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.
Saturday, July 19, 2008
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.
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