Beta and Sectors

I meant to post something about the interest rate environment and tactical asset allocation, but I haven't gotten around to it since the results aren't that spectacular. Still kind of interesting. Anyway, I've been reading Eric Falkenstein lately over at the Falkenblog and his website DefProb.

One point that he makes is that historically buying low Beta stocks has better returns than buying high Beta stocks (though there are periods of significant underperformance such as the internet bubble). I found this result interesting (risk is inversely related to returns, how could that not be interesting?) and so decided to look into a similar strategy using sectors.

I used weekly dividend adjusted data of the 9 Sector Spiders since they began at the end of '98 along with SPY. I calculated Beta vs. SPY using at least a year's worth of data and no more than 5 years worth of data. At the start of every year I ranked the Sectors on the basis of Beta and formed a high Beta and low Beta portfolio with three Sectors each. I also calculated a portfolio investing equally in each Spider to serve as comparison (SPY is market-weighted).

Over this period (from Jan. 2000 to the end of last week), the equal-weight portfolio return 2.4% annually (15.7% std), the high beta portfolio returned -.14% (20.7 std), and the low beta portfolio returned 4.3% (14.3% std).

I then calculated the 40 week (200 day) moving average and considered a signal at the beginning of the month good through the end of the month (since that is how the 10 month TAA works and I wanted it to be somewhat comparable). The results are reported below:
(After accidentally inflating the returns of the high portfolio) The results indicate that the low Beta portfolio outperforms when the market is above the 40 week moving average and slightly outperforms when the market is below the 40 week moving average which confirms the argument that Mr. Falkenstein had made (note that the Sharpe ratio is higher for the high than the low in the below 40 week, I think that the Sharpe ratio is an incorrect method of comparison when returns are below 0). That doesn't change the fact that investing when below the 200 day moving average is very risky.

CFO advisory posted yesterday regarding the sector momentum strategy (which I have covered before on this site) and noted that a significant portion of the return has been due to XLE. The low Beta portfolio included XLE from 2000 to the beginning of 2007; however, from 2007 until recently XLE return 35% annualized compared to 11% from 2000 to 2007. So I would argue that the performance of the low Beta portfolio doesn't suffer from the XLE criticism (note that I really agree with it anyhow).

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.

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.

Component Tactical Asset Allocation: Part 3

This is the final of three posts on Tactical Asset Allocation. Part 1. Part 2.

The subject of this post is the theory of the market process and tactical asset allocation and why I believe that the former implies the latter will be a more successful strategy than buying and holding index funds.

The fundamental implication of the Efficient Markets hypothesis is that if information will be quickly incorporated in security prices. Mathematically this implies that stocks follow a random walk with jumps when new is absorbed by the market. Based on this assumption, the ideal investment strategy under the Capital Asset Pricing Model is to hold the market portfolio for the long-term (I know I’m ignoring Treynor-Black).

Beyond the typical objections to EMH, there are two main insights from the market process school that leads me to reject the EMH and I believe they are the most important observations of the school.

First, there are significant government interventions that make the market remarkably inefficient. The most important is the business cycle and monetary problems that in the 20^th century has almost always been caused by central banking. The standard Mises-Hayek theory of the business cycle is that by pushing the interest rates lower than the natural rate of interest, a central bank encourages investment beyond what would happen in the free market. Eventually the investment works its way into a boom for the producers of consumers’ goods and prices begin to increase. In order to stop the boom (to prevent runaway inflation), the central bank must raise rates. This action ends the boom and the process to correct the malinvestments made in the boom period. Since capital intensive industries are more exposed to interest rates, they typically feel more pain than consumers’ goods industries.

Moreover, governments intervene in other ways that are frequently not understood well enough by investors or they don’t always understand the implications. Economics is not a terribly difficult discipline and figuring out the implications of dumb government policies isn’t that difficult. If the government subsidizes ethanol production, farmers will use less land for the production of the typical agricultural products and those prices will have to rise. If there is a war in the Middle East, it is likely that oil (unless they have refineries in the country in question) and defense stocks will typically increase in value. Investors react in the short-term, but over the course of 6 months to a year or longer, these plays are still profitable. I’m not sure whether it is the uncertainty of these situations or that investors systemically do not think the government is as bad as it is (possible given the state of business school economics courses, also it is very difficult to quantitatively test), but investors do not react strongly enough.

Second, the market process school emphasizes the role of the entrepreneur in moving the market to equilibrium prices. EMH doesn’t care about why prices behave in certain ways, it merely attempts to model them. However, what is seen as a random walk are actually deliberate actions taken by entrepreneurs engaging in speculation and arbitrage. Entrepreneurs who have greater foresight will outperform those who don’t. Furthermore, the investing, particularly derivatives, are referred to as zero-sum games. The profits are zero-sum; however, ex ante, all of these trades are positive sum in terms of utility. These trades show ex post profits or losses depending on the skill in forecasting of the entrepreneur.

Finally, as Hayek notes, there’s no such thing as perfect knowledge, as is assumed by the actors in CAPM. Knowledge is dispersed throughout society and the purpose of the market is to organize that knowledge. Market prices reflect the knowledge of all market participants.

Combined these three factors make tactical asset allocation an attractive prospect. Since there are cycles that can be observed by students of the Austrian School, it makes little sense to buy and hold equities when there are lengthy periods of time where you can lose a significant sum of money. Also, not only is there a purpose to being an entrepreneur which is ignored in the EMH, but paying attention to what happens to prices can reveal knowledge about other market participants’ knowledge and opinions in the market. Michael Covel notes in his book about trend following that trend followers tend not to be in the business of predicting trends, they have imperfect knowledge and as a group they have no opinions on the market. However, if the market is going up, they would be more than happy to buy and vice versa to sell. The logic is essentially the same for TAA. Mr. Faber isn’t providing a service in predicting the market, he’s trying to improve on the buy and hold passive strategy by staying out of the market when market participants have a negative outlook. Nothing wrong with that.

Component Tactical Asset Allocation: Part 2

This is the continuation to the previous Component TAA: Part 1 post.

First I will present the results with a single momentum strategy comparing the AA, TAA, and Momentum TAA strategies with 0 leverage and with 2-1 leverage. Then, I will present alternate momentum strategies using different js and ks, but investing in a constant number of ETFs followed by a constant j and k with a different % of ETFs available. I will conclude with work in progress to improve it further. I might add an additional post describing why the economist in me prefers Tactical Asset Allocation as an investment philosophy to the Efficient Markets Hypothesis and the Capital Asset Pricing Model.

Before I begin, I should note that the Domestic ETFs I invest in a separated into two groups, sector and style. Whichever one I can invest in earlier (sector), I will use that return and then later, I average the two's returns. I might get a better return without doing this, but that particular market is so broad that I wanted to investigate the combined effect. Not only do some sectors out perform, but sometimes value outperforms growth and large-cap outperforms small-cap. I wanted to be able to include this relationship as well, I'm just not sure how much stronger this effect is compared to the sectors. I also had a longer list of sectors that I cut down on prior to running these returns, so the ranking since I updated the data can actually choose from more sectors and gets better returns. I'm only reporting a sector basket with the 9 Spider select ETFs.

The first table represents a unlevered comparison of the AA, TAA, and Momentum TAA (with j=4 and k=2 investing in the ETFs ranking in the top 25%) with equal asset allocation between the 5 asset classes and the Risk Parity weights discussed in the previous part. The TAA beats the AA which is the conclusion reached by Faber. However, the Sharpe Ratio (@ 6% for all) increases with a more normal kurtosis (3=normal, greater than 3 indicates fat tails) by using the risk parity weights. There are similar results comparing the TAA and Momentum TAA, however it seems like the Kurosis for the TAA portfolio is relatively constant. This makes sense since the data is cut off prior to 1998 and excludes some of the larger price movements.


The next table is the same strategies and comparison as above, but with 100% leverage. It is more for general interest than comparison. The method used in the paper by Panagora was to use the Risk Parity weight and then lever the portfolio to a desired return (such as the S&P500's average return) so that variance would be minimized. In this case, the return on the TAA without Risk Parity Weights would be greater than the standard deviation on something like the S&P500. You could use roughly 20% leverage to increase the return of the TAA Risk Parity to roughly the return on the normal TAA (this same argument works to target the standard deviation as well). However, the Sharpe ratio in this case would be less than if you had not used leveraged. The return is the same, but the variance is actually greater (the same holds true for AA, TAA, and Momentum TAA). So even without the large 2-1 leverage reported below, if you measure your investment success by your Sharpe ratio, then it won't make sense to use leverage. However, relatively speaking, the risk parity weights outperform the equal weighted portfolio. If you're an investor seeking to maximize profit or would be willing to accept more risk in exchange, then you should use the risk parity instead of the equal weight portfolios.



The third table presents the CAGR, Standard Deviation, and Sharpe Ratio comparing different momentum strategies. Recall from the previous article that j represents the number of periods to look back to and k represents the number of periods to hold (since k can be greater than 1, then even if you hold 6 ETFs when k=1, it will be variable for k>1). Using more complete data, it is clear that the Sharpe Ratios increase as j comes to 3 or 4 and declines after that. However, there is no clear trend on what happens with k. It usually increases to 2 and declines after that, but it is not consistent. If at all possible, I would prefer a larger k to a smaller k since it guarantees that I will have less turnover.



Finally, the last table shows the returns with j=4 and k=2, but investing in a different percentage of the ETFs that have sufficient return histories. The trend in this case is clear, return increases as you increase the percentage until it tops out between 25 and 33.3%. However, these returns are all gross and the others could relatively increase if transactions costs are included. Furthermore, I would suspect the tax consequences are greater. Instead of picking the best sectors, at 75% you're getting out of the worst. For portfolios with less than half a million dollars, there might be too many ETFs to be able to use the 75% or 50% to make it worth it. However, I should also note that the benefit of the original TAA model is that each position can be approximated with futures contracts which could possibly reduce costs and provide an easier method to use leverage.



To conclude, gross returns and gross Sharpe ratios are greater using the Momentum TAA with risk parity portfolios. However, there are still additional ways that it could be improved. This strategy can be considered a component in a larger overall strategy. For example, Mr. Faber discusses alternative strategies such as mean reversion and following hedge fund managers that produce significant returns. I think that there are strategies in options, distressed debt, value investing, macro investing, mean reversion, and statistical arbitrage (or investing in hedge funds that specialize in stat, risk, or convertible arb) that can add to this return while not being correlated with the TAA or Momentum TAA. Unfortunately, with the exception of mean reversion, these strategies are either not quantitative (macro, distressed debt, value) or are difficult to backtest (options - competence, and arbitrage are arbitraged away).

Next, there are additional beta factors that can be considered or thought about in different ways. For example, a recent paper indicates that the returns for currency managers are largely Beta. Those returns could be an additional asset class that could be added with little correlation to the others. Also, there is evidence that investing in commodities based on their term structure (buy most backwardated positive roll-return commodities, short most negative roll-return contango commodities). These two strategies, combined with mean reversion of the five assets used in TAA and the Momentum TAA risk parity weights, could be particularly strong and they could be included in a broader portfolio using the risk parity weights.

Finally, I recently discussed a probit model I use to forecast recessions. I am considering linking that model (and augh converting it to Matlab) to this program so that I choose margin based on the probability of a recession. The returns of this strategy outperform the S&P500 during the bad times, but they still underperform compared to the remainder of the period. I'm going to consider increasing leverage when the probability estimates are low and cut off leverage when the probability begins to increase. I believe this can improve returns.

edit: There was a slight discrepancy with the interest rate data in the original results that has been corrected.

On to Part 3.

Component Tactical Asset Allocation: Part 1

Mebane Faber published an article in the Journal of Wealth Management in the Spring of 2007 called a Quantitative Approach to Tactical Asset Allocation. The thrust of the paper is that if you invest in U.S. stocks, foreign stocks, bonds, commodities, and REITs when they are above their respective 200 day moving averages and invest in commercial paper otherwise, you can achieve returns similar to equity investments with significantly lower volatility. Mr. Faber has graciously provided the monthly returns from the strategy as well as much more information on his website, World Beta. Based on the data on the website (more up to date than the original paper), the timing model returned 12% since 1972 with a standard deviation of 6.43% (.93 Sharpe) compared to an 11.5% return on the buy and hold asset allocation strategy (20% in each asset mentioned above) with a 9.78% standard deviation (.56 Sharpe). I programmed his strategy into Matlab using the same data and found similar results (slightly different due to the vagaries of Matlab rounding and computing returns statistics based on monthly data instead of yearly data).

Lately I have been interested in how to improve on this concept. First, I would like to discuss two additions I made and I will make an additional post to discuss the results of what I tested.

On his blog, Mr. Faber compares different methods that readers have requested to improve the returns (that he doesn't use). The first is to enter long positions above the 200 day MA and short positions below while the second is to enter each position "all in," equally weighted for each buy signal, no positions in cash . Each of these methods fails to improve the Sharpe ratio. I expect the L/S portfolio fails due to the fact on that most of the top 50 best and worst days are when the market is below the 200 day moving average. It is possible to profit by shorting the worst, but you can get burned on the best.

I believe the "all in" portfolio fails by ignoring the correlations between the assets (and would require more re-balancing costs than the traditional TAA). In order to test this, I followed a white paper by Panagora Research which describes the Risk Parity Portfolio. Their concept is to adjust the weights of a portfolio so that the amount you can risk on each position is equal. The traditional method to do this is to estimate the Value at Risk for a portfolio and break it into the component parts for each security. This method takes into account the correlations among each asset and the Beta. As a technical concern, I waited a year to create the Risk Parity weights (but used the initial 20% allocation during that period to make comparisons to Faber's paper) and brute forced the first weights using the covariance matrix and existed at the time of investment decisions and only changed the weights if the Component Value at Risk of an individual asset went outside predefined bounds. The weights stay relatively constant over time, but I could have created tighter bounds where they would change more often. As of the time of writing, bonds would have 34.8% weight, REITs 15.9%, Commodities 19.3%, Domestic Stocks 15.1%, Foreign Stocks 14.9%. In other words, REITs and Stocks would have their shares reduced and bonds would increase their weights in order to take into account the fact that they are more strongly correlated with each other than Commodities and Bonds and have higher variances. Based on the research provided by Panagora, I expected a slightly lower return, but a substantially reduced standard deviation.

The other method I used was investigating the j-k Momentum strategy proposed by Jegadeesh and Titman. In this paper, J and T investigate ranking stocks based on their returns from j periods ago and holding them for k periods forward. They used this model to show that stocks have a momentum factor like a size or value factor that helps determine their future returns. Within the context of the TAA model, I chose to test this strategy by choosing a proportion of the ETFs for an asset class and then applying the j, k methodology to a proportion of the ETFs with returns. I waited until a certain proportion of the total ETFs (in each classand that I considered representative of the asset class) began to trade to start the momentum strategy for that asset class. I will only report (and compare) the returns since the earliest strategy began to take effect (Select Spiders began trading in December of 1998, but it requires j months before the strategy can work). Since they have uneven start times, I used the returns from the normal TAA strategy when the Momentum strategy cannot work. I should emphasize that I am not using only a Momentum strategy on ETFs, but investing in a j-k Momentum strategy based on a TAA model. Within each Momentum category, the ETFs are equally weighted and I don't think it makes sense to use Risk Parity Portfolios in this context.

Furthermore, if I am not mistaken, Mr. Faber uses a method similar to this in actual practice, however, he does not report his results using this method. The most obvious reason is that he created his model in Excel which is substantially more cumbersome the model gets more complex. Also, ETFs have a short history that may not be indicative of the 35 years of returns where the TAA model has shown considerable strength. There's also no doubt that using ETFs in this strategy would require more trading costs and more taxes (unless in a tax-free account). Even if this strategy is not successful (it is), it is at least interesting to investigate and note the return characteristics for different levels of j and k.

The next post will compare the Equal Allocation (no TAA) model to the TAA and their Risk Parity equivalent portfolios, it will compare the TAA models with the Momentum TAA models (equal allocation and risk weighted), and some discussion about future additions I plan on testing.

On to Part 2.