In part3, model error has an attribute of a normal distribution. This signifies that the model is usually not too far off predicting the market within a reasonable bound. If there is an instant that the model error is exceedingly high, one may expect that the model error would reduce back toward zero in the next iteration, and prices would converge back to a long term average (or mean) that the model suggests. This behavior is called mean reversion. It turns out that the regression model is suggesting the market price mean reverts approximately to

Mean = ConstantA / (1 – ConstantB)

And the standard deviation of the modeled price is

ModeledPriceStd = ModelErrorStd / (1 – ConstantB^2) ^ (1/2)

If the current market price exceedingly lower than the modeled mean, one could long the asset and gain the advantages of mean reversion. Ie buy low sell high. But what is the measurement of when is the best time to enter a long position? S-Score is a simple comparison of how much the current price is away from the Mean and its relation to ModeledPriceStd.

S-Score = (CurrentMarketPriceMean) / ModeldedPriceStd
S-Score of +1 implies that the current market price is one Modeled Price Std higher than the mean.
S-Score of -1 implies that the current market price is one Modeled Price Std lower than the mean.

One may plan a set of trading rules using S-Score and thresholds similar to as follows:

Trade Entry
Long when S-Score is < -1
Short when S-Score is > +1

Trade Exit
Close Long Position when S-Score is > +0.5
Close Short Position when S-Score is < -0.5

Stop Loss
Stop Loss Long Position when S-Score < -1.2
Stop Loss Short Position when S-Score > +1.2

One would need to defined the thresholds levels based on personal’s favorite asset being traded and accepted risk levels. In the next post, we will go over some results of a trading strategy that strictly follows a S-Score rule.


Another Firm with Multi-Level-Marketing Direct Sales Business Model

Why is NUS following HLF?



Previous Post on Berkshire Hathaway BuyBack

A few days ago it was reported that Berkshire Hathaway bought back $1.2 Billion dollars worth of CLASS A Berkshire Hathaway(股票代號: BRK-A).  The purchase was not done on the open market, and it was all purchased from a single long time investor.  For comparison purpose, the company has spent only $126 Million dollars for the net purchase of shares the last four quarters combined.

Berkshire Hathaway has announced raising its maximum target price of Class A shares to 120% of Book Value.  Previously the most Berkshire Hathaway was willing to pay was 110% of Book Value.  Obviously Book Value is a number updated at most quarterly because it is a balance sheet item.

There is a speculative possibility that Warren Buffett sees an improving economy through the lens of his collections of businesses.  Aside from insurance and investment, Berkshire has a number of housing related businesses.  I am not sure about the rest of the country, but in the San Francisco bay area, especially the silicon valley, I notice a dramatic positive attitude shift towards housing, and prices are appreciating rapidly.  This could mean the company is becoming even more undervalued.  The Net Present Value of purchasing its own share could be more favorable than many other investment projects that the company has looked at.  Buying a dollar for fifty cents is the primary motive of any value investor.

However, I think, once again, this recent vote of confidence on its own share is just a cover up.  This could be part of the succession transition plan.  By reducing the float in circulation, this move probably serves to further solidify future management and board control of the company through Class A share, which is worth 1500 times a Class B share but 10,000 times the voting rights of a share of Class B.  This large purchase of not-from-the-open market signals the company’s concern of “CONCENTRATION OF POWER” outside the company insiders.  In stead of Buying Back on the open market from a variety of retail investors whose individual proxy impact is negligible(Why? Because each share Class A costs $130,000.00 yeah! More than the average “ANNUAL” salary!), Buy Back from one large shareholder, who has the potential ability to influence proxies against management’s wish, in essence eliminates future troubles such as proxy fight.

This is not an attempt to undermine Berkshire Hathaway as an iconic company.  On the contrary, Berkshire Hathaway will remain an economic powerhouse for years to come.  As long as the management and board serve with the best interest of all the shareholders in mind, shareholders will benefit from the insights and expertise of the managers.  A corporation is rarely a place for democratic rule.

Most traders and investors are short sighted.  We are wrapped up as a whole in the daily price movement of a stock.  It is true that the SHORT TERM RETURN of a stock can come from capturing share price fluctuation.  However, LONG TERM RETURN can only come from the long term actual profit the underlying business generates.

Berkshire takes it one step further whenever it can,  it buys whole business and skip the waiting for the profit reflection on a stock price.  This way Buffett and company have direct access to the profit generated and apply that capital to make more investments that churn out more cash.  The current Free Cash Flow after paying for debt service is about $17 Billion a year.  The company has about $46 Billion on its balance sheet.  That is a lot of ammunition, and the company is yearning for the next big investment.

With Berkshire’s business model and Buffett and company’s sharp investment acumen and unwavering mentality, this is how INTEREST COMPOUNDING can truly work to make people wealthy.

I am long term bullish.  A price floor may have been temporarily established at 120% of current book value due to buyback.  However, always proceed cautiously and buy with a margin of safety.

We welcome comments and thank you for your supports.  Have a Safe and Happy Holidays!


CAT product demand is driven by global economic growth, construction activity, commodity prices, government spending on infrastructure, and end users’ access to capital.
It’s lagging currently, partly because of its relatively weak exposure to agriculture (drought depresses crops yield and heighten food price) compare to peer like Deere.  On the other hand, mining and energy exploration has been held back by lower commodity price.
I like CAT the business and company in general, it is definitely one of the best among its peer group.  But my enthusiasm for CAT is temporarily dampened due to Macro headwind.  (Short term skeptic, long term bull)

The revenue streams are strategically diversified, less than 30% is from North America, (the good recovering economy), revenue stream may continue to weaken, unless 1) spending on infrastructure, 2)urbanization, 3)mining, 4)construction, 5)Capital Ex Investment, pick up, which are entirely possible.  The reasons could include government stimulus spending, economy picking up around the world.
Revenue and Net Income have been increasing dramatically at least over the past 3 years, but Operating Cash flow has stayed relatively range bound.
This company operates on rather high leverage historically, and as a result the Return on Equity for last year has been spectacular.  The current ratio is 1.4 with about 40 billion of Total Debt, the company has raised more debt capital since last year, and the Total share outstanding has increased from 628 to 666 million shares.  The average nine years ROE has been about 33.89%, but that could be skewed because we went through the construction boom from housing and infrastructure both domestically and abroad, urbanization of emerging markets, and commodity boom for the past decade.  The company has nevertheless, demonstrated uncanny ability to meet obligations, as well as expectation of revenue and income growth.
Buffett once said, he would rather buy a great company at a fair price, then a fair company at a great price.  If we simply take the Net Income reported at face value, couple with the current consensus 5 year earning growth rate analysts predict, the fair value could be somewhere around $101.2/share.  Please proceed with caution and an appropriate margin of safety as always.

In part 2, Linear Regression technique was used to calibrate the relationship between Current Price and Last Price. The model error of the relationship was introduce. It turns out that the model error roughly follows so called a standard distribution.

To understand standard distribution. Consider the men height in U.S. The average men height is around 5’10″. The shortest man is around 2’3″, and the tallest man is around 8’11″ feet (according to Google). Men’s height, more or less, follows a normal distribution where majority is around 5’10″, then less men at 5’9″, …, then finally only handful of men is below 3′. Below graph illustrates a normal distribution. Standard deviation can be thought as a measurement of the dispersion of data. Majority of the population is around the average, and only handful data points are far away from the average.

Going back to the Dow Jones example in part2. The model cannot perfectly represent all data point in the graph. Some data points are perfectly aligned to the linear line, some are far away. The distance of each data point from the linear line is called model error, and the average error is around 13.06, and the standard deviation (or dispersion / scatterness) of the error is around 84.12.

Majority of the error is within 0.5 standard deviations away from the average. There are rare occasions where the model and observed price disagree by 1.5 standard deviations or more. In this case, if the model is consistence, high model error could mean that the market may have mis-priced data points. Thus, building a trading strategy to trade at prices with high model error could be profitable. In the next post, we will refine the model error into trading signals using expected long term model return and S-Score.

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