This article has been mentioned on a few sites, I saw it first at Free Exchange.
It notes that prices that end in .99 induce customers to purchase a much higher percentage of sales than would be suggested. It is particularly true for lower priced items, but a purchase like a washer/dryer wouldn't have much effect.
While it is easy to design an experiment in a retail setting to test that theory, it would be much more difficult to test it in the financial markets. However, it seems to me that it would most evidently manifest itself in support and resistance points. I don't think support and resistance really translate well into trading systems. However, they can be useful in explaining behavior in the market (though I admit more value in hindsight than at the time). For instance, a stock might test its five year high several times and after breaking through on higher volume, it will surge significantly. A more active trader could see that and place buy stop orders above the resistance level. The problem with using a system is that sometimes it will go slightly above the resistance and then drop significantly. It is done more based on feel and that's also the problem with testing the effects of support and resistance lines using standard statistical techniques. A sustained, high volume move through a resistance point is more important than a weak one.
Getting back to the BBC article, a resistance line can be thought of like a price of 8 euro. The marginal asset manager might think that a stock is worth no more than 25 dollars. He would be interested in selling at 25 and willing to buy at 24.99. However, in the real world, the decision would really be how much of his portfolio to sell at 24.99 vs. 25.00 and not whether he is buying at 24.99. Due to the same effects noted in the BBC article, he would be much more willing to sell at 25 than at 24.99. The situation works in the reverse for a support line at 25, a manager might only be willing to buy a little at 25.01, but he might be willing to buy more at 25. You may ask shouldn't it be 24.99 where he wants to buy more to be consistent with the article? However, the real meat of the article is that people don't react linearly to these price changes, the same way that portfolio managers or traders might react.
There's one problem with this analysis that I can figure out so far, the prices in the BBC article are all small. While the prices of stocks can be reasonable on the face of it, even a retail investor would probably be buying 100 share lots and a PM would purchase significantly more. So the question is, is it the dollar value that matters or the price that matters? I'm not really sure of the answer, but I would say at the very least support and resistance are important enough that every technical trader would pay attention to them. There has to be some "inefficiency" here.
Testing this would be another problem, but I'm sure some finance professor is already looking into it. I really think that the key would be to look at when it comes to resistance points with light volume or heavy volume. For instance, after identifying resistance points, I would calculate whether they are above a moving average of volume to determine whether a day is a light volume or heavy volume day (might want to do relative to the market as a whole as well) and then I would look at how the stock performs relative to the market. I would identify resistance points using something like Average True Range relative to the stock price. For instance, a 6 dollar stock that moves 25 cents a day might have have support or resistance at the $1 level, but Goldman you might look 20 dollars away for support/resistance. That way you can do all the stocks together and then compare quartiles of stocks based on price or trading volume. Finally, all you have to do is look if high volume violations of resistance points or confirmations of support lines result in prices above those points over the next month (or 3) more so than the low volume.
That's probably a publishable paper right there, biggest problem is probably identifying the resistance points. It would make sense to do it in multiple ways to avoid the criticism that you measure it wrong. If you don't remove earnings days or something, you'll also need to make some kind of assumption to deal with them.
Sunday, August 31, 2008
Wednesday, August 20, 2008
TAA and switching to bonds
First off, anybody see the ads for Crusoe on NBC during the Olympics, makes me want to break out my MES.
Second, if anyone remembers/cares I took the level 2 exam of the CFA back in June and ended up passing. So congratulations to my brothers.
Third, some ideas come to me that are rather simple, but make a lot of sense looking back on them. I had tried using bonds instead of cash in the TAA model previously, but was unimpressed due to larger volatility. However, I hadn't considered using the TAA investment in bonds. In other words, use the return series that invests in bonds when above the 10 month average and cash otherwise instead of a pure cash index for some asset classes.
The two asset classes I meant to target with this strategy were the two that historically have performed the worst on a Sharpe ratio basis, commodities and foreign equities, in the TAA strategy. I still have the TAA rule for each, but before I evaluate that I look at whether the US equity or foreign equities are below the 10 month average, if that is the case, I will have them invest in the bond TAA strategy. Then, if above the 10 month MA, they invest in that asset class, otherwise they invest in cash.
For comparison, in recent years (since 1990), the TAA strategy for commodites returned 8.8% annually (16.69% s.d., Sharpe .27 with r.f. @ period average), this simple change increases the return to 13.6% (11.8% s.d., Sharpe .79). For foreign equities, the return goes from 7.6% (12.59% s.d., Sharpe .27) to 12.2% return (12.43% s.d., Sharpe .64). The overall strategy improves from 10.7% return (6.85% s.d., Sharpe .94) to 12.5% return (7.01% s.d., 1.17 Sharpe).
Again, the reason I focused on these two was because they perform the worst. Using the strategy on US equities seems to work (Sharpe goes to 1.16) and for REITs (Sharpe goes to 1.15). Overall Sharpe goes down slightly, but for the individual asset classes the Sharpe increases suggesting the decline is due to decreased diversification and higher variances. A 5% increase in the Sharpe ratio individually doesn't impress me as much as the ones for commodities and foreign equities.
I also tested my original intention, just using the bond TAA instead of cash (and nothing more complicated like above) and it works well for REITs, but works best for equities. A marginal improvement on a risk-adjusted basis for the portfolio, but interesting nonetheless.
Second, if anyone remembers/cares I took the level 2 exam of the CFA back in June and ended up passing. So congratulations to my brothers.
Third, some ideas come to me that are rather simple, but make a lot of sense looking back on them. I had tried using bonds instead of cash in the TAA model previously, but was unimpressed due to larger volatility. However, I hadn't considered using the TAA investment in bonds. In other words, use the return series that invests in bonds when above the 10 month average and cash otherwise instead of a pure cash index for some asset classes.
The two asset classes I meant to target with this strategy were the two that historically have performed the worst on a Sharpe ratio basis, commodities and foreign equities, in the TAA strategy. I still have the TAA rule for each, but before I evaluate that I look at whether the US equity or foreign equities are below the 10 month average, if that is the case, I will have them invest in the bond TAA strategy. Then, if above the 10 month MA, they invest in that asset class, otherwise they invest in cash.
For comparison, in recent years (since 1990), the TAA strategy for commodites returned 8.8% annually (16.69% s.d., Sharpe .27 with r.f. @ period average), this simple change increases the return to 13.6% (11.8% s.d., Sharpe .79). For foreign equities, the return goes from 7.6% (12.59% s.d., Sharpe .27) to 12.2% return (12.43% s.d., Sharpe .64). The overall strategy improves from 10.7% return (6.85% s.d., Sharpe .94) to 12.5% return (7.01% s.d., 1.17 Sharpe).
Again, the reason I focused on these two was because they perform the worst. Using the strategy on US equities seems to work (Sharpe goes to 1.16) and for REITs (Sharpe goes to 1.15). Overall Sharpe goes down slightly, but for the individual asset classes the Sharpe increases suggesting the decline is due to decreased diversification and higher variances. A 5% increase in the Sharpe ratio individually doesn't impress me as much as the ones for commodities and foreign equities.
I also tested my original intention, just using the bond TAA instead of cash (and nothing more complicated like above) and it works well for REITs, but works best for equities. A marginal improvement on a risk-adjusted basis for the portfolio, but interesting nonetheless.
Monday, August 18, 2008
TAA and commodity overheating
Just wanted to do a quick blog on the TAA model noted earlier on this blog.
I created an extension to the model based on it achieving a certain return after a set number of months. After that, I looked at whether it makes sense to get out completely or to use a different exit rule (like a 5 month MA instead of 10 month MA). It doesn't get back in until the next time the 10 month MA crosses back over. The general idea is that if an asset class goes up that significantly in such a short period of time, it is unlikely that the returns in the future will be strong, despite being above the 200 day return
I started with a 20% return in a quarter and getting out completely. In that model, there is an improved return. However, closer analysis reveals that it is almost exclusively in the commodities sector. It stays out of almost five years worth trading (239 months vs. 294 months) changing an asset class with 8.8% return and 16.8% volatility to one with a 13.3% return and 13.12% volatility.
I also experimented with different combinations of returns, periods of time, and whether to use a MA average rule to get out or just permanently get out. Several of them perform better than the original TAA rule, but almost all the benefit comes from the commodities sector and the other sectors don't improve enough to be worth it.
I should note that my analysis didn't include the current period (ended in early 08), but the knowledge I take from my analysis is that when commodities rise 20% in a quarter, they historically have a correction.
Note: I also created a more complicated algorithm for the other asset classes that will get back in if the past three months did not have the quarterly 20% return which seems to help reduce volatility and improves the portfolios Sharpe ratio (though the individual ones don't appear that much better. Basically the same thing as the commodity strategy except it is willing to get back in (keeps the same returns for the commodity strategy). 11% return for the overall strategy here with 5.43% volatility. (compared to about 6.85% for the original TAA model).
I created an extension to the model based on it achieving a certain return after a set number of months. After that, I looked at whether it makes sense to get out completely or to use a different exit rule (like a 5 month MA instead of 10 month MA). It doesn't get back in until the next time the 10 month MA crosses back over. The general idea is that if an asset class goes up that significantly in such a short period of time, it is unlikely that the returns in the future will be strong, despite being above the 200 day return
I started with a 20% return in a quarter and getting out completely. In that model, there is an improved return. However, closer analysis reveals that it is almost exclusively in the commodities sector. It stays out of almost five years worth trading (239 months vs. 294 months) changing an asset class with 8.8% return and 16.8% volatility to one with a 13.3% return and 13.12% volatility.
I also experimented with different combinations of returns, periods of time, and whether to use a MA average rule to get out or just permanently get out. Several of them perform better than the original TAA rule, but almost all the benefit comes from the commodities sector and the other sectors don't improve enough to be worth it.
I should note that my analysis didn't include the current period (ended in early 08), but the knowledge I take from my analysis is that when commodities rise 20% in a quarter, they historically have a correction.
Note: I also created a more complicated algorithm for the other asset classes that will get back in if the past three months did not have the quarterly 20% return which seems to help reduce volatility and improves the portfolios Sharpe ratio (though the individual ones don't appear that much better. Basically the same thing as the commodity strategy except it is willing to get back in (keeps the same returns for the commodity strategy). 11% return for the overall strategy here with 5.43% volatility. (compared to about 6.85% for the original TAA model).
Sunday, August 3, 2008
The Economics of Registering to Vote
Well, I should say that it is more the cost/benefit analysis of registering to vote. I recently moved from Queens to Jersey City and there were some thirty-ish professionals outside the PATH entrance who wanted to register me to vote. I am registered in Indiana (where KF's parents live and went to college) and still have my Indiana driver's license.
Walking to the registration table, I figured that (outside of time wasted filling out the form) I was making a cost-less decision. I probably won't vote, but I figure that the margin difference in New Jersey in the general election will be smaller than the margin difference in Indiana. So, if my vote matters at all (probably not), it matters a fraction more in Jersey than Indiana. So the benefits side of the calculus is the expected value of me voting and that influencing the election (probably of me voting times value of my vote and also all future voting decisions and their weight discounted to the present).
However, I didn't realize the costs of voting until a man who either was an unemployed, alcoholic construction worker or homeless (probably the latter) began to convince me not to register. His early arguments weren't that convincing focusing mostly on how much the vote matters and staying off the grid (the first I already knew, the second I didn't care about). However, he mentioned that one of two places they pull jury duty from is the voter rolls. If I am pulled to do jury duty twice a decade in New Jersey that means that I earn like $3.50 (how much the lochness monster takes) and lose a vacation day, I presume.
The problem of how to value the cost is difficult for two reasons. First, the call for jury duty is random and could be modeled like a Poisson process. An easy work around would be that I have jury duty in five years and ten years and discount the costs on those dates back at 6% or so. The second difficulty is valuing a vacation day. I can assume that the value of a vacation day would increase as my income increases since leisure would become more scarce and I would imagine that my income grows significantly five to ten years from now. I could probably model it, but it shouldn't matter that much, as will be seen. My gut feeling is that, in terms of dollars, a vacation day shouldn't affect salary (I get paid the same) and you could assume that it doesn't affect your bonus. However, if you don't use all of your vacation days, you might have worked harder and deserved a higher bonus by accomplishing more work. There is some probability that it will increase your bonus by not taking the vacation day, but it is small and would probably not be a big effect after discounting*. The real place to value the vacation day is in subjective value. The proper trade off is the net benefit of sitting in the sun or skiing out west or sitting in a jury room.
The subjective benefit to skiing with friends relative to sitting in a jury room, for me, outweighs the money (from bonus or the 3.50) and the benefits of being able to vote in New Jersey. I'll stay registered in Indiana and avoid jury duty like the plague.
I'm pretty sure they don't let people who think like me on juries anyway.
*It is small on the margin because it would probably only be if you had like leftover vacation days from the day before and just dropped out from work for like a month. That would probably affect bonus.
Walking to the registration table, I figured that (outside of time wasted filling out the form) I was making a cost-less decision. I probably won't vote, but I figure that the margin difference in New Jersey in the general election will be smaller than the margin difference in Indiana. So, if my vote matters at all (probably not), it matters a fraction more in Jersey than Indiana. So the benefits side of the calculus is the expected value of me voting and that influencing the election (probably of me voting times value of my vote and also all future voting decisions and their weight discounted to the present).
However, I didn't realize the costs of voting until a man who either was an unemployed, alcoholic construction worker or homeless (probably the latter) began to convince me not to register. His early arguments weren't that convincing focusing mostly on how much the vote matters and staying off the grid (the first I already knew, the second I didn't care about). However, he mentioned that one of two places they pull jury duty from is the voter rolls. If I am pulled to do jury duty twice a decade in New Jersey that means that I earn like $3.50 (how much the lochness monster takes) and lose a vacation day, I presume.
The problem of how to value the cost is difficult for two reasons. First, the call for jury duty is random and could be modeled like a Poisson process. An easy work around would be that I have jury duty in five years and ten years and discount the costs on those dates back at 6% or so. The second difficulty is valuing a vacation day. I can assume that the value of a vacation day would increase as my income increases since leisure would become more scarce and I would imagine that my income grows significantly five to ten years from now. I could probably model it, but it shouldn't matter that much, as will be seen. My gut feeling is that, in terms of dollars, a vacation day shouldn't affect salary (I get paid the same) and you could assume that it doesn't affect your bonus. However, if you don't use all of your vacation days, you might have worked harder and deserved a higher bonus by accomplishing more work. There is some probability that it will increase your bonus by not taking the vacation day, but it is small and would probably not be a big effect after discounting*. The real place to value the vacation day is in subjective value. The proper trade off is the net benefit of sitting in the sun or skiing out west or sitting in a jury room.
The subjective benefit to skiing with friends relative to sitting in a jury room, for me, outweighs the money (from bonus or the 3.50) and the benefits of being able to vote in New Jersey. I'll stay registered in Indiana and avoid jury duty like the plague.
I'm pretty sure they don't let people who think like me on juries anyway.
*It is small on the margin because it would probably only be if you had like leftover vacation days from the day before and just dropped out from work for like a month. That would probably affect bonus.
Saturday, July 19, 2008
SEC exempts Market Makers
This big news in the market these days has been the new SEC naked short sale regulations. According to this article, market makers in equities and options have been exempted from the short sale regulations.
In my view there are three main criticisms of the original regulations. The first is resolved by this adjustment. The options market, in particular, was effected by these regulations since it can disrupt hedging operations. Since activity in the options market feeds into the equity markets, if you create regulations that make it less likely someone will make markets in some options, there will be some big effects. The second criticism is the one pointed out by Mish several times that the firms exempted from the shorts has been chosen rather arbitrarily. Finally, is the whole this prevents these companies from going quickly to a fair value and serves as a form of relief for privileged, politically well-connected banks. People lost their life savings on internet companies and rules like this weren't put in place. And I'll leave it at that.
In my view there are three main criticisms of the original regulations. The first is resolved by this adjustment. The options market, in particular, was effected by these regulations since it can disrupt hedging operations. Since activity in the options market feeds into the equity markets, if you create regulations that make it less likely someone will make markets in some options, there will be some big effects. The second criticism is the one pointed out by Mish several times that the firms exempted from the shorts has been chosen rather arbitrarily. Finally, is the whole this prevents these companies from going quickly to a fair value and serves as a form of relief for privileged, politically well-connected banks. People lost their life savings on internet companies and rules like this weren't put in place. And I'll leave it at that.
Thursday, July 17, 2008
Merger Arbitrage
*I generally don't post about specific stocks, but I haven't gotten around to some of the research I meant to do and something I am looking at is increasingly looking worthwhile.
Merger arbitrage is the art of buying companies that are getting acquired and selling companies that are acquiring. When the merger goes through, you collect the spread between them. If the merger doesn't go through, the spread widens and you lose money.
Alpha Natural Resources (ANR) is a coal stock and Cleveland-Cliffs (CLF) is an iron and coal stock. Cleveland-Cliffs announced on July 15th that it will purchase ANR for $22.23 and .95 shares of CLF. On the 16th, ANR opened up around 119 after trading around 95 the past few days and then proceeded to tank back down to a close of around 96 at the close of the 17th. CLF was trading around 110 prior to the announcement and has come down to about 97.25.
Based on current prices, 100 shares of ANR should be worth 22.23*100+97.25*95=$11,462 and only cost $9,580 on the market. Since the value of the ANR is dependent on the value of CLF, you would sell short the CLF in a merger arb situation. This way when you receive the 95 shares of CLF you can deliver them to whomever you borrowed the stock from.
For example, assuming the existing prices are where you buy and short and the merger closes, that means that ANR will be priced such that what you can buy equals 22.23*100+p*95, where p is the price of CLF. If CLF closes out at 100, ANR should be worth 117.23 per share. After your ANR shares are converted to CLF, you can close out your short (worth 95*100 dollars) and keep 2223 (22.23*100). The merger is supposed to complete at the end of the year and depending on how your margin account is handled, it looks like you could put up about 20k for an annualized return of about 20%.
That's not to say that this isn't risky. Merger arbitrage is a very risky business and it admittedly isn't mine. Given how that ANR has fallen fairly significantly since the announcement came out, the market is pricing (excluding shorting costs and TVM) that the stock is only worth three-quarters a share of CLF. I will be waiting for more details, particularly the proxy. Do your homework and certainly don't blindly follow me. I would have bought it on the open of 7/16 and have lost like 20 dollars a share already on ANR and not made it back on CLF. At these prices and this spread, I feel like it would be less risky given the potential gain.
SEC 8-K form
Press Release
edit: Harbinger Capital increased a position from 3/31 of about 8.73% to about 18.36% and announced in a 13D that they would oppose the merger.
Merger arbitrage is the art of buying companies that are getting acquired and selling companies that are acquiring. When the merger goes through, you collect the spread between them. If the merger doesn't go through, the spread widens and you lose money.
Alpha Natural Resources (ANR) is a coal stock and Cleveland-Cliffs (CLF) is an iron and coal stock. Cleveland-Cliffs announced on July 15th that it will purchase ANR for $22.23 and .95 shares of CLF. On the 16th, ANR opened up around 119 after trading around 95 the past few days and then proceeded to tank back down to a close of around 96 at the close of the 17th. CLF was trading around 110 prior to the announcement and has come down to about 97.25.
Based on current prices, 100 shares of ANR should be worth 22.23*100+97.25*95=$11,462 and only cost $9,580 on the market. Since the value of the ANR is dependent on the value of CLF, you would sell short the CLF in a merger arb situation. This way when you receive the 95 shares of CLF you can deliver them to whomever you borrowed the stock from.
For example, assuming the existing prices are where you buy and short and the merger closes, that means that ANR will be priced such that what you can buy equals 22.23*100+p*95, where p is the price of CLF. If CLF closes out at 100, ANR should be worth 117.23 per share. After your ANR shares are converted to CLF, you can close out your short (worth 95*100 dollars) and keep 2223 (22.23*100). The merger is supposed to complete at the end of the year and depending on how your margin account is handled, it looks like you could put up about 20k for an annualized return of about 20%.
That's not to say that this isn't risky. Merger arbitrage is a very risky business and it admittedly isn't mine. Given how that ANR has fallen fairly significantly since the announcement came out, the market is pricing (excluding shorting costs and TVM) that the stock is only worth three-quarters a share of CLF. I will be waiting for more details, particularly the proxy. Do your homework and certainly don't blindly follow me. I would have bought it on the open of 7/16 and have lost like 20 dollars a share already on ANR and not made it back on CLF. At these prices and this spread, I feel like it would be less risky given the potential gain.
SEC 8-K form
Press Release
edit: Harbinger Capital increased a position from 3/31 of about 8.73% to about 18.36% and announced in a 13D that they would oppose the merger.
Thursday, July 10, 2008
Tuesday, July 8, 2008
Increasing 200 day moving averages
I did a quick study of what happens if you look at whether the 200 day moving average is increasing or not. I used the same asset classes and methodology as this which through February of this year showed a return of 11.98% (6.82% std, .875 Sharpe). I looked at three improvements which probably do not have different enough results to tell a priori which is better.
I had originally assumed it would be in less. I wanted a method that would use the same entry and get you out quicker when the market begins to tank, but it appears that the benefit comes from keeping you in the market longer (roughly 70% of the months that are different are from the second method having a buy rather than a sell) and these months, particularly for commodities and stocks, generate strong returns and the handful of months avoided have relatively mixed returns. However, when they are down, they are down pretty significantly (real estate is an anomaly that acts opposite both effects). I was also surprised to find out that on average the TAA method generates on average 50 entry or exit signals per asset class whereas the second method generates about 45.
In conclusion, the TAA model can benefit by being in the market longer and not necessarily trying to avoid more periods.
- 1. If the 200 day moving average is increasing a buy signal is generated, invest in cash otherwise.
- 2. Entry order is only generated when the price is greater than the 200 day MA, only exit if the 200 MA decreases.
- 3. Same entry order, but exit if below 200 day MA and 200 day MA decreases.
I had originally assumed it would be in less. I wanted a method that would use the same entry and get you out quicker when the market begins to tank, but it appears that the benefit comes from keeping you in the market longer (roughly 70% of the months that are different are from the second method having a buy rather than a sell) and these months, particularly for commodities and stocks, generate strong returns and the handful of months avoided have relatively mixed returns. However, when they are down, they are down pretty significantly (real estate is an anomaly that acts opposite both effects). I was also surprised to find out that on average the TAA method generates on average 50 entry or exit signals per asset class whereas the second method generates about 45.
In conclusion, the TAA model can benefit by being in the market longer and not necessarily trying to avoid more periods.
Tuesday, July 1, 2008
Probit and Interest rates
I'm curious how the historical shape of the yield curve can assist in the prediction of returns for holding government bonds. This is a preliminary post that plans to detail some of the basic lines of thought I am pursuing. I am heading to DC for the 4th, so I would like to perform an out-of-sample test to look into how this line of thought actually performs when I get back. I have some skepticism and doubts about this method that can only be confirmed upon more research (more on this later).
I began by collecting total return series for 1, 2, 3, 5, 10, and 30 year government bonds along with interest data that's available for bills, bonds, and corporate debt. Some of the series are active in some time periods and not in others, so I just stuck with 3 month t-bill and 1, 3, 5, and 10 year bonds, along with BAA corporate interest rates.
I first looked at the returns for the different bonds. In general, I am interested in holding for several months, so I took the geometric average three month returns and created holding 10 year (5 years back, five years forward) windows to evaluate each time period. The evaluation was simply which (not decile or quartile, but) quintile or 20% range the return would fall into. So if a time period is ranked a five, it would perform in the top 80% relative to the performance five years prior or forward. This way the select periods of time where bonds dominate don't outweigh the whole dataset and there are still runs where it makes sense to be in bonds. The only reason I don't do the whole series is that I believe doing so would result in too much trading.
The chart above is the average monthly (not 3 month) return for each of the bonds I looked at and each decile. Below that is the same chart except if given a 4 or a 5 above, the left-most column is a 1 and 0 otherwise. Since we expect that bonds with longer maturities should have longer durations it makes sense that the 30 year has the largest spread and the greatest opportunity to profit or lose. I also looked into the correlation of the returns to the 6 bonds. For the most part correlations like 3 year vs. 5 year are very high, but as you get larger differences, there are larger differences. However, what is striking is that the correlation between many bonds, even like the 10 year vs. 2 year, are higher than 80%. That suggests that for the most part if you can build a good model for one of them, the idea should work for all (with the 10 and 30 relative to the 1 year having lowest correlations).
I think it is interesting to look at conditional means (or categories) for different statistics. For example, what are the returns like on average over the next three months when the yield curve inverts (or steepens). The only problem with that is that I have so much data and so many different yield curves to compare. I didn't want to specify one way that would work best (ie. do I only look at when the 10 year inverts relative to the 1 year, or do I look at 2 and 5, do some outperform in different central bank regimes?). To give myself as much flexibility without doing something crazy like a neural network, I decided that it would be best (at least in a preliminary sense) to look into using a probit model to categorize the returns.
I described what probit models are and how to use them to look into the probability of a crisis or recession previously. Essentially, I have the series of 0s and 1s and the goal is to use the independent variables to estimate the probability that an event will occur (in this case, the event is that it is worthwhile to invest in bonds for at least three months). I estimated the model for each bond series using two methods, in the first I focused on the interest rates mentioned above without reference to their past values, in the second I used the interest rates and each of the past 12 lags. The first method is less successful than the second, but it also avoids a lot more curve-fitting problems than the first method. The first method classifies 63% to 72% (from 30 year to 1 year) correctly whereas the second method is up to 73% to 80% (from 30 year to 1 year). For comparison, using the binary decision of greater than the 10 month MA or less, classifies at about 60% for each bond (and including it in the decision-making doesn't help). Note that I consider classifying correctly to mean a probability greater than 50%.
What will be interesting is to look at the false positive rate and the returns in situations when there is a false positive. In other words, I think the value of the probit model is identifying risk/return better than other models. If I can identify situations with good average wins relative to average losses, then I can control my risk better. Using the model incorporating 12 lags (which I am worried about), I calculated the times where there are false positives for the 10 year bond and found a 2% annual return with 3% volatility compared to a 18% return with 9% volatility for the normal (note that this is just what the returns are and ignores the fact that it will be in cash for significant periods of time, just want to get an idea of the conditional means). As expected, the periods when the model says to get out of the market, there are negative annualized returns(-10% with 7% volatility). However, I am a little worried about false negatives, but after looking at how often the model invests (since it invests for three months), it appears that the problem goes away. Obviously the problem with this is that I use the whole series to develop the probit model rather than going with information available to develop the coefficients. I would suspect that these good returns would get slightly reduced by using the actual trading model (which is what I intend to test when I am back from DC). In comparison, the 10 month MA rule, returns 8.5% with 8.5% standard deviation (ignoring interest) though it is invested more often. Incorporating commercial paper yield into the second model would reduce its return (though risk/reward stays high) though also reduce volatility by more in this model than in the 10 month MA rule.
Nevertheless, it appears to be an interesting development, I am worried that the coefficients are a bit difficult to interpret (too black boxy) and that they won't be stable enough to generate significant returns. I also don't doubt there are problems with autocorrelation, but fixing that in probit models can be a pain.
I began by collecting total return series for 1, 2, 3, 5, 10, and 30 year government bonds along with interest data that's available for bills, bonds, and corporate debt. Some of the series are active in some time periods and not in others, so I just stuck with 3 month t-bill and 1, 3, 5, and 10 year bonds, along with BAA corporate interest rates.
I first looked at the returns for the different bonds. In general, I am interested in holding for several months, so I took the geometric average three month returns and created holding 10 year (5 years back, five years forward) windows to evaluate each time period. The evaluation was simply which (not decile or quartile, but) quintile or 20% range the return would fall into. So if a time period is ranked a five, it would perform in the top 80% relative to the performance five years prior or forward. This way the select periods of time where bonds dominate don't outweigh the whole dataset and there are still runs where it makes sense to be in bonds. The only reason I don't do the whole series is that I believe doing so would result in too much trading.
The chart above is the average monthly (not 3 month) return for each of the bonds I looked at and each decile. Below that is the same chart except if given a 4 or a 5 above, the left-most column is a 1 and 0 otherwise. Since we expect that bonds with longer maturities should have longer durations it makes sense that the 30 year has the largest spread and the greatest opportunity to profit or lose. I also looked into the correlation of the returns to the 6 bonds. For the most part correlations like 3 year vs. 5 year are very high, but as you get larger differences, there are larger differences. However, what is striking is that the correlation between many bonds, even like the 10 year vs. 2 year, are higher than 80%. That suggests that for the most part if you can build a good model for one of them, the idea should work for all (with the 10 and 30 relative to the 1 year having lowest correlations).
I think it is interesting to look at conditional means (or categories) for different statistics. For example, what are the returns like on average over the next three months when the yield curve inverts (or steepens). The only problem with that is that I have so much data and so many different yield curves to compare. I didn't want to specify one way that would work best (ie. do I only look at when the 10 year inverts relative to the 1 year, or do I look at 2 and 5, do some outperform in different central bank regimes?). To give myself as much flexibility without doing something crazy like a neural network, I decided that it would be best (at least in a preliminary sense) to look into using a probit model to categorize the returns.
I described what probit models are and how to use them to look into the probability of a crisis or recession previously. Essentially, I have the series of 0s and 1s and the goal is to use the independent variables to estimate the probability that an event will occur (in this case, the event is that it is worthwhile to invest in bonds for at least three months). I estimated the model for each bond series using two methods, in the first I focused on the interest rates mentioned above without reference to their past values, in the second I used the interest rates and each of the past 12 lags. The first method is less successful than the second, but it also avoids a lot more curve-fitting problems than the first method. The first method classifies 63% to 72% (from 30 year to 1 year) correctly whereas the second method is up to 73% to 80% (from 30 year to 1 year). For comparison, using the binary decision of greater than the 10 month MA or less, classifies at about 60% for each bond (and including it in the decision-making doesn't help). Note that I consider classifying correctly to mean a probability greater than 50%.
What will be interesting is to look at the false positive rate and the returns in situations when there is a false positive. In other words, I think the value of the probit model is identifying risk/return better than other models. If I can identify situations with good average wins relative to average losses, then I can control my risk better. Using the model incorporating 12 lags (which I am worried about), I calculated the times where there are false positives for the 10 year bond and found a 2% annual return with 3% volatility compared to a 18% return with 9% volatility for the normal (note that this is just what the returns are and ignores the fact that it will be in cash for significant periods of time, just want to get an idea of the conditional means). As expected, the periods when the model says to get out of the market, there are negative annualized returns(-10% with 7% volatility). However, I am a little worried about false negatives, but after looking at how often the model invests (since it invests for three months), it appears that the problem goes away. Obviously the problem with this is that I use the whole series to develop the probit model rather than going with information available to develop the coefficients. I would suspect that these good returns would get slightly reduced by using the actual trading model (which is what I intend to test when I am back from DC). In comparison, the 10 month MA rule, returns 8.5% with 8.5% standard deviation (ignoring interest) though it is invested more often. Incorporating commercial paper yield into the second model would reduce its return (though risk/reward stays high) though also reduce volatility by more in this model than in the 10 month MA rule.
Nevertheless, it appears to be an interesting development, I am worried that the coefficients are a bit difficult to interpret (too black boxy) and that they won't be stable enough to generate significant returns. I also don't doubt there are problems with autocorrelation, but fixing that in probit models can be a pain.
Monday, June 30, 2008
Bear Stearns in Vanity Fair
The article in Vanity Fair regarding the collapse of Bear Stearns was fascinating. Particularly for an essentially anonymous trader who was able to profit (by shorting other financial stocks as Bear went down) from their collapse. The day that Bear did the final drop (I can't pull up the ticker on any of my normal methods so I can't be sure which day it was) it was up 10 dollars at about 9 o'clock only to get beaten down to flat by 9:30 and then got smoked (pretty sure it dropped at least 25%-50% the next half hour). My only insight is that most traders just see what is happening and react.
Though the entire article is worth a read, I found the following quote particularly enlightening.
The 2005 BAPCA bill was a giveaway to credit card companies, but it seems like this statement doesn't really make sense. First, it depends on if the securities are in margin account or traditional customer accounts. Margin accounts are held in the name of the brokerage, so it makes sense that those would be able to be taken in bankruptcy. Though I'm not an expert, by any means, I would assume that this hasn't changed. Within customer accounts, SIPC protects cash and securities less than numbers only lawyers remember. So based on the statement above, the 2005 BAPCA would allow the immediate seizure by creditors of the customer's cash and securities held at Bear Stearns. To me that just means that if Bear declares bankruptcy, it would be forced to liquidate. It couldn't go into bankruptcy protection and eventually hope to emerge. The equity would be worthless. In other words, senior management would never consider bankruptcy for Bear. I could be totally mistaken, but it appears that if it weren't for the BAPCPA bill, Bear could (big assumption) have tried bankruptcy and not purchase by J.P. Morgan. I'm not an expert enough to know if this is the case, but it would be interesting to look further at the influence of this bill and the collapse of the company.
Though the entire article is worth a read, I found the following quote particularly enlightening.
It was then that Gary Parr and the bankruptcy attorneys patiently explained that bankruptcy was actually not an option, not for a major securities firm. Changes to the bankruptcy code in 2005 would force federal regulators to take over customer accounts. All its securities would be subject to immediate seizure by creditors.
Thursday, June 19, 2008
Natural gas inventories
Natural Gas inventories were surveyed to change by 58 and came in at 57 (prior was 80). Natural Gas proceeded to fall 3% (at writing). For those who aren't traders, generally the natural gas inventories usually don't move the market enough to be worth trading (though they were three and four weeks ago), but I haven't seen such a strong, lasting move on this number when the inventories came in essentially in line. It looks like around 11 there was news (according to Briefing.com) that China would raise some prices of gasoline and crude, but this decision wouldn't affect natural gas. I guess I'm kind of at a loss to describe it.
Generally the trend is your friend, but I can't help put think that this is oversold (the front contract is at 12.72 and UNG is as 60.30 as of this writing). However, bottom picking this kind of strength on the downside can be vicious unless you are looking to hold for a long enough period. Thankfully my only position in UNG was in a play account on updown because I have been wanting to bottom pick this for at least an hour and it just keeps going down. The futures are at 12.65, down 4.3% from the open.
Edit: Looks like I was about ten minutes off the bottom. Also edited for grammar.
Generally the trend is your friend, but I can't help put think that this is oversold (the front contract is at 12.72 and UNG is as 60.30 as of this writing). However, bottom picking this kind of strength on the downside can be vicious unless you are looking to hold for a long enough period. Thankfully my only position in UNG was in a play account on updown because I have been wanting to bottom pick this for at least an hour and it just keeps going down. The futures are at 12.65, down 4.3% from the open.
Edit: Looks like I was about ten minutes off the bottom. Also edited for grammar.
Monday, June 16, 2008
Volatility Smile
The Black-Scholes-Merton model makes the assumption of constant volatility. In practice, we observe something called the volatility smile. Basically, options struck at the money have less volatility if you solve for volatility in BSM than options struck far in or out of the money. This is an interesting phenomenon that finance professors like to write about and hedge funds try to exploit.
I wonder whether equity index options (in particular just b/c I know that the 10 month MA strategy works on them and they have a long history) experience different volatility smiles when above the 10 month MA or below the 10 month MA. If the volatility doesn't change, I would look to a situation where calls are cheap when the market is trending up and puts are cheap when the market is trending downwards. I imagine it would take significant work to look into this. If no one else does (let me know if you do), then I might take a stab at looking into this problem sometime within the next six months. Nevertheless, I think it is an interesting question and could present arbitrage opportunities. Volatility is traditionally higher when equity markets are below 200 day moving averages, but I wonder if it is high enough given historical volatility during these times and the small (mostly negative) returns.
I wonder whether equity index options (in particular just b/c I know that the 10 month MA strategy works on them and they have a long history) experience different volatility smiles when above the 10 month MA or below the 10 month MA. If the volatility doesn't change, I would look to a situation where calls are cheap when the market is trending up and puts are cheap when the market is trending downwards. I imagine it would take significant work to look into this. If no one else does (let me know if you do), then I might take a stab at looking into this problem sometime within the next six months. Nevertheless, I think it is an interesting question and could present arbitrage opportunities. Volatility is traditionally higher when equity markets are below 200 day moving averages, but I wonder if it is high enough given historical volatility during these times and the small (mostly negative) returns.
Thursday, June 12, 2008
Beta and Sectors
I meant to post something about the interest rate environment and tactical asset allocation, but I haven't gotten around to it since the results aren't that spectacular. Still kind of interesting. Anyway, I've been reading Eric Falkenstein lately over at the Falkenblog and his website DefProb.
One point that he makes is that historically buying low Beta stocks has better returns than buying high Beta stocks (though there are periods of significant underperformance such as the internet bubble). I found this result interesting (risk is inversely related to returns, how could that not be interesting?) and so decided to look into a similar strategy using sectors.
I used weekly dividend adjusted data of the 9 Sector Spiders since they began at the end of '98 along with SPY. I calculated Beta vs. SPY using at least a year's worth of data and no more than 5 years worth of data. At the start of every year I ranked the Sectors on the basis of Beta and formed a high Beta and low Beta portfolio with three Sectors each. I also calculated a portfolio investing equally in each Spider to serve as comparison (SPY is market-weighted).
Over this period (from Jan. 2000 to the end of last week), the equal-weight portfolio return 2.4% annually (15.7% std), the high beta portfolio returned -.14% (20.7 std), and the low beta portfolio returned 4.3% (14.3% std).
I then calculated the 40 week (200 day) moving average and considered a signal at the beginning of the month good through the end of the month (since that is how the 10 month TAA works and I wanted it to be somewhat comparable). The results are reported below:
(After accidentally inflating the returns of the high portfolio) The results indicate that the low Beta portfolio outperforms when the market is above the 40 week moving average and slightly outperforms when the market is below the 40 week moving average which confirms the argument that Mr. Falkenstein had made (note that the Sharpe ratio is higher for the high than the low in the below 40 week, I think that the Sharpe ratio is an incorrect method of comparison when returns are below 0). That doesn't change the fact that investing when below the 200 day moving average is very risky.
CFO advisory posted yesterday regarding the sector momentum strategy (which I have covered before on this site) and noted that a significant portion of the return has been due to XLE. The low Beta portfolio included XLE from 2000 to the beginning of 2007; however, from 2007 until recently XLE return 35% annualized compared to 11% from 2000 to 2007. So I would argue that the performance of the low Beta portfolio doesn't suffer from the XLE criticism (note that I really agree with it anyhow).
One point that he makes is that historically buying low Beta stocks has better returns than buying high Beta stocks (though there are periods of significant underperformance such as the internet bubble). I found this result interesting (risk is inversely related to returns, how could that not be interesting?) and so decided to look into a similar strategy using sectors.
I used weekly dividend adjusted data of the 9 Sector Spiders since they began at the end of '98 along with SPY. I calculated Beta vs. SPY using at least a year's worth of data and no more than 5 years worth of data. At the start of every year I ranked the Sectors on the basis of Beta and formed a high Beta and low Beta portfolio with three Sectors each. I also calculated a portfolio investing equally in each Spider to serve as comparison (SPY is market-weighted).
Over this period (from Jan. 2000 to the end of last week), the equal-weight portfolio return 2.4% annually (15.7% std), the high beta portfolio returned -.14% (20.7 std), and the low beta portfolio returned 4.3% (14.3% std).
I then calculated the 40 week (200 day) moving average and considered a signal at the beginning of the month good through the end of the month (since that is how the 10 month TAA works and I wanted it to be somewhat comparable). The results are reported below:
(After accidentally inflating the returns of the high portfolio) The results indicate that the low Beta portfolio outperforms when the market is above the 40 week moving average and slightly outperforms when the market is below the 40 week moving average which confirms the argument that Mr. Falkenstein had made (note that the Sharpe ratio is higher for the high than the low in the below 40 week, I think that the Sharpe ratio is an incorrect method of comparison when returns are below 0). That doesn't change the fact that investing when below the 200 day moving average is very risky.CFO advisory posted yesterday regarding the sector momentum strategy (which I have covered before on this site) and noted that a significant portion of the return has been due to XLE. The low Beta portfolio included XLE from 2000 to the beginning of 2007; however, from 2007 until recently XLE return 35% annualized compared to 11% from 2000 to 2007. So I would argue that the performance of the low Beta portfolio doesn't suffer from the XLE criticism (note that I really agree with it anyhow).
Thursday, June 5, 2008
TAA and avoiding pullbacks
I should probably be studying, but this didn't take me that long to work out and was pretty interesting.
This could be considered another extension of the tactical asset allocation system developed by Mebane Faber that I have blogged about several times. The original strategy is to invest in five asset classes (US bonds, US stocks, Foreign stocks, Commodities, Real Estate) when they are greater than their 200 day moving average and commercial paper otherwise.
I modified the system slightly, maintaining the 200 day moving average requirement, but I added an additional constraint: it could not be the case that it was above the 5 month (4 and 6 have similar results) moving average and the return over the previous month was negative. The point of this was to take into account periods being overbought and then getting back in quickly. The periods above the five month that have negative prior month returns have very poor risk to reward ratios, most significantly for stocks and REITs. So making this simple addition can take a system with an 11.9% historical return with 6.8% standard deviation (.867 Sharpe at 6%) to 11.8% with 5.68% standard deviation (1.026 Sharpe). Though there is not a statistically significant difference in means, there is a significant difference in standard deviations according to an F test.
Not only is this improvement a significant, easy to implement improvement, but it is based on logic. Most trends do not continue up continuously. There tend to be pull backs. This strategy maintains the idea that the trend is your friend and attempts to stay out of a pull back if it happens two months in a row.
Note: the portfolio leveraged 50% has a 14% return with 8.5% standard deviation compared to 13.5% with 9% standard deviation for the original version. The best benefit in reducing standard deviation is in keeping the risk to reward statistics strong when using leverage.
This could be considered another extension of the tactical asset allocation system developed by Mebane Faber that I have blogged about several times. The original strategy is to invest in five asset classes (US bonds, US stocks, Foreign stocks, Commodities, Real Estate) when they are greater than their 200 day moving average and commercial paper otherwise.
I modified the system slightly, maintaining the 200 day moving average requirement, but I added an additional constraint: it could not be the case that it was above the 5 month (4 and 6 have similar results) moving average and the return over the previous month was negative. The point of this was to take into account periods being overbought and then getting back in quickly. The periods above the five month that have negative prior month returns have very poor risk to reward ratios, most significantly for stocks and REITs. So making this simple addition can take a system with an 11.9% historical return with 6.8% standard deviation (.867 Sharpe at 6%) to 11.8% with 5.68% standard deviation (1.026 Sharpe). Though there is not a statistically significant difference in means, there is a significant difference in standard deviations according to an F test.
Not only is this improvement a significant, easy to implement improvement, but it is based on logic. Most trends do not continue up continuously. There tend to be pull backs. This strategy maintains the idea that the trend is your friend and attempts to stay out of a pull back if it happens two months in a row.
Note: the portfolio leveraged 50% has a 14% return with 8.5% standard deviation compared to 13.5% with 9% standard deviation for the original version. The best benefit in reducing standard deviation is in keeping the risk to reward statistics strong when using leverage.
Thursday, May 22, 2008
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.
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.
Tuesday, May 20, 2008
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.
Monday, May 19, 2008
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.
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.
Wednesday, May 14, 2008
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.
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
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
Thursday, May 8, 2008
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.
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.
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