The Hedge Fund strategy that wasn't?

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

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

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

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

Stops

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

TAA update

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

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

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

Spurious

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

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

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

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

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

Donchian Channels

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

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

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

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

OverBought/OverSold part 2

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

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

OverBought/OverSold

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

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

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

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

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

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

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

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

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

BRK

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

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

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

Wish you were here

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

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

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

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

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

Here's for not understanding GDP numbers

In addition to the plethora of economic information coming out today, advance GDP numbers came out for quarter 1 early this morning. I'm not surprised that the current account deficit narrowed, that is to be expected with a weaker dollar. Looking at the percentage change table, it is clear that inventories were strong and services were strong. The increase in inventories was responsible for a 20 billion dollar increase, but the increase in services was responsible for a 40 billion increase. The Q4 inventory data was pretty awful, so I'm not surprised there was a bit of mean-reversion. However, I'm more surprised at services being as strong as they are.

If you go into table 2.3.1 (or 2.3.6), you will see why services are strong. Basically, in spite of a housing recession, spending on housing (services, not to be confused with residential investment) goes up. I'm not surprised that housing operation is going up (electricity is increasing at a 15% rate), but I'm a little baffled why in the middle of dramatic decreases in home prices and sales that spending on housing would be increasing. Medical care and household operation (electricity mostly) make up a big percentage of the increase in services (and therefore services), roughly half. And another large increase is due to other. The big question I have is, why isn't spending on housing services decreasing in the GDP numbers rather than consistently increasing? The durable goods section showed only a small decrease, but the average increase since 2006 in the housing services number has been .6% and increased by .55% this time. Effectively in line. Granted that the ISM non-manufacturing index was below 50 the entire quarter, it makes even less sense why services would be increasing.

Ultimately, if you use better inflation numbers or per-capita figures, this would probably be the second quarter of a declining GDP. Not the best definition of whether we are in a recession, but it's what the financial press usually talks up.

Long-term Component Timing Model

My primary concern here is to test a component (subsector) timing model going back more years than ETF data is available. Total return data isn't available for sub-sectors for all asset classes in a way that could be approximated with ETFs available now. However, there are total return series available that replicate them well enough to be comparable with prior results developed in this space (here). For domestic equities, I was able to use the S&P indices (used in Rydex ETFs). For commodities, I was able to use the DJ-AIG indices (just using futures is not comparable to total return indices. I used total return series for a number of foreign equity indices. Finally, I added a AAA corporate bond index to the 10 year treasury since none of the other bonds really are that impressive for the long-term (30 year has strong returns, but too much volatility). Reits are kept the same.

The general strategy is as simple as the TAA strategy. If the subindex is above 10month SMA, invest, otherwise stay in commercial paper. For equities, I also entered the entire asset class in CP when the broad index is below the SMA. They have much stronger correlation to the index than the other asset classes. Asset classes are equally weighted. I'll only report since 1991 (when I have data for commodities). The returns are consistent over time, they tend to slightly decrease, but with consistently lower volatility.

For reference, the AA strategy has a return of 9.65% (7.8% stdev) and the TAA is 10.8% (6% stdev). Extending the strategy with the component timing model gives 10.4% (4.7% stdev). Adding in a currency strategy similar to this* will reduce returns to 9.9% (4.2%).

*including interest rates from holding foreign currencies, but not counting the movements of currencies when in domestic currency since other asset classes do not control for value of the dollar which makes it not comparable to past strategies, all this does it lower the return and keeps volatility relatively constant, just wanted to be conservative

For the unlevered strategies, the alpha of each strategy is highly significant (<.01%) at 3% (.64 Beta) for the original, 3.6% (.46 Beta) timing w/o currencies, and 3.2% (.42 Beta) with currencies. The alpha of the timing (w/o curr) vs. the TAA strategy is significant at 1.7%. Using 2:1 leverage (except for the currencies), the TAA strategy has an alpha 4.86% (1.2 Beta), 6.3% (.92 Beta) timing w/o currencies, and 5.4% (.8 Beta) with currencies. Note that the levered returns are 16.1% (12% stdev) for the TAA, 15.6% (9.4% stdev) for the timing w/o currencies, and 14.3% (8.1% stdev) with currencies. Using even more leverage (1.5x), would give an even larger return for the timing model with roughly the volatility of the 2:1 TAA strategy.

Note that I did not use a momentum strategy, just the timing model. This means that there would be relatively small transaction costs, but you could not use futures contracts to implement it (except commodities and foreign indices). Nevertheless, it shows that there is significant evidence that this strategy has worked over a significant period of time with a variety of asset classes. I expected the returns to be different since I am using more equally weighted portfolios than cap-weighted as the indices are (within each it is cap, between each it is equal), but I was pleasantly surprised at how well it performed over the past 18 years or so (and 30 years) which gives further evidence that the momentum strategy for the component TAA strategy or a strategy like this with much less in trading costs.

Value Investing

I would recommend that anyone who thinks the markets are efficient should read this research.

Commodities and Countries Update

I added in the combined the j/k momentum model and the TAA model for the commodity and currency strategies I described yesterday(before it was only TAA, but I know follow the guidelines described in this post). The results confirmed the reasoning in yesterday's post. Commodities historically (tested since 83) do not have a very powerful momentum strategy. However, the j/k strategy with countries and the TAA model combined outperforms using the TAA model individually on each country. However, the TAA model generates very few signals and would be better for a longer-term investor. The j/k model (with j=4, k=2, and investing in the top 25%) with TAA overlay has a CAGR/Stdev of 2.18 (CAGR: 9.5%) compared to .99 (CAGR: 12.4%) for the EAFE TAA strategy. The EAFE without currencies in the TAA has a Sharpe of about 1 and 1.14 with them. Those increase to 1.07 and 1.23 (1.04 and 1.19 for yesterday's). However, regressing the new excess returns on the individual TAA excess returns does not generate significant alpha (annualized 26 bps), but the Beta is only .81. Unlike yesterday's strategy (ex-currencies), this strategy does have a significant alpha (at 10%) of 50 basis points relative to the original TAA strategy with a Beta of .78 (it improves to significant at 5% with 55 basis points with the currencies relative to TAA with currencies compared to 30 bps for the strategy yesterday).

* 50% decreases the Sharpe of the foreign strategy by themselves, but increases the Sharpe of the OVERALL strategy, I just wanted to be consistent with previous posts

addendum: I should note that the returns to this strategy are over a long period of time, particularly since the currency strategy benefits from high interest rates. The Sharpe ratios come down significantly over the past ten years compared to the past thirty years. Since the strategy has maintained a more constant growth path (ie not the early/mid 80s), the country strategy improves the Sharpe from .83 to .96 for the TAA strategy (individual country TAA is .93). However, the inclusion of the currency strategy has a smaller effect (I don't take into account the declining value of the dollar on any assets besides currencies, so this could be understated) increasing the Sharpe ratio by .04-.05. It seems that compared to the 50% momentum strategy over the past ten years, the EAFE has outperformed historically so that the momentum strategy is relatively constant, but the EAFE outperforms. (.4 10 year Sharpe vs. .1 30 year) in the past few years. I'm not sure how long the EAFE will continue to outperform, but I would prefer the less volatile Sharpe ratio. Right now my thinking is that after taking into account the depreciation of all of these assets in dollar terms, the best cash strategy would be the currency strategy, but I'm not sure yet.

Not impressed with JPM

JPMorgan put out earnings before the open today. It opened up 4% and despite the initial squeeze, it is up about 1% from that point as this statement is being written (9:55). JPM has traded from a low of around 37 to around 47 since November so a two dollar move in this range (after getting beaten down the past week) isn't all that impressive. Even though it is roughly at the average price since November, I still am unimpressed by results that "beat estimates."

Of course Wall Street cares more about coming in line with estimates than actual figures (EPS down 50% yoy, 20% qoq, "could have been worse, buy"). However, if you actually look at the 8-K instead of looking at the headline number, you would notice that JPMorgan made about a billion dollars on the Visa deal. The Corporate/PE division had 1.027 billion in net income which is actually 72 if you subtract out the Visa deal. I don't expect them to make any one-time deals with this much profit over the next year so I would guess that the next earnings will come out much lower than this quarter's. I would expect the remaining quarters to be closer to an average of last year's profit for this division and then a rosy estimate would be that the other divisions keep net income constant (or growing/declining at the rates from Q4 to Q1, effectively flat overall). In this case, Net Income would be 600 million lower (assuming same level of credit losses which I really have no way to estimate, could be lower could be higher and would have a big effect on Net Income) or at 1.8 billion. That would put a crude estimate of EPS for next quarter at .50 or down about 25% qoq (or similarly for this quarter assuming the IBanking revenue was not above average and down 43% qoq from that perspective).

These are crude assumptions, but an exceptional one-time event like the largest IPO in history should not be the saving grace during the credit crunch. I care about earnings going forward.

Note: WFC actually does have a pretty good business model. Over 90% of their loans are prime. They're going to lose some money, but be in a much better position coming out of this crisis. All of their business segments showed declining yoy, but that will likely turn around better than other banks.

JPM is still up .75% from the open (10:20).

Commodities and Foreign Countries

Continuing on with my theme of finding ways to improve the TAA model (here, here, and here), I thought I would do some more research into a longer examination of a timing strategy, but breaking apart an index into its component parts. I don't use the momentum strategy described in my Component TAA, Part II post (noted above), but just the normal timing model after breaking apart the EAFE and GSCI into their components. The strategy is to go long the components above the 10 month SMA and be in cash otherwise, just like Mr. Faber's TAA strategy.

I'll start with the GSCI. I used data available from the Global Financial Database on Commodities futures since 1983 (except Natty Gas which is since 1990). Unfortunately, they didn't have all of the energy contracts and were missing a few of the other contracts. I kept each commodity subgroup (livestock, ag, energy, ind. metals, precious metals) the same weight and scaled up the components. I confirmed that this index has about a 94% correlation with the GSCI. I was a little disappointed with this figure (preferring higher than 97.5%), but I will make due with what I have. I tested just performing the timing on the sectors (since 91) and on the individual components (since 83). One thing is very clear, the GSCI is dominated by energy you cannot compare an equally weighted TAA strategy with the market-weighted portfolio in GSCI. If you compare the strategies, use weights close to GSCI.

With sectors and a buy and hold strategy, my returns are initially different than the GSCI, so I don't expect the best comparison for the timing, but with 94% correlation, I would expect similar trends. However, I found that the return/sd ratio increased for the GSCI strategy, but not the component strategy. Variance decreased, but returns decreased as well and the effect was not economically significant. On the other hand, the returns to the GSCI strategy are enhanced considerably. The returns and correlations are roughly the same if you break it down into all of the contracts weighted by what is in GSCI. I wouldn't be surprised if some of this result is due to the fact that many of these commodities contracts show considerable seasonal variation that cannot be reduced easily by using the 200 day MA the way that an equity indices returns are improved (they lack the seasonal variations) and that the aggregate figure trends better. A more complex strategy, such as taking advantage of contango or backwardation, might be more appropriate for the components of the GSCI. There are other indices that I could use to test this method since I didn't have all the contracts (I will use the CRB indices except energy which I will have to recreate).

Countries, on the other hand, do trend well and the timing strategy works very well on them. I used total return data and replicated the EAFE index since 1994 with a 99% correlation. Before that time period, I replaced the FTSE-100 with the All-Shares index and some other total return indices are used that don't have futures contracts for them.

(begin digression: I had to use alternative indices for some countries that didn't have total return indices for the whole period, however, the question is how the strategy improves on this Buy and Hold strategy and not necessarily on the EAFE. If it improves returns over a long period of time, you could reasonably assume that it would continue to outperform in the future with futures contracts available and that the returns that you have are highly correlated with what you would have had with futures contracts. The returns are probably slightly better since the indices used are all-share instead of focused, but you would also expect the variance to be higher, it is equivalent to using the Wilshire 5000 instead of S&P500: end digression).

I also didn't use all of the indices in the EAFE since some of them have very small weights and the countries don't have actively traded futures. The top 12 or so are good enough. In general the equal weighted strategy outperforms the EAFE weights (due to the 25% weight on Japan). The difference isn't large enough to concern ourselves about over the long-term (1.26 CAGR/STD vs. 1.25). Over the long-term, the buy and hold returns were different between the EAFE and weighing the individual components (since there are times when I don't have France or Singapore's total return indices), but again the comparison I want to make is between the trends and not the absolute levels. From 1970 to February of this year, the Buy and Hold for the EAFE had a CAGR/std ratio of .715 (CAGR=11.7%) and the component strategy was .82 (CAGR=13.1%). Overlaying the timing strategy increased the Sharpe ratio on the EAFE to .99 (CAGR=12.4%) and the component to 1.25 while increasing the return to 13.6%. Since 1988 (when I have data on France), the spread between the strategies has stayed strong although overall returns aren't as strong. The Buy and Hold on EAFE went from .43 to .64 and with the component strategy it went from .62 to .95.

The 6% Sharpe ratio of the original TAA strategy was about 1.0 (12.4% CAGR) since April of 1980 and 1.14 (12.3% CAGR) with a currencies strategy. Replacing the EAFE increases the Sharpe to roughly 1.04 (12.5% CAGR) in the original and 1.18 (12.4% CAGR). The excess returns show an insignificant alpha over the original TAA strategy, but with the currency strategy included there is a significant alpha of 30 bps which reduces to about 25 bps when currencies have a 3x weight (Sharpe of 1.31 vs. 1.27 originally).

Also note that this is a timing model just like the one before. There isn't the excessive trading costs of a momentum strategy. You would be in each country about 60-75% of the time and frequently for years at a time. Someone with a large account could use this strategy to help reduce risk while keeping returns constant (meaning more leverage could be used).

The Simon Hypothesis and Investing

I try to attend the weekly NYU Colloquium on Market Processes when the market is relatively boring (it was after the business with PBR). This week I learned of something called the Simon Hypothesis (named after the Nobel Prize winning economist). It is stated thus, "Human beings, viewed as behaving systems, are quite simple. The apparent complexity of our behavior over time is largely a reflection of the environment we find ourselves in." He comes to the hypothesis by describing an ant needs to arrive to a destination. Does the ant go straight to the destination? No, it lives in a complex environment of ups, downs, and possibly dangerous run-ins with birds. The ants system could be as simple as see block, go left (or see bird, hide). The ant's path is complex not because the ant is complex, but because the environment the ant finds itself is complex. The hypothesis is asking if there is any way to predict which way the ant will take on a second journey?

That is an empirical question, but I think most people's first hunches would be that it would be impossible to predict. I would argue that this much is true for many walks of life, particularly investing. We might know the ant's final destination ahead of time (or the subprime crisis, or the internet bubble to burst), but how we get to that conclusion would be different every time. So while a backtested strategy might look sound on paper, ultimately, there is no way to tell if the path which reached a destination in the past will reach the destination in the future. The most important aspect of long-term investing is thinking about why the fundamental economic reasons why the strategy should earn abnormal returns in the future (if you can't think of any good ones, put your money in index funds and T-Bills). In the TAA case, I believe it takes advantage of the boom/busts inherent in markets (with central banks). A deep value investor or distressed debt investor survives through their entrepreneurial foresight (much more important to the Austrians than the neoclassicals which could be one reason why they don't teach value investing with a tenth the attention payed to CAPM), and so forth.

I guess the key insight is that you need to be flexible. You're not sure where the path can take you, so you should always try to find the shortest route when you can. You're never sure what surprises can force you to take twice as long a route, but in markets like this, it isn't hard (WB, BSC,ABK, WM,etc).

Currency Strategies

Just to note: compared to the previous post, this post looks into currencies with proper data and more importantly, accounts for interest rates.

There are four main sources of currency beta: value, momentum, carry, and volatility. Value is described as the PPP strategy, taking advantage of relative differences in long-term reversals to the mean of currencies with overvalued or undervalued currencies (on the basis on inflation and interest rates). Momentum is a trend-following strategy. Carry is investing in high interest rate countries and borrowing in low interest rate countries. A volatility strategy uses options on currencies and would be more exotic than a retail investor would want to use (and is most likely used to take into account exotic strategies a hedge fund manager uses and show that they are most likely just long/short volatility).

Well, I have been interesting in including the Beta of currencies in tactical asset allocation portfolios (see here for original post) and I wanted to experiment with these strategies. I generally am skeptical of the mean-reversion strategy since I've seen the charts of countries deviating from PPP estimates for decades. It's too hard to compare a basket of consumption goods between the countries to measure PPP accurately enough for me to be confident enough to invest using it. Volatility would also be too difficult to test and I've never traded currency options. It might be something to add in the future, but I'm guessing that strategy is too volatile for me...

So I set my eyes on the carry and momentum strategies. The carry strategy is particularly interesting to me since there already is an ETF which does that for you. DBV goes long the highest yielding currencies and short the lowest yielding ones to profit from the spread of the interest rates so long as exchange rates do not move very far. I replicated the strategy using all of the currencies that the ETF uses (and before the Euro I used France and Germany) going back to 1980 (when I could get decent interest rate data for some of the smaller countries). I replicated the DBV strategy as best as I could, except that I had to use some alternative interest rate data with longer histories instead of Libor (and then I continued to use that instead of switching to the country's interbank rates after the interbank data becomes available). I got a 95% correlation with the DBV since it has been in existence with a 10% return with a 7.8% standard deviation since 2000 (however, they report a cumulative return of 518% (14.67% annualized) since inception and I only showed 354% (8.5%), not sure how they account for the Euro, this could be the reason why). It's not perfect, but it's good enough (mine is crude since it may not always be market neutral b/c I'm lazy and don't plan to use it to invest with)

Taking the strategy further back (to 1980), there was a smaller return 6.3% (with 9% std) which could be attributable to wider (or more volatile) interest rate spreads during the 1980s which converged to roughly .4% in recent years. Ultimately the strategy has a very low correlation with the timing strategy that's been developed here and at WorldBeta and with the momentum strategy I will detail below. Also, based on my crude analysis, applying a 10 month moving average to this strategy increases the return:risk ratio from .694 to 1.15 (without including the benefit of being in CP when not using it it is .89). This strategy increases the correlation of the carry trade with both the initial TAA model and the momentum strategy. The increased correlation with the momentum strategy is due to the large influence of currency movements on the carry trade. Interestingly enough, the worst declines in this strategy have been when the market in general goes down (like in 1987 and 1998). However, the momentum strategy does not have the same volatility or exposure to what happens in the equity markets.

The momentum strategy is basically the same as the TAA strategy. I bought currencies above their 10 month MA and stayed in dollars when not in a foreign currency. However, due to the nature of the currency markets, except by hedging, you can never really have no exposure. If I bought euros and converted them to dollars, I'm effectively taking a position in dollars even though it is my home currency. The benefit of this strategy is that I'm always receiving an interest rate, it is either the dollar interest rate or a foreign one, and unless I lever this strategy, I don't necessarily have to borrow in any of them (unlike the carry trade). Anyway, this strategy has a return of about 11.4% with a standard deviation of about 6.6% with practically no correlation to the timing strategy.

Based on the returns and correlations of the two currency strategies, (and between only these two), I originally thought I should allocate about 70-80% of the currency strategy to the carry trade since that is where the Sharpe ratio is greatest for those two strategies. However, that isn't what happens in the context of the entire portfolio. Since the carry trade has greater correlation with the components of the timing model, the Sharpe ratio in an equally weighted TAA portfolio including currencies is maximized when the carry trade has no weight in the currency strategy. Giving this strategy equal weight in the TAA strategy* since April of 1980 would have decreased returns from 12.4% (with std of 6.42%) to 12.3% (with std of 5.5%) and increased the Sharpe ratio from about 1 to 1.14. Giving the currencies double or triple weight would increase the Sharpe ratio further. Even a triple weight on the currency momentum strategy will only reduce the returns by about 20 basis points historically and drops the standard deviation down below 5. Not sure yet the effect on leveraged portfolios, but that is my next step.

Since it was effective to include currencies in the TAA strategy and it is essentially a way to invest in cash, I wondered if it should it be included as the default cash strategy (eg. when the TAA model goes to cash, should it invest in currencies instead)?

Well, that answer is no. Despite the fact that the model outperforms cash with little correlation to TAA, it still will go with the market in the worst periods when the TAA strategy in general should be in cash. However, the cash returns (esp. standard deviation) do not take into account the depreciation of the dollar. All in all, it would probably be a wash and better to just keep the strategy separate, but it might be interesting to test after including the effect of depreciation (and volatility!) of the dollar.

* To be clear, what is tested is using the 10 month strategy on the countries and then investing in that as BH strategy itself. Additionally applying the 10 month strategy to the currency strategy does improve returns and Sharpe ratios for the currency strategy, but does not improve the Sharpe ratio for the overall strategy for some reason. I tested this as an afterthought, but I never wanted to test that as an original strategy, the 10 month MA is already applied individually and it makes little sense to complicate things further, IMO.

Checking your assumptions

Let's say you develop two investment strategies. One is based on tried and true methods and the other is new and innovative. If you discover that you can maximize your excess return:risk by allocating a large portion of your portfolio to the new strategy, check your assumptions.

I've been researching strategies for currencies and adding them to the Tactical Asset Allocation strategy (here). This strategy is already very successful so I was surprised to find out how good a simple currency momentum strategy was when added to the portfolio. I didn't realize at first how important it was to check the assumptions regarding the data. I downloaded the data from the St. Louis Fred website and it was monthly data, I assumed it would be fine. The problem was that the data isn't end of the month data, it is the average of a month's daily data. This is a good thing for running regressions with exchange rates or using them to adjust accounting information, but it's not good for trading strategies. Even creating new month time series with the end of the month or middle of the month dates will dramatically underperform the average series (Global Financial Database has the numbers based on end of month which I will be using in the future). You can only know the average rate for the month at the end of the month so by assuming you get out at the average rate you're assuming that you know the entire month's returns sometime that is not the end of the month.

I originally performed this research by looking at several different currencies until I realized what I did wrong, but it is easier to illustrate with one currency.

Just to illustrate how far off it is, using the strategy (L/S 2 period MA timing) on the Pound going back to 72 (including interest rates), will give a return of about 15.6% (8.1% std) on the average of the month data, 9.64% (10.3% std) on the end of the month data, and 12.4% (9.7% std) on the middle of the month data. The best thing about the strategy is that it has virtually 0 correlation with the TAA model (why it deserves such a huge weight in it originally) using any of the datapoints. That alone leads me to believe that currencies should have a position in a well-diversified portfolio. With the British pound strategy as a proxy for how well the complete momentum (it isn't, but I suspect that strategy will be better), the Sharpe ratio will be increasing with a positive weight on the currency strategy until about 40% (for the middle of month, 25% for end of month). I'm comparing it with the basic TAA model with equal weights on the remaining assets. I can only guess that the well-diversified currency strategy will perform even better and should receive a larger allocation.

To test this without compiling all of the interest rate data and combining everything (next project: recreate the carry trade) I tested a j=4, k=2 momentum strategy on the currency ETFs that are available since September of 2006. This is a very short time frame when all of these ETFs performed very well, but it would represent at least the long-side of the strategy accurately. The strategy would be in either two or three currency ETFs and has a CAGR of 13.8% with a 5.6% standard deviation. I would reiterate again that this is a period of a massive decline in the dollar and it is not expected that this kind of risk:return ratio would continue in the future (the return is expected more than the risk). Over this time period, the strategy (absolute returns) has a correlation with the TAA model of 19%. 19% isn't 0, but it still should be important enough to add to the portfolio after completing a more rigorous long-term examination of the strategy.

Tactical Margin Overlay

I recently posted to try to improve on my probit model by tactically adjusting margin, but it appears that there was an error in my calculation and the results are not as good as I had posted.

However, if you fade my previous results, that will tend to be have a stronger Sharpe ratio. In other words, my previous results were that you could increase your Sharpe ratio by increasing leverage when the model is in more assets. The new results are that you can increase the Sharpe ratio relative to what you would have had otherwise by increasing leverage when you're supposed to be in few assets. In the original results, the risk-parity portfolio underperformed since you were using more leverage on assets like bonds, but in this case the risk-parity portfolio performs much better. The 50% margin portfolio that uses 0 leverage when in 4 or 5 asset classes and 100% leverage in 1 or 2 asset classes has a .0364 better Sharpe ratio in the risk parity portfolio (.012 for equal weighting). Some of the cost of leverage can be made up, but the excellent returns I originally posted are not the case. Unless I combine the probit model with this model and the results are impressive, I would prefer to stick with the original model without leverage rather than these.

Momentum Average and TAA

Damian in the comments asked if I could use the average of four returns: the 1 month, 3 month, 6 month, and 12 month to rank the components of the momentum strategy from the previous post.

The results were as I expected. The momentum strategy isn't that good more than six months out and averaging the good Sharpe strategy with the bad Sharpe strategy really doesn't improve the returns. Intermediate trends are strong enough for ETFs that that should be the focus. I was able to improve on his idea by changing it to an average of 1 month, 3 month, and 4 month returns and the 1 month and 4 month are an improvement still above the momentum average. They still don't outperform the j=4, k=2 model in backtests, but they could outperform other models and there's no reason why it can't outperform in the future. The two bottom strategies at least relieve some of the burden on the 4 month.


I should also note that I am continually refining these strategies including the calculation of interest, margin, and the risk parity weights. I'll always post a comparison to a base model whenever it is different from anything posted in the past. The difference in returns from this model to the original reflects better accounting of interest returns. I also took out the previous inclusion of the style ETFs. Sector momentum has previously been far more important than style momentum and I expect that to continue in the future.