Saturday, April 30, 2011

Hedge: Another Try

Previously I discussed the unexpected behavior of the bottom 20 stocks by fundamental ranking that resulted an unsuccessful hedge strategy. Later on I found that stocks only within the bottom 50 has such unexpected behavior. The finding encouraged me to device a new hedge strategy with stocks that ranked bottom 51 through 70. Hopefully with the bottom 50 (those ill-behaved stocks) removed, I could see some improvement.

The result is charted below. I do see some improvement, but there are things I don't like:
  • The maximum drawdown is reduced, but not by much. Originally it's about 60%, after it's about 50%.
  • The hedged portfolio shows higher volatility than the original one. Such as July, 2009 to September, 2009, and January, 2010 to May, 2010.
I may not choose this strategy, either.

ETF Ranking: Related Research

I was browsing on the web for related research on ETF ranking. My first impression is that this topic is overly crowded. Just look at how many Google ads associated to the keyword when you Google "ETF ranking".

Then I noticed that my blog post "ETF Ranking, Sector Rotation, And Business Cycle" is at the 6th place on Google. Not bad considering I've started this blog only a month ago.

OK, this is not the purpose of this post. The purpose is to give an overview on others' research on ETF ranking.

First, something about fundamental ranking.

Fluent investors may have noticed the similarity of my fundamental ranking system and Greenblatt’s magic formula. Although I didn’t know about magic formula when I started to work on my ranking system, I do agree with Greenblatt in many fronts. He suggests using magic formula on large groups of stocks, that’s why I settled with ETF ranking. He also commented that once applied to large groups of stocks, any differences between the various return on capital formulas will not have much effect on the performance. I'd like to use this as an excuse of not revealing my formulas.

Now on ETF ranking. It appears that many companies provide ETF ranking as a financial service to investors. Enumerating all service providers is not my purpose. I just try to enumerate all different approaches, and pick one representative website for each approach. And by no means the list is complete. I stopped at about page 4 on Google.

A little bit brag first: although there are many different approaches, none of them provides data to show the relation of their ranking system and short term return, at least I didn't see any public data. It appears that my ETF ranking is the only one that is designed for short term return and has data to show the strong statistical relation between ranks and short term return.

Enough for bragging.
  1. XTF’s structural integrity. ETFs are ranked based on (a) Tracking error, (b) Efficiency: daily alpha before expenses, (c) Market Impact, (d) Concentration Risk, (e) Tax Efficiency: Capital Gains, (f) Expense Ratio, and (g) Bid-Ask Ratio. No doubt all of them are important for institutional investors. But by no means this is a fundamental based ranking and I'm certain there is less likely to be any relation to short term return.
  2. Admittedly their idea is similar with mine. They first rank stocks in the ETF's portfolio by their risk and reward, and then sum up to the rank of the ETF. Although I don't have additional information, my guess is the risk and reward should have at least some fundamental flavor. And the sum-of-parts approach is the same with mine. Nonetheless, there is no data show the relation to short term return.
  3. Value line. An introduction is here. This is by far the closest one to mine. It is value based, which has to be fundamental. And it is sum-of-parts. However, their ranking system is designed for 6 months to 12 months holding, while mine is for 1 week rebalance. The introduction did say they have one year data to show the performance, though.
  4. Sabrient’s SectorCast model. The rank consists of two parts: fundamental data and analyst's projection of company's future performance, such as forward P/E. The idea sounds brilliant, but I'd like to question the soundness of using analyst's projection. More often than not, analysts are just chasing public opinions. The performance data is not persuading. Actually the best ranked ETFs generated negative return while the market is rallying. Due to this, their model is evolving constantly. The risk is that they are just tweaking the model to fit the curve.
  5. Ranks based on past 3 months or 6 months' performance. Such as The information is good for momentum or trend trader. Both are mysterious and certainly not based on fundamentals.
  6. Ranks based on technicals such as 20 day moving average and 50 day moving average from This is another way to express trend, and certainly not based on fundamentals.
  7. Ranks based on number of new highs and new lows of constitutes from Yet another way to describe the technical strength, and certainy not based on fundamentals.

Wednesday, April 27, 2011

Short Low Rank ETF Still Good Hedge

I spent a little bit more time to dig into the problem whether shorting lower ranked stocks or ETFs is a good hedging strategy. The data I got yesterday are on the bottom 20 stocks. If you still remember what I have discussed in my post on effectiveness of fundamental ranking, you will know that those stocks' ranks are below 1. They are not good hedge because they are garbages, and when the market turns from bear to bull, the rising tide lifted garbages a lot faster than those boats, i.e., stocks with higher ranks. Miserably you will see the market rallying while your portfolio falling if you short the garbages as a hedge.

But currently the sector ETF with the lowest rank is XLF. Its rank is around 20 as discussed in my post on ETF ranking. The question is whether rank 20 behaves like garbages or boats. If it is like boats, it may still server as good hedge.

In my post on effectiveness of fundamental ranking, I only calculated the estimated annualized return of the upper half of the spectrum: from rank 100 to rank 50. Using the same method, I calculated the return of the lower half. The result is shown in the chart below. Unlike the upper half where the best curve fit is 1/x^4, the lower half's best least square fit is a straight line.

On the chart each point represents a group of 100 stocks. The lowest 100 stocks, rank 0 to 3, still behave like boats. They are the worst performing stocks in the spectrum. So the garbage is only the lowest 20 stocks? To answer this question, I calculated the return of the lowest 50, 20, 10, and 5 stocks.

The bottom 50's return is lower than that of bottom 100. But bottom 20 is a lot higher, and it go up steeply all the way to bottom 5. So really the garbages are the bottom 20. No wonder I see such a bad performance when hedging with them.

Some key take away:
  • The bottom 20 stocks behave like garbages, one should never touch them, no matter long or short.
  • The market neutral strategy mentioned in ETF ranking would still be a good strategy if the shorted ETF's rank is above 15.
  • One can short an ETF with low rank to hedge a portfolio with top k stocks, as long as the shorted ETF's rank is above 15. But that would be a little bit too complicated. In this case, short SPY may be a simpler hedge.
By the way, now you can subscribe to weekly ETF ranking update via email. You'll receive the highest ranked and lowest ranked offensive sector ETF every weekend. Go to the top right corner of my blog, enter your email address and click on "Subscribe". The "Subscribe" button will pop up a confirmation page hosted by, a free service provider. You will also receive a confirmation email from TinyLetter ( titled as "Confirm your subscription to Weekly Update On ETF Ranking". You need to click on the link within to confirm your subscription.

Tuesday, April 26, 2011

Not A Good Hedge

Investors and traders that ever thought about a mechanical trading system may be familiar with Sharpe ratio and maximum drawdown. Both measure the risk associated to a system. While I have not decided yet whether to device a mechanical system on top of my fundamental ranking system, this is an interesting topic and I'd like to waste some of my spare time. Calculating Sharpe ratio takes a little bit more effort. But maximum drawdown I can simply eyeball on the chart, which is roughly more than 60%. Admittedly one has to have a super strong stomach to trade such a system.

Hedging is a technique adopted by professional investors to manage risk. Naturally I'm thinking to short the bottom ranked k stocks all the time as a hedge. Those stocks are on the other extreme and should constantly move lower. So by shorting the bottom ranked stock maybe I'll earn extra returns. I pulled out the data of the bottom 20 stocks. As shown in the chart below, they generated a negative return in the past 10 years. Looks good so far.

But when putting together with the top 20 stocks, the overall return is not pretty. I scrutinized the data and find out the problem. Below is the chart of the top 20, the bottom 20, and the hedged portfolio between November, 2007, around the top of last bull market, and present. Bottom 20 moved down in lock steps with top 20 during the 2008 bear market, providing a good hedge to the portfolio and reducing the drawdown from over 60% to about 20% (in the bear market). It is good, but it comes at a price. During the 2009 sizzling rally, bottom 20 moved up a lot faster. A rising tide lifts all boats, and it also lift all garbages, and garbages got lift sooner than boats. Only until recently the bottom 20 slowed down a little bit, and the hedged portfolio is catching up. But still, if you didn't notice, the hedged portfolio is in the negative territory since November, 2007, while both top 20 and bottom 20 are up more than 60% from previous top.

I shall admit that the chart didn't tell the whole story. Bottom 20 started to move down in mid 2006. So from mid 2006 till end of 2007, the hedged portfolio gained extra return. But is it a good hedge? It depends on which one you'd prefer between a 60%+ maximum draw down; and a 40%+ maximum drawdown and watching the entire market rally but your own portfolio plunge. I'd choose neither.

Graham in his early years adopted similar strategy: longing undervalued and shorting overvalued. But later on he focused on only the long part. I think I know the reason now.

And by the way, in my ETF ranking post, I suggested to long the top ranked sector ETF and short bottom ranked one to stay market neutral. Now it looks not a brilliant idea. Yes you are "neutral", but if your portfolio is not moving anywhere, neutral is not a good word.

Monday, April 25, 2011

ETF Ranking, Sector Rotation, And Business Cycle

As discussed in previous posts on ETF Ranking and Sector Rank Spread, the fundamental ranks of sector ETFs measure the tendency of money flowing out of lower ranked sectors and into higher ranked sectors. Actually there is a term for this phenomena: Sector Rotation. During a business cycle, the underlying structural changes will drive certain sectors to outperform while others to under-perform. Different phases favor different sectors. I borrowed from MarketScalpel a chart that shows the sector rotation model. MarketScalpel did a good job of maintaining a list of various resources (even including an academic papers) on this topic. Read more here if you are interested.

If we put this chart side by side with the ETF ranking chart, we see XLE is the top ranked offensive sector and XLV is the top ranked defensive sector. Where are these two sectors locate in the business cycle? The late expansion phase. See below for the ETF ranking chart.

As their ranks are still high comparing to other sectors, we may still be in the beginning of this phase. But I would recommended to stay cautious as the next phase will be in recession. A contraction of the sector rank spread would be a flashing yellow light. Or if XLU, the sector that will outperform in the next phase --- the early recession phase, replaces XLV to be the top ranked defensive sector.

That said, the SRS still expanded a little bit last week. So maybe we still have a couple of months or even years to indulge ourselves.

Sunday, April 24, 2011

Stock Market A Voting Machine Even In The Long Run?

I'm reading Gannon's articles on and come across to his article "Book Review: Active Value Investing" and see he quoted Katsenelson saying:
...I wanted to see what would happen to the average P/E of each quintile if I bought each quintile in the beginning of the range-bound market (January 1966) and sold it at the end in December 1982...The highest-P/E quintile exhibited a P/E compression of 50.3 percent. The P/E of the average stock dropped from 29.3 in 1966 to 14.6 in 1982. That portfolio generated a total annual return of 8.6 percent. The lowest-P/E quintile to my surprise had a P/E expansion of 34.8 percent. Yes, you read it right. The P/E of the average stock in my lowest-P/E quintile actually went up from 11.8 to 15.8 throughout the range-bound market. That portfolio produced a nice bull market-like total annual return of 14.16 percent...
Interesting! Interesting! Interesting! The quote of Katsenelson on P/E sounds to me a lot like saying that the stock market is a voting machine even in the long run. To my shallow understanding, voting is about relative value, while weighing is about absolute value. Katsenelson simply said that low P/E relative to the market will expand over years. The number is 16 years here (1966 - 1982), which is fairly long enough to me as in the long run. Although I may not die in 16 years if I'm fairly lucky, considering my age :D. Of course low P/E may also imply low absolute value. But then it means that voting and weighing is not like black and white.

Introducing Sector Rank Spread

What is Sector Rank Spread? It is the maximum spread over the ranks of the offensive SPDR sector ETFs. For example, as of last week, the highest rank in the offensive SPDR sector ETFs is 69.86 of XLE, the lowest rank is 22.18 of XLF. Thus the Sector Rank Spread is 69.86 - 22.18 = 47.68. This week the highest is still XLE and the lowest is still XLF, but the spread increased a little bit to 47.83. Read more on ETF Ranking and Fundamental Ranking.

Where is SRS? It is located to the lower right corner on my blog. Unlike the Big Money Index, SRS is calculated and updated every weekend.

Why SRS? Economists use the velocity of money to measure the activeness of the economy. My understanding is that standing still money doesn't create any economic value, money create economic value whenever it flows. GDP, the economic barometer, is the sum of the dollar amount of trade, i.e., money flow among parties. Similarly in the stock market, money flow drives price appreciation and depreciation. Money flowing into an asset class will help to mark up the price of the asset class, and vice versa. The SRS is designed to gauge the tendency of money flow among offensive sectors. Sectors, represented here by the SPDR sector ETFs, with higher fundamental ranks offer better economic value, and thus attract more money flow. Therefore, the larger the SRS, the better the chance that money will flow out of the one sector (supposedly with lower rank) and into another sector (with higher rank). If the spread is minimal, money flow would stall. So SRS is another way to measure the money flow, and the activeness of the stock market. Intuitively, high SRS indicates the market can still move up, while low SRS may prelude consolidation or correction. That said, I don't have historical data to show how high is high and how low is low. This is a new indicator and I only have two data points. Let's watch it overtime to see how it evolves.

Saturday, April 23, 2011

Big Money Index In The Past Two Years

Below is the chart of the Big Money Index vs. S & P 500 in the past two years. Divergences are marked out on the chart.

Performance Review Of Fundamental Ranking

Last weekend I've picked some stocks from and published their fundamental ranks. Now it's time to review their 1 week performance. As shown in the chart below, there is clear tendency that higher ranked stocks outperform lower ranked ones, though the deviation is much larger than those ETFs as shown here. I wouldn't say anythings more. The number speaks for itself.

Friday, April 22, 2011

The Underlying Ideas Of Fundamental Ranking

Below are what I've said during the discussion with a value investor. It is about the underlying ideas of fundamental raking. This may help one to understand where it comes from.
I think although every individual should be objective when valuing a company, [...] the valuation is collectively subjective. It is collectively subjective because the market is a voting machine (in short term, of course). With this in mind, should a value investor always try to use the most popular ratio, i.e., P/E, when he [tries] to value a company? At least to start with?
[Using P/E is] not following the majority, [it is] taking advantage of it. [Value investor's] logic is fact = right = profit, and non-fact = wrong = loss. I'm OK with the first part, [the] part that fact = right and non-fact = wrong. But I just want to point out that more often than not, right <> profit and wrong <> loss.
The [fundamental ranking] system is not based on fact, it is based on behavior, i.e., it tries to chase what the market would think the most important and make profit in short period. So I think I couldn't afford to reveal the formulas, because behavior, not like fact, does evolve over time, and it does respond to [feedback].
[The idea of fundamental ranking is] from the opposite side [of value investors]. [It is designed for] a trader [...]. I spend time to study the structure and the behavior of the market. But then I learned that one couldn't make big profit by only knowing structure and behavior. The market has something else in its mind, and lately I start to realize it is "value". It may not be the true value in the mind of a successful value investor, but that would be OK. As long as the market chases it, it might be a good idea to chase it in short term. That's how I come up with this ranking system.
Revealing the formulas has at least three effects. [One is to invite verification.] The other two are: to invite followers, and to invite competitors. In some sense followers are competitors, but they have different functions. In the world of trading, followers help you to mark up the price, while competitors squeeze out your profit margin. I'd like to have followers but not competitors. So I think the best way to do is, for a specific company, [to reveal] only the formulas that is most important to value that company. Most brand name research firms are doing this. [...] But to reveal the whole package? It's too dangerous to me.

Thursday, April 21, 2011

ETF Ranking

There are two problems with the fundamental ranking system T-Rank 2.0 if one would like to use it as a mechanical trading system: liquidity and volatility. Liquidity is mainly discussed here, and volatility is touched, though lightly, here. I was struggling with them for a couple of days and didn't have any good solution that satisfies me. Then suddenly an idea popped up to me following the discussion with an value investor on something totally irrelevant (it was good discussion and it opened my eyes). I can rank and trade ETFs. The rank of an ETF is the weighted average of ranks of the stocks in its portfolio. ETF hit two birds with one stone: it is naturally diversified, thus less volatility; and it has much better liquidity.

My research tool doesn't support the calculation required by my ETF ranking method. So I couldn't do back test on this. I manually calculated the ranks of the 9 popular sector ETFs: XLB, XLE, XLF, XLI, XLK, XLP, XLU, XLV, XLY, using today's weights and last weekend's stock ranks. Then I relate it to their one week return. Tomorrow the market won't open so today's close is weekly close. The result is charted below.

At the first glance, there is tendency that higher ranked ETF has better return. But the points do not align nicely on a straight line. I looked at it for a couple of minutes and figured out that it is because the offensive sectors vs. defensive sectors. Among the 9 ETFs, 6 are deemed to be offensive, they are B, E, F, I, K, and Y. The rest 3, P, U, and V, are defensive. It appears that offensive ETFs aligns well to a straight line, as well as the defensive ones. The least square fits are plotted on the chart also.

Although I have only one week data, the deviation from the least square fit is minimal and I believe this shows that there is significant statistical link between the ranks of ETFs and their short term return. Two remarks:
  • Offensive sectors and defensive sectors do behave differently.
  • An market neutral strategy is to long the top ranked ETF and short the bottom ranked ETF.

Wednesday, April 20, 2011

Change The Big Money Index Back

Sorry I have to change the Big Money Index back. The image version is not stable. It appears to me that the image will only work for a couple of minutes and then the link is broken, which force me to regenerate another image. I think there are some glitches with the image version. Nonetheless, the latest version is interactive. Point your mouse on the lines you will see the date and the index value.

Minor Change to Big Money Index

You may noticed the changes I've made on the Big Money Index. Now it is an image, and you can see the full-sized version when click on it. But it won't automatically refresh itself. You have to refresh the webpage to get it reloaded. The chart is still updated every five minutes, just you need to reload the page to see the update. I've put my name on the image to make sure it won't get stolen that easily.

Big Money Index Added To My Blog

Some of my friends may know about the Big Money Index, an index I composed to gauge the money flow into or out of the equity market. Supposedly the money flow drives the price. So the market, usually represented by the S & P 500 index, will move higher if money flow is positive, and lower if money flow is negative. Most of the time S & P 500 moves along with BMI. Occasionally we may see a divergence, meaning that the money flow is not reflected by the market, yet. Since eventually we expect S & P 500 to follow BMI, such divergence offers good trading opportunities.

I've added BMI to my blog to the lower right corner. Although the chart will be automatically updated every five minutes, you don't have to fix your eyes on it. For one this is mainly for updating S & P 500. For two usually we are looking for a divergence spanning a couple of days.

As of today we see a positive divergence between BMI and S & P 500. So I expect S & P 500 to make new high soon, if BMI still works.

Tuesday, April 19, 2011

Liquidity And Performance Of A Fundamental Ranking System

I was worrying that the performance of T-Rank 2.0 would be impacted if I require higher liquidity. I ran some back tests and the result shows that requiring more liquidity will have negative impact on overall return, but the impact is manageable. In fact, there is really no big difference on overall return among portfolio size $100K, $200K, and $500K.
  • Worst case $40K: $3 per share and average 50K shares per day in the past 20 days. So the worst case daily dollar volume is $150K and one would like to not put more than $2K per stock. With 20 stocks in the portfolio, the worst case size is $40K. Annualized return is 26.70%.
  • $100K: The liquidity requirements are combined into one such that the average dollar volume traded per day in the past 60 days is at least $375K, and no more than $5K per stock. Annualized return is 22.96%.
  • $200K: average dollar volume is at least $750K, and no more than $10K per stock. Annualized return is 21.51%.
  • $500K: average dollar volume is at least $1.875M, and no more than $25K per stock. Annualized return is 22.72%.
Below is the performance chart.

Monday, April 18, 2011

Usage Models Of A Fundamental Ranking System

A friend asked me whether I'm going to rebalance every week if I trade T-Rank 2.0. My answer was that I'll if I trade the top 20 stocks returned by it. I think that's the discipline a trader wants to follow if he ever wants to trade a mechanical system. However this raised another question: How to make good use of the fundamental ranking system. Some options are discussed below.

1. Use It As A Mechanical Trading System
I derived T-Rank 2.0's historical performance data from back testing. A trader may want to follow strictly the trading schemes used in the back testing to copy its performance. The schemes are straightforward and should be easy to follow:
  • On every weekend compute the ranks of all stocks that satisfies the liquidity requirements documented here.
  • Pick the top k stocks. In my back testing I used 20 because I think 20 is the maximum size that is manageable by an individual to reduce volatility. But any constant k would work.
  • Allocate fund equally among the k stocks. If you have $200K and want to trade 20 stocks, then each stock gets $10K.
  • Place order to buy at market price at market open on Monday.
  • Hold the portfolio for n weeks. Any n between 1 and 6 would work and should generate similar returns.
  • On the Monday of the (n+1)-th week, liquidate the portfolio at market price at market open.
  • Repeat the first step. If a stock is reselected, you can save the steps to sell and buy it back.
In the back test, a 0.5% slippage was deducted from every transaction. As long as that 0.5% covers your commission and bid / ask spread, you should get the same performance.

But there is one concern and that is the liquidity. The liquidity requirements ask for $3 per share and 50K shares daily average volume. So the worst case scenario is that you only have $3 * 50K = $150K traded per day. I think you couldn't put in more than $2K to your market order without significantly moving the price. Multiply that with 20, the size of your portfolio, in the worst case scenario, is only $40K, and the annualized return is $40K * 26.70% = $10.68K. Not bad but you are not going to get rich with this.

I know this is the worst case scenario and you can always allocate more money on stocks with higher liquidity to circumvent this problem. But that may or may not hurt your overall return. I don't have data on this yet. Maybe I should run more back test on this.

Furthermore, the liquidity constraints prevent one from sharing his trading ideas with his friends, which may upset either the trader or his friends.

2. Use It As A Screener
In this way maybe I could publish the top 300 stocks, or stocks with rank above 90 each weekend, and my fellow friends could pick several, say up to 20, from the list and trade. This model works the best if each of my friend has his own way to pick stocks, be it fundamental based or technical based. One may use support and resistance to select the most promising opportunities, while another may check overbought and oversold conditions.

However there are still restrictions:
  • Their methods should be different from one another.
  • The ranks may not be published together with the stocks, to prevent everyone from simply picking the top ranked stocks.
  • Everyone still needs to spend a lot of effort to comb through the 300 stocks, which is time consuming unless they have some automated way to pick stocks.
  • It is up to the trader to determine entry and exit. The general suggestion is that one can hold a stock as long as it keeps showing up in the top 300 list.
3. Use It As A Ranking System
So each trader has his own watch list. They are supposed to derive such list based on their own knowledge, market sense, and interest. Then they consult the ranking system to decide which stocks (those with high ranks) they want to put on trade and for the rest they may want to wait a little bit.

This will remove the conflicts among traders that share the ranking system, but it also has higher requirements on each trader.

So each option has its pros and cons. There is really no such thing as free lunch.

Growth You Don't Want To Chase

One of my early post mentioned that growth is actually not good for short term traders. My explanation is that the growth number got priced in the shares well before it went to 10K and 10Q reports. Gannon's latest insightful article says that even for long term investors, there are certain type of growth not worth to chase. To quote what he said:
A business that is getting more efficient ... is achieving a totally different kind of growth than a company that is growing by growing its size and maintaining the same efficiencies.
The good growth will put more money into investors' pockets, while the bad growth will not. I'd suggest everyone to read Gannon's article throughly to understand this.

Sunday, April 17, 2011

Weekly Summary

It has been a week since my first post on fundamental ranking. Looking back, it appears I've made good progress this week. Below I summarize the key points of my little research.
  • T-Rank 2.0 is a fundamental based ranking system. It ranks stocks purely by their fundamental indicators, including: valuation, financial condition, and return on capital. Growth was not included because it actually has negative impact on the short term return. Blog posts covering this topic are here, here, and here.
  • T-Rank 2.0 is designed for short term trading. If an investor build a portfolio with the top 20 stocks returned by T-Rank 2.0 and rebalance the portfolio every week, his annualized return in the past 10 year is 26.70%. Considering that we have a giant bear market in the past 10 years, this result is fairly good. Related blog post is here.
  • T-Rank 2.0 is effective. Effectiveness is defined as the relation between the rank of a stock and its 1 week return. T-Rank 2.0 returns a numerical rank from 0 to 100. If an investor moves up 10 rank point, his annualized weekly return should improve 1.7%. And the further he pushes up, the better it gets. If he moves from 90 to 100, his annualized weekly return should improve 3.6%. Related blog post is here.
Other interesting observations are listed below:
  • Although T-Rank 2.0 uses weekly rebalance, it actually automatically finds the optimal holding period, which is 6 weeks in average per stock. Related blog posts are here, here, and here.

Effectiveness Of Fundamental Ranking

The T-Rank 2.0 was designed as a fundamental ranking system, but so far I used it as a stock screener. All my previous blog posts, except one, talked about only the top 20 stocks returned by the T-Rank 2.0. I know the discussion was not complete. This posts will quantify the effectiveness of T-Rank 2.0.

To quantifies effectiveness, I looked into the relationship between the rank of a stock and its short term, such as 1 week, return. For each week, I computed the ranks of all the stocks that satisfy the liquidity requirements as discussed here. There were around more than 3000 stocks that satisfy the liquidity requirements every week. So this is a very large stock universe. And I put the stocks in groups by their ranks. Each group has 100 stocks. That is, the first group contains the top 100 stocks returned by T-Rank 2.0, the second group contains the next 100 stocks, and so on. Then I calculated each group's weekly return over the past 10 years. Intuitively, the group with higher ranks shall have better return than one with lower rank. Thus I define the effectiveness to be the difference of return between the k-th group and the (k+1)-th group.

To make the number easier to comprehend, I use annualized return instead of weekly return. The estimated annualized return is simply the weekly return times 52, the number of weeks per year. This estimation is a little bit conservative as it didn't compound the return. But the benefit is this is easy to compute. It also gives a simple way to compute the annualized standard error of the return, which is the weekly standard error divided by square root of 52, assuming the return follows normal distribution. It's worth to point out that modern portfolio theory suggested that investors can reduce standard error by holding a portfolio of multiple stocks. Assuming certain independence, the standard error of the portfolio is the standard error of the individual stocks divided by the square root of the size of the portfolio.

To summarize all the formulas:
  • Estimated Annualized Return = Weekly Return * 52
  • Annualized Standard Error = Weekly Standard Error / SQRT(52)
  • Portfolio Standard Error = Individual Standard Error / SQRT(Size of Portfolio)
T-Rank 2.0 uses a numerical rank from 0 to 100. The stock universe contains more than 3000 stocks, so a group of 100 stocks covers, roughly speaking, 3 rank points. That is, the first group contains stocks with ranks from 97 to 100, the second group contains stocks with rank from 94 to 97, and so on.

With this, the chart below shows the relationship between the rank of a stock with its annualized 1 week return.

The x axis is the ranks, the y axis is the estimated annualized return in percentage. The center points of the red bars are the estimated annualized average return of a group over past 10 years. The height of the red bars is their annualized standard error, which is about 5%.

The chart says that if an investor picks a stock with rank above 97, holds it for one week, and repeats this for a year, his return should be around 24% and the standard error of the return should be around 5%. Considering we have a giant bear market in the past 10 year and the data are derived from the past 10 years, the result is fairly good.

As discussed above, holding a portfolio of multiple stocks can reduce the standard error. The height of the green bar is estimated standard error of a portfolio of 20 stocks, which is about 1%. So if an investor picks instead of 20 stocks with rank above 97, the standard error of the return will drop to only 1%, meaning his annualized return of 24% is quite consistent. This matches with the annualized return discussed here.

To quantify the effectiveness, I want to fit the points into a function curve. The chart suggests that a straight line may not be a good fit. I tried to fit the points to several simple functions using the least square method, and calculated their accumulated error. The one with minimum accumulated error is 1/x^4. The blue line in the chart above is the fitted curve. The functions and their accumulated error are listed in the table below.

Now I have a little bit problem with the definition of the effectiveness. When I was thinking about the definition, I thought it would be a straight line so for any k, the difference of return between group k and group k+1 should be the same. But now it turns out to be not a straight line.

So I define
  • The maximum effectiveness is the difference between the 1st group and the 2nd group, and
  • The average effectiveness is the average difference between groups.
So the maximum effectiveness of T-Ranks 2.0, as shown on the chart, is 1.6%. And the average effectiveness is 0.5%. Since one group covers roughly 3 rank points, the data implies that if an investor moves up 10 rank points, his annualized return should improve 1.7%. If he moves from rank 80 to 90 to rank 90 to 100, his annualized return should improve 3.6%.

As mentioned before, most of the data I have here are based on the assumption that the return follows normal distribution. The chart below shows there distribution of the return of the top 100 stocks over the past 10 years, which suggests that normal distribution is not a bad approximation. The green line is the curve fit by a normal distribution.

A Minor Tweak On Liquidity

I forgot to mention that I made a minor tweak on the liquidity requirement on T-Rank 2.0. The new requirement is now:
  • The last market close price is at least $3.00, and
  • The average of volume of the last 20 days is at least 50,000 shares.
Previously the liquidity requirement (as discussed in this post) uses the accumulated trading volume of the past 1 year, which may not be good for short term trading. It may happen that a stock was heavily traded 6 months ago (institutions were dumping it) but barely trades recently.

The tweak actually improve the annualized return quite a bit to 26.70% from 21.81%. Below is its performance chart.

Saturday, April 16, 2011

Eat My Own Medicine

I want to forward test my ranking system, T-Rank 2.0. I picked up stock symbols from, which is mainly for fundamental investors. The symbols should be the stocks fundamental investors are interested in. Below are their ranks as of 4/16/2011. Let's see how things work out in 1 weeks, 2 weeks, ..., up to 6 weeks, which is the optimal average holding period.

N/A means that the stock may not have enough liquidity, which is not good for short term trade, anyway.

JNJ 93.89
AAPL 91.39
INTC 90.12
BBY 79.58
ABT 79.43
MSFT 79.01
CSCO 65.32
GLW 63.92
GOOG 60.68
DELL 59.3
PDLI 57.74
AIG 56.05
WMT 54.82
TEVA 54.12
COCO 50.27
SHLD 46.32
WFC 36.95
CLX 36.7
AGO 22.02
SVU 17.76
GE 15.55
C 12.33
BAC 9.11
MBI 4.02
JEF 1.68

From Value Ideas & Strategies forum of
GM 86.06
NS 72.46
PH 70.03
CSCO 65.32
TGT 63.55
PRE 54.24
MTU 48.94
TSCDY 37.68
ARLP 34.52
RCI 11.77

Wednesday, April 13, 2011

Between Holding Period And Turnover

I just discovered a link between the optimal holding period and the turnover. The optimal holding period for T-Rank 2.0 is 6 weeks as discussed in my previous post. In the same post, the average turnover for weekly rebalance is 15%. So the average holding period for a stock is 1 week / 15% = 6 weeks, which equals to the optimal holding period. It appears that with weekly rebalance, T-Rank 2.0 automatically finds the optimal holding period for each stock in the portfolio. This also explains why the annualized return doesn't change much between weekly rebalance and 6 week rebalance.

Tuesday, April 12, 2011

Optimal Rebalance Period

I'd like to thanks the person who asked about turnover. I did more back tests on different rebalance period. The optimal period is 6 weeks. The corresponding annualized return is 23.39%, and average turnover (every 6 weeks) is 36.20%. Nonetheless, there is no big difference from rebalancing every week to every 8 weeks. The annualized return starts to drop for periods longer than 8 weeks. The longest period I've tested is 1 year and the annualized return dropped to 14.91%, with turnover (every 1 year) at 75.50%.

On The Turnover Of T-Rank 2.0

Someone asked me about the average annual turnover. My answer is: the portfolio is rebalanced every week, and the average weekly turnover is 15%. I know this would be a huge number to fundamental investors. Turnover shouldn't be a big problem as far as performance is concerned. A 0.5% slippage is deducted for every transaction.

T-Rank 2.0 And Impact Analysis

I played with it a little bit and finally decided to remove the entire growth category. I also tried to tweak the weights of the remaining three components, but it turns out that the original assignment gives the best performance. Below it's the final setup of T-Rank 2.0:
  • Valuation, 2/5;
  • Financial condition, 2/5;
  • Return on capital, 1/5.
Impact analysis is conducted as well and results is listed below. The order of significance didn't change. Valuation still comes first, then comes financial condition, and return on capital comes last. Nonetheless, the impact of return on capital is a nontrivial 6.48% annualized return. An interesting observation is that the impact of the components roughly matches with their weights, 15 to 12 to 6.5 is about the same ratio of 2 to 2 to 1.

Lastly the performance chart.

Monday, April 11, 2011

More On The Ingredients Of The Ranking System And An Impact Analysis

I shall name the ranking system the Trustamind Rank 1.0, or T-Rank 1.0, hereafter for convenience.

The idea comes from the StockGrader from Barron's subscriber has free access to it. StockGrader evaluates the fundamental strength of a stock in four categories: growth, value, profitability, and cash flow. For each category, a letter grade is given based on the fundamental data such as P/E, P/S, etc. And the four letter grades sum up to a number grade that represents the fundamental quality of the stock. I was using it to guide my investment for about a year, trying to combine it with technical techniques such as resistance, support to determine entry and exit. Overall speaking, the performance is good. But sometime I got trapped into a position for a couple of months before its fundamental strength kicks in. I know I shouldn't complain for this as a fundamental investor, but I'm not satisfied.

So I was trying to come up with my own ranking system. I still want it to be based on pure fundamental indicators. Furthermore I want it to be short term oriented. That's why I enforced weekly rebalance. If it's profitable when the minimum holding period is just a week, I'd say my goal is accomplished.

Growth and value made good sense to me. But profitability and cash flow didn't, so I removed them. My short term perspective suggested to check the financial condition to make sure it won't go bankrupt in near future. So my ranking system has three categories with equal weight:
  • Growth, 1/3;
  • Valuation, 1/3;
  • Financial condition, 1/3.
Lately I was heavily influenced by the blog posts and articles by Gannon, a knowledgeable and insightful fundamental investor and blogger. He suggested that return on capital is an important fundamental indicator, which usually includes RoC, RoE (return on equity), and RoI (return on investment). So I also add return on capital to the mix, but only give it half weight as I'm not familiar with it. Below is the final version. And now you know where the 7 comes from.
  • Growth, 1/3.5 = 2/7;
  • Valuation, 1/3.5;
  • Financial condition, 1/3.5;
  • Return on capital, 0.5/3.5.
The initial back test looks good as shown in an earlier post.

As a logical next step, it's worth to understand the contribution of each of the components. So I did a little bit research which I called Impact Analysis. I remove each category from the ranking system and see how the resulting APR changes. The greater the change, the greater the impact, thus the greater the contribution and significance the category bears. Actually this statement is not perfect, the contribution a category has comes in two folds: its own contribution and its interaction with other categories. It's possible that you have two indicators that each, when applied alone, has good performance, but when combined they works poorly.

The table below shows the result where the categories are ordered by their impact. Valuation is the most significant one, not a surprise. The second place holder is financial condition, which is explainable by the short term perspective. Then it comes to return on capital. It is to my surprise because it only has half weight, but I'm sure Gannon and other RoC advocators won't be surprised. The funny thing is that growth comes to the last. Not only that, it has a negative contribution, -3.46%, to the ranking system.

I know that I should respect the data, not my gut feeling. But this results is well beyond my imagination. I thought about it for a while and coined a theory to explain it. The theory is that, the market overly chased growth in the last decade. Consequently, the entire security analysis industry devoted a large portion of effort into forecasting growth. If you pay attention to those research reports, you'll see a lot stuff like this: research firm ABC upgraded stock XYZ as in the latest channel check they found that shipment increased by ijk%. So the growth is largely priced into the shares before it goes to the quarter or annul reports, and to us fundamental investors, the growth is a lagging indicator.

I'll start to work on T-Rank 2.0, to see whether I should simply remove growth or tune up its weight. I'll report my discovery shortly.

My Up-To-The-Minute Trading Ideas On SeekingAlpha

Please check out up-to-the-minute trading ideas on my SeekingAlpha Instablog here. Most of them will be technical oriented trading signals thus do not fit into the scope of this blog.

Enjoy your trade, folks.

Fundamental Analysis For Short Term Trade?

Yes, it's doable. I just completed a stock ranking system that is based on pure fundamental indicators such as valuation, growth, financial condition, etc., yet it is good for short term trade. I created a portfolio that contains the top 20 stocks returned by the ranking system, and rebalance it every week. As show in the chart below, the performance is good. Annualized return is 18.35% vs. merely 2.56% of S&P 500.

The stock universe used here is
  1. Market cap is at least 250M. So we only trade small cap and above.
  2. Accumulated one year dollar volume is at least its market cap. So liquidity is good.
I wouldn't reveal the formula, but I can provide some information on its ingredients and their weights in the ranking system:
  • valuation, 2/7
  • growth, 2/7
  • return on capital, 1/7
  • financial condition, 2/7
It's very late now. I'll post more on this later.