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.
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