (13.76% standard deviation) for the S&P500 timing model. When there are two consecutive months of buy signals, the similar statistics are 6.25% return (13.48% standard deviation). For the S&P500 when there is a sell signal in the month prior and a buy signal in the present month, the average excess return has been .09% with a 12.81% standard deviation. However, if you look at all of the assets, commodities and foreign stocks have very strong returns that keep the overall strategy strong. Excluding the S&P500 dates until there are two buy signals slightly reduces the standard deviation while keeping returns positive, though it doesn't appear to be statistically significant.

For the 24 times since 1974 that if you bought the S&P500 at the beginning of the month when price crossed above the 10 month SMA, you probably wouldn't have any return, but the standard deviation of equities.

Spurious

I generally like Bespoke. They make some good recap posts of what sectors or countries are performing relative to each other. However, I was disappointed with today's post. Their point is that if you graph the S&P500 since October and compare it to June1990 to July1991, we follow a pretty consistent pattern.

I've seen arguments like this made before, "this is just like the conditions leading up to the '87 ('29 or what have you) crash." To the extent that some market participants believe this (as it can be generally be heard in the financial media), there might be some predictive power in that. I'm not sure, I would have to test it. However, my complaint is that simply graphing one time series onto another and positing a special relationship that could indicate future returns is sloppy statistics and bad practices all around. At a bare minimum, you should report the correlation today vs. that time period, how many times there has been similar correlations over time, and the returns in those situations. There's certainly more you can test, but I would suspect that it would make sense to check whether or not the relationship is spurious.

Well, I decided to look into this a little deeper. I use the weekly S&P500 data and compute the correlation of rolling time periods with May of 2007 through the end of the first week of May. Out of 3,011 weeks that correlations were computed, 457 (15.2%) showed correlations with the recent time period greater than 50% and 135 (4.5%) showed correlations with the most recent time period greater than 75%. The most highly correlated periods showed 90% correlation only 3 other times and two happened in 1953 and the other was 1990. However, if you look at the 75% correlation periods, it is clear that every time there has been a downturn, the market tends to look like it is now. They're right that on average, the market has bounced when it was highly correlated with today, 1.7% over the next three months (7% annualized). However, the standard deviation was also 8.5% (17% annualized) which means that it isn't statistically different than zero. On a six month basis, the return increases to 4.87% (9.7% annualized), but the standard deviation increases to 14.7%(20.8% annualized). So if you wanted to take advantage of the historical correlation, you would also be looking to take on a lot of risk.

Another point I wanted to note is that when you have a series like stock returns that have unit roots, you generally need to difference the series or log difference the series to tease out relationships. A unit root basically means that the process is not stationary, it doesn't have a consistent mean and standard deviation. But, if you put the returns in the form of percentage increases, then the returns might have the same mean and standard deviation over long periods of time. The problem is when you compare two series that both have unit roots (as both comparisons are here) and if you regress one on another and find a large R^2 value and positive autocorrelation. If the residuals are also integrated order 1, then you have what is called spurious regression. If the residuals are integrated order 0, then you have cointegration. Cointegration is like the relationship between gold and gold mining stocks (or oil and oil services stocks). Spurious regression would be like the relationship between defense spending in the U.S. and the population of South Africa. Both go up, but there's no fundamental reason. I can't think of any reason why the stock market would necessarily behave exactly the same way twice, but the way to test this would be to set up a Matlab program that iterates through every week of data and looks at the returns of highly correlated months and invests when they're significant. All things considered, it wouldn't be hard to test (this is just one time period).

For example, if you were looking at 6 month correlations on October 5th, 1987 and would hold for 3 months if the correlation were greater than 75%, then you would find an annualized return of about 10.6% with 11.4% standard deviation (pretty consistent even including the awful 1987 data with the whole series). You might choose to invest and lose 20% over the next three months. The risk/reward ratio looked even better on a 85% basis. Interestingly enough, the situation of greater than a 90% correlation with the 6 months leading up to the 1987 crash has never happened and neither has it happened looking at it including October (despite what anyone else will tell you). My point is that a correlation with a previous time period, or a chart pattern similar to what happened before, may or may not be robust, but it should be statistically tested and caveats given before being used as a buy/sell.

Donchian Channels

A Donchian Channel is the formed by the high and low of the past n days. For my purposes, I used weekly data on the S&P500 from 1950 through May. I ignored interest compared the returns (w/o considering dividends) with a strategy investing when the market is above the 40 week (200 day) average. I checked several different ns, but 20 weeks (100 days) seems fairly standard. The results are generally consistent no matter how many weeks are chosen. When a 20 week high is hit, then a buy signal is generated and similarly a sell signal is generated for the 20 week low. I used a 10 week ATR to measure a trailing stop (high-2*ATR or low+2*ATR) as my exit.

When in a position, the SMA strategy generates a 10.6% annualized return with 12.05% standard deviation (1983 weeks).

The short side of the strategy generally underperforms. In other words, equity markets (as represented by the S&P500), do not tend to trend downwards after hitting 20 week lows. The long side of the strategy generates a 7.6% return with a 14.1% standard deviation in 3005 months. I wouldn't be surprised if additional filters would allow the long-side to have strong profits. For example, an additional requirement for a buy signal (not as an exit) with price greater than the 20 week moving average increases return to 8.3% and a 12.3% standard deviation. Combining the two original strategies together generally results in a return not significantly different from 0%. Since this is the basis for the turtle trader strategy, I would consider this pretty important. Unless you're a short-term trader, quant, or hedge fund, I would recommend staying away from shorting equities. Since the turtles mostly traded commodities and currencies, I wouldn't be surprised if this type of strategy works better on the individual components (as this would probably work better on individual stocks rather than equities as an asset class). I still feel that keeping things simple with the 200 day would probably be your best bet.

Since the short strategy generally results in the underperformance, I considered flipping a long when at the 20 week low and the market is greater than the 25 week SMA (no cases when this occurs for the 20 week). This strategy by itself produces a 14.9% return with 14.1% volatility. Unfortunately, over more than 50 years, this happens in only 55 times. I did some other tests in TradeStation with the ADX which also seems to be a successful filter, but the data I was using wasn't nearly as long a time period. I wouldn't be surprised if short-term reversals in equities generate strong returns, but those strategies generally require strong risk management

OverBought/OverSold part 2

Regarding yesterday's post with OverBought and OverSold indicators, I combined that with the TAA model from before (5 asset classes, buy above 200 day, invest in Commercial paper otherwise). I just wanted to add in RSI since that had a tendency to be most effective (can't use lower bollinger band since already out, not enough data for stochastics). I started with the method from yesterday (only invest when RSI is less than 75) which works very well with equities, but this method does not work as well with the other asset classes and it significantly underperforms as a diversified strategy. However, it remains significant for equities, so I will leave it in place for them. EAFE benefits from staying away when there is an RSI less than 50, but the other asset classes are already out of the market enough due to the TAA that it really doesn't improve their situation that much (25 results in no change for any of them) and the change just for commodities won't change the results significantly (statistically or economically). Ignoring the OverBought RSI figure for everything except equities also improves returns (different time periods are slightly improved by reducing them to 98 or 95, but it is not statistically or economically significant).

In other words, what is true for yesterday was likely true just for the S&P500 and not something applicable to a diversified strategy. However, just including it for equities can raise the Sharpe ratio from .88 to 1 over the entire time period and from .94 to .99 since 1990. Not a statistically significant difference for the overall strategy, but since it is statistically significant for the underlying, it might be worth considering an addition. A strategy that avoids situations where the monthly return is greater than the 2 (or 2.5 or 3) stdev Bollinger Band does not improve returns overall.

OverBought/OverSold

One of my interests is looking into ways to improve investing returns. I decided to look just at the S&P500 on a monthly basis since 1967. Mebane Faber has noted that the returns to a 10 month simple moving average strategy earns significant returns. In this sample, the returns are statistically significant with a 12.2% return (13.5% standard deviation) compared to a statistically insignificant 5.8% (18.3%) when below. I wanted to test three common OverBought/OverSold indicators on a monthly basis and then check to see if they would be any benefit when combined with the 200 day strategy.

The three indicators I used were Relative Strength Index, Slow Stochastic, and Bollinger Bands. I would imagine that most people who would come to this site has heard of these concepts (which you can google if my explanations aren't good enough), but I'll explain their basic concepts anyway. The Relative Strength Index scales the ratio of the size of recent up moves to down moves. If there are more up moves, then the ratio will tick up which is then scaled from 0 to 100. The %K fast stochastic indicator measures where the most recent close is relative to the range the stock has been trading in. If it is trading near recent highs, then it will be closer to 100 and closer to 0 when trading near lows. Slow Stochastic is a 3 month MA of the fast. Bollinger Bands measure 2 (or n) standard deviations away from the moving average. For all of these, I use ten months as the initial range. I'm only able to do the slow stochastic since 1988 since I couldn't get highs or lows before then.

The biggest problem with these is that compared to the 10 month strategy, these have relatively few occurrences. So instead of being concerned with Sharpe ratios, I'm mostly concerned with statistical significance.

The results are that few of the indicators result in statistically significant returns. Overbought/oversold points on the 2 stdev Bollinger Bands are not significant with almost zero return when greater than the 2 and too few observations when less than the -2 (though that return is about 20% annualized). With breakpoints at 20 and 80, the oversold RSI is not statistically significant, but the Overbought is statistically significant in the positive direction. In other words, when the RSI is greater than 80, the market generally keeps going up. However, at the 90 breakpoint, it is no longer statistically significant. Combining those two signals (greater than 80, less than 90 (or 95) is statistically significant and occurs in about 72 months (14.5% of total). This indicates to me that the RSI does work as a momentum indicator and as an OverBought/OverSold indicator. Finally, the Slow Stochastic with 20 or 80 is significant (though both are positive). There are only five cases where the Slow Stochastic was under 20 (including March) and the average return in the next month has been 5.4% (this April did not disappoint). Increasing the low breakpoint up to 25 still gives significance and increasing the high breakpoint all the way up to 95 still shows significance with positive returns (I expected negative). This would indicate to me that Stochastics are not particularly good as OverBought/OverSold indicators on a monthly basis. However, it is really the most extreme readings that really generate statistically insignificant results. So it might make sense to look at a stochastic of 98, but a stochastic of 85 or 90 is probably more indicative of momentum than anything else.

So how would an investor incorporate these into a strategy? In general, you would want to stay away from situations where you do not generate statistically significant returns and invest when they are. Including the strategy when the slow stochastic is greater 80 or 90 combined with the 200 day MA does not change returns. The 200 day covers the momentum effect already. Avoiding the situations where it is above 98 does not result in a statistically significant difference between the two results. The below 20 or 25 is not statistically significant either. However, both of those two increase the Sharpe ratio of the strategy (note I use since 1988 for this part, but since '67 for the rest).

For the Bollinger Bands, you may as well ignore the OverSold indication since it always comes when you are out anyway due to the 200 day. The OverBought indication increases the Sharp ratio, but its inclusion is not statistically significant compared to the 10month SMA strategy.

What is true for the OverSold in Bollinger Bands, is also true for the RSI. The 200 day already gets you out of the market. Even the best combinations of the OverBought indicator (noted before at 80 and 90) do not improve significantly on the 200 day MA. However, if you reduce the break down to 75 and do not invest when the momentum is greater than that, then you will significantly increase returns at the 10% level. I just kind of pulled that number out of the air so I was surprised it works and am more afraid that it was a bit of curve fitting. The only problem is that if you are an investor looking for total returns, you will reduce the months of investing by almost 50%. Even still, though, if you include the risk-free return, then the historic returns for this strategy are at 11.5% (10.7% SMA) with a standard deviation of 8.1%(11.6% SMA). That ratio of return to risk is consistent over multiple time periods. The ratio is also fairly consistent going down through 70 (and below, though the returns suffer since you are in that many fewer days). The good thing about the RSI is that it is easily incorporated into other strategies since it only uses closing prices.

One additional improvement (that could be some curve fitting action) would be to make three requirements for a position, the first is SMA or below 25 on the stochastic, the second is RSI less than 75, and the third that the stochastic is not greater than 95. This return is significantly greater than the original SMA almost at the 2.5% level. After incorporating the risk-free return, the Sharpe ratio is .71 vs. .63 for only the RSI requirement, and finally .43 for the SMA. I plan on backtesting the TAA strategy with the RSI requirement, but I cannot backtest the complete method since I don't have high/low information for total return indices on bonds and REITs. ETFs have the information, but the time frame is smaller which makes comparisons difficult (though implementation is still possible).

In conclusion, OverBought and OverSold indicators can have some value in pointing out time periods to avoid (or get in), but they seem to have the most value when used in conjunction with each other. There are many dangers with curve fitting when using this kind of analysis, so the general rule is to keep it simple stupid and test a strategy that works on one set of data on other sets and look for some kind of consistency in the returns.

BRK

Berkshire Hathaway held their annual meeting over the weekend. There has been some news about how lower returns on the insurance business and their derivatives positions (specifically equity index puts) hurt their bottom line. I love to take the time to gloat that I called it (it being losing money on the puts in the short-term).

However, I don't think the coverage of the loss has been that great. He only has European puts which require payment at expiration, so the loss is unrealized. He has paid out no money and won't have to pay out any money for many, many years (if at all, which is what I argued). I'm by no means an expert in the way that derivative contracts are accounted for (see FAS 133 if you want to figure it out), but traditional equities or fixed income can be classified as held-to-maturity, available-for-sale, or trading securities. If a derivative contract were classified under the fixed income or equities held-to-maturity method, then the historical cost would be recorded on the balance sheet and any realized gains or losses would be recorded as they occur. Short of bankruptcy, I can't imagine a situation where Buffett would get out of these positions. I guess I don't understand why he isn't allowed to use this method of accounting since it most fairly represents the value of the position. FAS133 seems to require any derivative that is not part of a hedging operation to have the gains or losses recorded each quarter. That seems inaccurate and misleading. If I were performing equity analysis on Berkshire Hathaway (or any company with large derivative positions that they could never possibly lose money on if they held to maturity and are well-capitalized), then I would restate that part of the balance sheet as if they were held-to-maturity.

Also, I should note that the numbers on the balance sheet that are reported as liabilities and occasionally mentioned in the press for his derivative positions, might also include new positions. A quarter of the increase in liabilities (383 million of 1.6 billion) on equity index puts is due to new positions, and a third (229 million of 667 million) of the CDS losses. I don't know much about the underlying content of the CDS positions, but losses on these positions could be outweighed by the (unrealized) profits on the index puts if the market improves. A little strange that he would lose money on both (market still collapsing in March, but credit conditions improving). Overall, he lost 1.2 billion on the equity index puts that he will never have to pay out. That would make Net Earnings per common of about 1382 instead of 1682 (decline of 18% instead of 64%). Considering other financial firms have performed significantly worse, I would say that isn't that bad. And Berkshire Hathaway will be able to show much greater (unrealized) profit if the market improves, even though we know that they really just gained back money written off.

Wish you were here

Here's for wishing that the BLS had an easier method for pulling data on the birth-death model from their website.

Anyway, this might just be pulling stuff out from nowhere since I didn't extend the series for long enough, but I did some manipulation of the Establishment survey data that came out today to get an idea of what the results would have been if the birth-death model hadn't been adjusting the data. Here's my big problem, when we compare results from now to the last recession, you're not comparing the same thing since the Birth-Death model has been adding jobs. There have been different methodologies over the past 8 years or so, but as they have changed, they have been adding more and more jobs through the BD model. Ideally if you wanted to compare all of the data, you would completely remove the influence of the BD model from non-farm payrolls.

For example, several financial reporters have noted that the decline in this month was not nearly as large as from March to April 2001 when the economy shed 281,000 jobs. The birth death model added 52k in March and 75k in April of 2001 which would mean that the net effect would be losing 304,000 jobs (note that this comparison may not be perfect since the Birth Death figures could be non-seasonally adjusted and I'm looking at seasonally adjusted payroll data). In comparison, the April figure for this year was -20,000 before taking into account the Birth Death model, but -145,000 after. In other words, we lost about half as much as many jobs as the beginning of the last recession. The numbers for Feb-Apr have all been negative and for the year we have lost 457,000 jobs compared to adding 1,090,000 all of last year. In comparison, the first four months of 2001 didn't shed as many BD adjusted jobs. (though most of the job losses came in the second half of that year).

Again, I'm not sure if this analysis is the best, but my point is that you can't compare historical recessions to this one using job data that has been manipulated. So when you hear financial reporters say that the job report isn't that bad, know that they really don't know what they're talking about.

Addendum: if you take everything in non-seasonally adjusted figures (Dec and Jan are vastly different), then March showed 573 after B/D adjustment and April showed 578 afterwards. This is compared to 571 and 382 in March and April of 2001, respectively. Again, you really need to then re-seasonalize the data (by whatever method the BLS does it) to really compare it to what generally gets reported in the financial press.