Modified Capital Asset Pricing Model

The CAPM or capital asset pricing model believes that the expected excess return over the risk-free rate is beta times the excess market return over the risk-free rate.

μ = θ + β (ν – θ)

Where μ is the expected stock return, θ is the risk-free return, ν is the expected market return, and β is beta coefficient.

I believe the stock market is mainly composed of two kinds of players – investors and traders. The investors are looking for long-term investment gains while traders are looking for short-term investment gains. The long-term investment gains are related to the expected return of stocks (mu) while the short-term investment gains are associated with the volatility of stocks (sigma). The total return is the balance of the interests of the traders and investors can be summarized by the following equation.

R = θ + α (μ – θ) + β (σ – θ)

Where α and β are alpha and beta coefficients.

In other words, the total return is a linear combination of the excess return of investors and the excess return of traders. A portion of the total return comes from the long-term holdings while another portion of the total return derives from the trading activities.

Constant Dollar Return from Assest Classes

Yesterday my walk was nice. I thought about the relationships between investment returns and investment risks. I was thinking that one should get the same return in dollars from each class of asset. For example, if the stock return is 12% per year and the bond return is 6% per year, then a portfolio contains stocks and bonds should have 2/3 in bonds and 1/3 in stocks. This way, each asset class contributes the same return in dollars.

Later in the day, I met Olina talking about the same idea about constant return in dollars. I realized that the same principle could be applied in real life. Fractional relationships can be established among various people according to their level of appreciations. She did not like this idea, but she could not establish any counter argument.

That’s might be why so many high-valued arts are stored in museum so every can pay a visit at a fractional time. I visited Venus and Mona Lisa in France. That’s was a fractional time experience.

My Dream about Casino Chips

Dreams are regular events of my life. I have had many dreams, about the past, about sexual desire, and about the future. Last night, the dream was totally new. The dream was more or less like this.

A friend of mine had some gambling losses. He got a loan from me and later on he paid me with some gambling chips. I was going to get my loan back by casing the chips from the local casino (operated by Korean people). They told me that the chips are no longer in use. So they paid me back some real gold and three other forms of jewelry. I was happy to get the gold but did not like the other forms of jewelry. So I wanted some other form of paybacks instead of jewelry. When I put the three pieces of jewelry back at the cashing counter, they were broken to smaller pieces. After a while the clerk said they were sorry and took the smaller broken jewelry to the back room and returned with a stack of papers which recorded the history of the casino chips. I guessed that the stack of papers were at lest 100 pages. They told me they did not know for sure where I could cash the gold pieces and the papers could be converted to real money. They said they were in one of the Texas cities. They mentioned San Antonio, Houston, and Dallas. There were much more details than I could remember now. The whole dream was more or less like this.

Investment Style Box to Style Cube

Currently there are two ways to divide the equity market. One is known as style while another is called as sectors. The style is a 3x3 matrix. The three rows are large cap, mid-cap, and small-cap. The three columns are value, blend and growth. So the investors can pick and choose from one of the 9 styles. Actually, this style matrix is a combination of two ways to think about the market.

One way to think about the companies listed in the market is to think them in terms of their sizes. The big companies and small companies may be operating under different set of constraints. So their performances can be different under different economic conditions. That is why sometimes the large-cap stocks are doing better than the small companies. In other times, the small companies can do much better than the large ones. In the last three years, the small-cap companies performed well.

Another way to think about the stocks is in terms of their relative valuation. There are many ways to evaluate a stock. Price-earning ratio (P/E ratio) is one of the most popular measures of stocks. When P/E ratio is high, the stocks are considered as growth stocks. Otherwise, the stocks are considered as value stocks. There are gurus in both camps of the style investments. One extreme well-known value investor is Warren Buffett. An example of growth investor is Peter Lynch.

Another way to divide the equity market is by sectors. There are three traditional sectors – materials, energy, and industrial. There are three consumers related sectors – consumer goods, consumer services, and healthcare. There are three capital intensive sectors – technology, utilities, and financial services. Another way to invest in the equity market is to pick and choose among the sectors. Some have developed extensive insights about how to invest the right sectors at the right time. This kind of investing methodology is known as sector-rotation.

I am thinking about the third way to divide the stocks – along the time history. One example of such index is the IPOX-100 index, which includes 100 stocks with trading history less than 1000 days since their initial publish offerings (IPO). First Trust has put this index into the market already. FPX is the ETF underlines the IPOX-100 index. If we combine the time history with style and market capitalization, we can obtain a three-dimensional matrix, which further expand the style box into a style cube. We can divide all stocks according to their IPO dates as young, mature, and seasoned stocks. After finishing the one world fund, the next project could be the style cube.

My Friend Pete Thoryk

Today is another hot day. It reached 107 degrees outside. I did not have time to take a walk until 4:00 pm. I called Olina around 3:30 pm after meeting with Pete. I was going to see if she had time for a tea break. The call did not go through. So I resumed to my regular activities. I took a walk around 4:00 pm. It was really hot. By the time I walked to the community pond, I was sweating already. I did finish my regular walk.

The chat with Pete was nice to. Since I moved to Dallas four years ago, I have been meeting Pete regularly, on every Wednesday afternoon starting around 2 pm. Sometimes the meeting lasts about one hour. Other time it can last about two hours. I met Pete soon after I moved to the apartment. Although we born some 40 years apart, we have many similar experiences growing up. The difference between China and the United States can be summed up by the age difference between us. He grew up during the Great Depression. He and his three brothers all went to the World War II and all came back alive. He had a very successful working career from a floor worker all the way to general manager of the company he worked. He is very proud of that he helped his two sons and one daughter during the years when they needed helps.

Now he lives by himself. His daughter and family live in the nearby neighborhood. His son-in-law Tom worked in the financial field for over 30 years. Now Tom works independently as an investor. Tom is one of the best international investors. He once managed an international fund over one billion dollars before he sold the company to a German Bank before year 2000 just before the crash of the US stock market. When I met Tom first, he was in the process of setting up a hedge fund. For some reasons, he decided to work independently as a global investor.

I have learned a lot from Tom and Pete about investment and American culture. Pete is one of the wisest men I ever known. Some time I think the potentials of senior people are not fully utilized in the country. In one way, I have benefited from knowing Pete over the last four years. When I met him first, he was worrying about a cancer in his stomach. Now four years have passed, he seems he is becoming stronger than he was when I first met him. I wish he lives a long time. So I have a father-like friend for a long time.

Chris Investment Ideas

I had two blogs before. I transferred all my blogs under the blog title "Chris Investment Ideas" to this new blog "Metabraid Capital." So now I only need to take care of one blog related to investment. I still keep the other blog "Family Loves Work," which is related to general thinking about life. Some times there are few thinking related to investment, but that should be more personal.

Every day, I have some thinking about investment. That can be analysis of current news, progress in learning, discussions with friends, business ideas related to investment. I started this blog a while ago to record my basic thinking about investment. Now I think this can be a tool for communication between me, my partners, and my friends, and my clients.

I will try to make this blog as friendly as possible. Since typing English is much easier for me now, I will basically keep this blog English only, at least for now. Olina suggested that I should consider a Chinese blog. I felt that my current life is more English than in Chinese in the investment related areas. I might consider writing some Chinese blogs in another blog entitled as "Family loves work."

Economic Diversity and Central Tendency.

Today is really hot. I took a walk like every day this morning from 10 to 11 in the morning. I saw only two people, probably a farther and his son, were riding bikes along the way I was working for the entire one hour. Wind was very slow. I could hold the umbrella against my left or right shoulders with one hand. I used another hand for holding a bottle of water. By the time I was back home. I was wet entirely. After taking a shower, now I am going to write down what I was thinking today or over the last few days.

There is a connection between individual instability and aggregated stability. The first example is the theory I learned about rivers. There is a relationship between the flow and the concentration of sediment in the flow. In it simplest form, the following equation represents this relationship.

C = K US / W

Where C is the concentration of sediment in flow, U is velocity of flow, S is the slope of the flow, W is the fall velocity of sediment in still water, and K is a constant.

This equation is very simple and used widely in predicting the sediment load in rivers. However, the errors between this predicted sediment loads and the actual measured ones are very large. The standard deviation for the errors can be as big as a few hundred percents relative to the mean estimates. Although the standard errors are big, the overall errors over an extended period time are quite reasonable. One example is the above equation can be used to determine the reservoir life (the time for the reservoir to be filled up with sediment) with quite good accuracy. This indicates that the central tendency of the relationship between flow and sediment is clearly explained by the equation.

Another example is related to the types and shapes of cars. At the beginning time of car manufacturing, there were many types of cars in many different shapes. Over the years, the types and shapes of cars are settled with limited numbers. The engines are standardized, the colors are standardized, the bodies are standardized, the tires are standardized, and the shapes of windshields are standardized. In my mind, each component is optimized over time by engineers at different manufacturers. All these components are standardized towards the central tendency.

The shopping experience has similar history. There were many small stores around each town in the United States. The types of stores owned by the diversities of people are gradually replaced by the standard stores built by Wal-Mart, Target, or Costco. One vivid experience of video store happened over a very short time period. There were many mom-&-pop video stores. After Blockbuster, all video rental stores are almost the same. This is another example of central tendency in shopping.

The civilized world seems moving toward certain central tendency with gradually reducing standard deviations. On one hand, the world is diversifying. On another hand, each diversified part is moving toward leanness.

The financial instruments should move in similar fashions. The financial instruments are generally divided into two categories: risky assets and risk-free assets. When looking at each class of risky assets, their volatility is great. Some can vary more than 50% around their means. However, the aggregated GDP (gross domestic products) usually vary only a few percents. Even the fast-changing China GDP is growing about 10% per year. If one can invest in the entire global economy with proper divisions among all asset classes, one could achieve the central tendency for optimal allocation of resources. This is one of the philosophical basis for our one-world fund.

Gotrocks Capital Management

What is Gotrocks?

It was the Independence Day yesterday. Zhen family and mine was going to the Plano Oakridge sports center where our sons could go swimming there. We met at Zhen’s home before the activity. Zhen said he read the Warren Buffett article at one family owns the entire US listed stocks. On the way to the Oakridge Center, Zhen and I talked more about the article. By the time we came back to Zhen’s home, we were almost certain that our goal was to create such a family to investors.

Since both Zhen and I could not remember the family name Warren Buffett referred in his article. We checked on the Internet via Google. Soon we discovered that the family name was Gotrocks. Originally the family name Gotrocks was used to refer rich family since 1930s. Gotrocks took the form from “Got Rocks” when rocks mean diamonds or dollars. So Gotrocks mean Rich in general.

Warrant Buffett was thinking about that in the Gotrocks household everyone grows wealthier at the same pace and all is harmonious. Since there is no such a family in the United States, Zhen thinks that so our goal is to create such a family for every investor to join.

This is the first time we come to understand our goal so clearly. So we will create one fund to fit everyone who believes that the Gotrocks own everything in the world. Zhen is suggesting we use Gotrocks in naming our company such as Gotrocks Capital Management.

Target Retirement Funds

Are Target Retirement Funds Right?

The target retirement mutual funds are getting popular among investors. Both Fidelity Investments and Vanguard Group offer similar kind of targeted date retirement funds. The general rule of thumps is that the weight of stocks in the retirement portfolio should be reduced over time when they are near the retirement age. The basic equation for this belief is the following.

S = g – v T

Where S is the percentage of stocks in the retirement portfolio; g is a growth factor, usually having values in the range from 100 to 125; v is a value factor, having recommended values are the range from 1 to 1.35; T is the years of age.

One commonly used equation takes the following form (with g = 100 and v =1).

S = 100 – T

The above two equations assume that the portfolio risk should be reduced if the holding time is short. In other words, risk is reduced if the holding period of portfolio is long. So that young people should hold large percentage of stocks in their portfolio while people near retirement age should hold small percentage of stocks in their portfolio.

Although this belief is popular among investment advisors and some investors, however it does not have rigorous theoretical bases. Several academic and professional studies conducted by university professors and industry practitioners do not have consistent results. Several studies concluded that the age-dependent portfolios have similar results as fixed proportions of stock and bond weights in portfolios

Low Correlated Asset Classes

Can Low Correlated Asset Classes Continue?

I was talking about investment with Zhen. One of his concerns was about the historically low-correlated asset classes are now becoming more correlated over time. The correlation between the US equity markets with the international markets is increasing. Even for the emerging countries, the correlation is increasing. He was worrying about the low-correlation asset classes may no longer exist in the future.

I addressed this question with two examples. One is the equity/bond pair. Another is the Equity/REIT pair. Their historically low correlation coefficients are still working. The basic reasons are due to their structural differences between these pairs.

Between corporate equity and corporate bonds pair, there are two forces are working consistently. One force is the equity/bond issuing corporations. The corporations have two choices to raise capital. One is to issue equity stocks. Another is to issue bonds. The corporation has a goal to minimize its cost of capital. When bonds are cheap, they will issue bonds. If equity is cheap, they will issue equity.

Another force is that there are two classes of investors. The growth-seeking and risk-taking investors are interested in stocks. The income-seeking and risk-averse investors are interested in equity. Since the two classes of investors have consistent behaviors over a long time. So the low correlation coefficients will continue to exist for a long time.

For the equity/REIT pair, this difference is even bigger. REIT is a real estate investment trust. Real estate investment is generally a local-event. In the North-Dallas area, there is a fast-growth area between North-Plano and South-Frisco around the area near Dallas-North Parkway and State Highway-121. There are several major investors in the area. One is Ross Perot, who was the head of EDS; own a big piece of land in the area. Another is the General Growth Properties, the largest mall REIT in the country. Between them, they own a big portion of land in the area. So the land price has increased several folds over the last decade.

For equity companies, most of their worth is in intangible assets such as brand names, operational procedures, intellectual properties. Physical properties are not the main holdings for them. They are looking for efficiency over the global scale. The may design products in the United States, manufacture them in China, distribute them in Europe. These companies are globally focused.

The difference between equity/Reit is structurally determined. Additionally, the legal structure is also different. REIT companies do not pay corporate taxes while most equity companies have to pay corporate taxes and investors has to pay taxes on dividends as well. So equity investors in general have to pay double taxes while REIT owners do not pay double taxes.

Portable Alpha Investment Strategy

Max sent to the stock group an article related to portable Alpha investment strategy. I thought that the efforts are good for portfolio managers. Here I just want to clearly understand the problem first. Below are some thoughts I have about Alpha or Beta.

RP - RF = Alpha + Beta * ( RM - RF )

RP = Portfolio Return
RM = Market Return
RF = Risk-free Return
Alpha = Constant
Beta = Constant

Based on the above theory, one can increase his portfolio return by either increasing Alpha or Beta. Beta is associated with covariance and standard deviation. Beta is a measure of risk.

Statistically, Alpha is just an error term. If the market is efficient, the Alpha's among various portfolio managers would have a probability distribution similar to standard distribution (Gaussian distribution). If some managers can consistently have positive Alpha's, then the market efficiency assumptions must be questionable.

Practically, Alpha can be considered as a measure to compare portfolio manager's quality. If one can increase Alpha without increasing Beta, he/she would be a great manager. When Beta increased, the risk is also increased. On a risk-adjusted framework, the increase may be meaningless for some investors.

Over all, the market is not-yet 100% efficient. That's why some manager can have consistently positive Alpha’s

This was prepared on June 30, 2006

Local Stock Market Gurus

Yesterday afternoon, Olina organized a small group meeting at the Escape. Olina bought tea for Bo and Max. I had water already. The meeting lasted three hours from around 4 pm till 7 pm. I got there first, then Bo came, then Max was there, Olina came at last. The discussions were very good. As a record, I am trying to write down what the discussion were about.

Based on my understanding, Max's model has the following logics.

(1) His model can identify repeatable historical patterns with 60% to 80% chance being right. Since each identifiable pattern is almost independent events, so there is an increasing probability of being right for N events. The probability of being right for N events is:

P = 1 - p^N

where p is the probability of being right in each event, N is the number of repeatable events, P is the total probability.

(2) He tries to reduce the time interval for his trades so that each trade is almost risk-free. This way he is avoiding the market risk. Since the trading interval is directly related to risk, so by reducing one can reduce its market risk. Many believe that the transformed stock price (y = Log X, where X is stock price) is a Brownian motion process. If that's case, then the standard deviation (a measure of risk) can be expressed by the following equation.

S = C t^ (1/2)

Based on the above equation, the shorter trading interval means the smaller standard deviation or smaller risk.

(3) His model tries to generate independent events. So the regression 0r autocorrelation coefficients among all trading events are minimized.

So based on the above system, I believe that his model will ultimately be successful. It is only a matter of time before his model works in real practice.

Bo Model actually has some fundamental rigor as well. Based on the discussions, I believe his model has the following logics.

(1) There are institutions which are intentionally jack-up stock prices for their private gains. By observing carefully, he has the ability to identify which stocks are under the manipulation of such institutions.

(2) These stocks are typically relative small (about 50 million outstanding shares). He believes that the manipulation institutions usually control 1/3 to 1/2 of the outstanding shares.

(3) Bo tries to get into such stocks after the institutions established their shares and sell before the institutions do. So he can make enough profit in the mean time.

Max's wife Xiemin tried to help Bo to find a job in Central Garden & Pet Company (CENT). However, the current opening is not available.

This was written on June 27, 2006.

An Evolution Process Model

In today's stockpoll group, Youhang Peng stated that he had long felt that one should model the market like an evolution process. He said that he was not really into building models so he once thought about asking Max to look into evolution models.

I have thought about the market process is similar to the evolution process for a long time. I thought that was very interesting that we had similar thinking along this line.

Human has been in the evolution process for six million years. It is one of the youngest life form on the Earth. Something like Crocodiles or Cock roaches have much longer evolution processes.

However, there are more recent evolution processes with much short time history. According to some analysis, the Agricultural Time has about 3000-5000 years of history. The Industrial Revolution has approximately 300 years of history. The Information Age has about 30 to 50 years of history.

The interesting thing is that all these new human-environment processes (agricultural, industrial, and Informational) are still very young and dynamic. Now biotechnology is entering the agricultural process; the nanotech is very promising to change the industrial process; genetic engineers are thinking about completely alter the information process with life computers.

Some time I am forced to think that we are in the most interesting time of all ages. At the same time, I am wondering if people lived in the Confucius time or the time of Newton would have the similar feelings.

I was preparing the above message while Jie came home. I was going to send these thoughts out to the Stockpoll group. Jie told me that I should keep this writing. So I put this into this Blog form. I am still new to use this Blog. I should use this more often to keep writing Blogs on a more regular basis.

This is prepared on April 20, 2006.

Can High Energy Price Cause Inflation?

I met Gaolan this morning at the neighborhood park. He was with his family. I was with my family.

While we were there, Gaolan was asking me about my comments about the current high oil price. His concerns are that the high oil price will pressure consumers to shift their spending from regular items to gasoline. So that the high oil price will produce an inflation or economic downturn.

I think this is a current state of minds in the United States. However, I think the high oil price will not affect the current economic expansions at all. First, the high oil price is just changing the wealth distributions rather than destroying values. The high oil price creates new economic activities in the energy industry. So there are more jobs. Before the high oil price, let's assume that there were 100 consumers; each of them spends $100. The total economic activities are $10,000 after the high oil price, now there are more consumers. Let's assume now there are 101 consumers and each of them spends $99. The new economic activities are now $9,999.

Secondly, the high oil price cannot change its course by itself without obvious economic impacts. I do not know how high the oil price will go. I do expect the trend will not stop until some detrimental economic impacts are everywhere.

Theoretical Causes of Inflation

What causes inflation?

There are four economical theories behind the causes of inflation. To inflate in English is to fill (something) with air or gas to make it swell. So the inflation can be naively explained by filling the economy with more money so the price levels of goods and services swell. Actually this is one of the four economic theories behind the causes of inflation. This is mainly caused by governments. When governments want to print more money, then inflation happens. There are many reasons why the governments have to print more money. I like call this cause as the institutional cause. The institutions involved in this are mainly the federal government and the Federal Reserve System.

Inflation can be caused by increases of aggregated demands. When there are more demands of goods and services, the price levels increase. This is known as the demand-pull inflation. When people want to consume more than the firms can produce, the firm can charge higher prices for their goods and services.

Another cause of inflation is decreases of aggregated supply. When the supplies of goods and services decrease, the price levels increase. This is known as the supply-push inflation. When firms reduce its contents per unit of goods and services, the unit prices of goods and services is increased. So the inflation happens.

The demand-pull and supply-push inflations are the results of imbalance between the firms and consumers. So the two causes can be summed up as the production-consumption imbalance inflation. I call this cause as the structural cause since the two pillars of the economy – firms and consumer are not exactly balanced structurally.

Inflation can be influenced by people’s expectation of inflation. This works as the self-fulfilling prophecy. Higher inflation expectation can actually cause higher inflation. Since people’s expectation of inflation can not happen all the time. Let’s assume people expect higher inflation 50% of the time. Then this cause of inflation works 50% of time. I consider this cause as the psychological cause.

In summary, there are mainly three causes of inflation – institutional, structural, and psychological factors. Historical inflation data suggests that the inflation rate is approximately 2.5% annually. I would like to attribute 1% each of each factor. Since the psychological factor only works 50% of the time. So the long-term average inflation caused by psychological factor is only 50 basis points.

An inflation rate of 2.5% annually might be a good theoretical number for the economy. In my previous blog I suggested that the inflation rate, real interest rate, and productivity are equal to each other. Then the theoretical nominal interest rate should be 5% when the productivity rate is 2.5%. This is approximately a reflection of the current US economy.

How Long Can Energy Price Shocks Last?

Energy price, especially the oil price, is keeping going higher. Today, the oil price reached a price of $78 per barrel. Many think that the high oil price will change the normal behaviors of consumers. The reasoning behind this thinking is that the price of gasoline is about $3 per gallon, which is about twice the number a few years ago. So people will go shopping less or combine their trips to shops. People will reduce their other discretionary spending such as restaurants, clothing, or sports events. However, I consider this change of consumer behavior temporary and short-lived. People can change their normal behaviors at the begging of a shock. Then the shock impact will be gradually reduced over time. So the initial shock impact will eventually goes away.

There is a Chinese saying “for ten years one is afraid of well ropes once bit by a snake.” Chairman Mao said that “There will be another cultural revolution in seven or eight years.” These quotes indicate that the shock-behaviors of initial impacts will gradually return to normal behaviors. The seven, eight, or ten years are just an indication how long the initial shock-behaviors can last. But the true human nature will eventually take place when the impact of initial shocks is decaying away.

Another economic rebalancing effect of the high oil price is the development of alternative energy sources such as nuclear power, wind power, solar power, coal-fueled power, and hydroelectric power. Although some of these alternative energy sources may take long time to develop, but the effect can be felt long before the actual completion of these alternative energy sources.

Based on this kind of thinking, the current worries about the hyper-inflation, stagflation, or even a slowing down of consumer purchasing power will eventually evaporate over time. These worries will be proven short-lived when people return to their truce nature and the effects of alternative energy sources are felt.

What is the origin of Capital?

Is capital created by labor or capital? Marx thought capital is created by labor via surplus value. Others thought capital is created by capital. Then where is the origin of capital? Here is my thinking about this.

One way to create capital is to have a game played by two people. Let’s define one winner and one loser for each game. If one wins, then the other looses. The winner will become the capitalist while the looser will become the labor. The capitalist will enjoy the fruits of labor. In this way, capital and labor are born. When this same game is played by millions of people, then there will be two classes of people – the capitalists and the labors.

How can capital be accumulated to such a huge number over time? First there is land, it was here before human. Then human beings come to occupy the land and work on the land. They have created the current structure of land, capital, and labor.

Capital is only a concept of human beings. There are three kinds of capital – permanent capital, transient capital, and organizational capital.

The land and resource capital is the enduring capital. This permanent capital can not be created or destroyed since this kind of capital is composed of materials and energy. This capital exists before human and will continue to exist after human.

The transient capital is the capital created by human beings over the history. This transient capital includes houses, roads, bridges, airports, transportation systems, computers, the Internet, and all other artificial products and goods. This transient capital can be consumed by human beings. It can not last forever. Over time it will be decayed back to the permanent capital.

The third kind of capital is the organizational capital. This kind of capital is the way how labors are organized. When the organizational structure is improved and optimized over time, the productive force will be increased. They become more capable to convert the permanent capital to transient capital.

So the total value of capital is the sum of all three kinds of capital. The permanent capital can be measured by the value of land. The transient capital is the sum of historically artificial products. These artificial products can be measured by their price. Every thing has a price. The organizational capital is a potential capital. It is a claim to all future artificial products.

The organizational capital is responsible for productivity. When the labors are organized better, the productivity can be increased. Land is responsible for inflation. Since land by itself can not do anything. It needs labor and transient capital to produce value. When the land has the potential to produce transient goods, the price of land can be increased. This Transient capital may be responsible to interest rate (something related to rental of transient products). If one moves into an apartment, he has to pay rents to the landlord in order for him to live in the apartment. The rental rate is related to interest rate of capital.

Now how can investors maximize their capital value? The land owners want maximum the inflation rate so that his land value is maximized. The owners of transient goods want the maximum interest rate so that the rental value of his transient goods can be maximized. The firms who organize labor want the productivities maximized so that they can gain more value from each labor they hire.

How can the economic system satisfy each of these owners? So there should be a balance among them three. A moderate inflation rate, a moderate interest rate, and moderate productivities are the best solution for them all. Since the nominal interest rate has two components – the real interest rate and the inflation, we should use real interest rate in determine the best rates among the three.

One proposal is to have equal rate among all three rates. Real interest rate equals to inflation or productivity rates. We need another equation to solve for the value of all three variables.

What is the other equation for us to determine the value of all three rates? I will think about this question next time.

A Brief History of Personal Fianance

Here I am going to summarize my personal history of financial matters. For first independent financial decision for me in the United States was to get a loan. I had only $100 when I arrived at the San Francisco International Airport. In order to rent a room, I had to pay a deposit. I borrowed $400 from Peter in order to rent a room in Oakland far from the campus. After a few weeks, I got my scholarship money from Hong Kong. I paid Peter back the $400. He was surprised that I did that. He thanked for by inviting me to a local Chinese Restaurant.

After several months, I saved a few dollars. One day I saw a new bank (American Savings Bank) opened a branch at the Telegraph Avenue next to Little Hunan, a small Chinese restaurant I went often to get my lunches. The bank had a promotion to new CD accounts. I got $20 bonus for opening a CD account. I told the new to several friends like Wang Huanchao and Liu Yong. They also have a few dollars. Wang Huanchao opened a CD account also at the same bank.

When I started working at Bechtel Corporation in San Francisco at one summer. My colleagues told me mutual funds had better returns than returns than CD. Jie and I went to a Dreyfus office not far from the Bechtel office to open a mutual fund account. I kept that Dreyfus account for many years until 2004 when I closed that accounts and move the money to Fidelity and Vanguard.

A friend of mine moved from New York to Alameda around 1988. He told me stocks were better than mutual funds. I did not believe him immediately. I jointed one collective action sponsored by a professor of USF where Jie went for her MBA. The collective action was each one contributed $500 to buy LTV stock. The stock was supposedly very low in price and was near or close to bankruptcy. The professor thought LTV would come out of the bankruptcy when Bush became the President. Bush did become the president. But LTV did not come back. Later the professor sold the stock and gave back to each of the partners a few dollars. However, I became very interested in stocks since this experience. During the Tiananmen Square event in Berkeley, I met a new friend Greg. He is an attorney working on helping retirees to get Medicare or Medicaid benefits. I learned the Half-a-loaf approach from him. This becomes one of the main principles later in my investment.

In 1991 Jie and I started working. So we started saving money to buy stocks. Since I like stocks so much, I cashed out all CD accounts (some CD accounts were sold to friends) and moved the money to PCFN (Personal Control Financial Network), one of the first online brokerage services offered through Prodigy Internet Service. Very soon our account value grew to $50,000. One bad investment in Kendall Square Research set us back to $40,000 in one year. Since then, all my investments in stocks had been limited to the top-five companies in their respective industries. I followed the same principle until I sold all my stocks in April 2000.

Around the time, I learned about hedge funds from a friend of Tony. He invested his money at various hedge funds. I did not do that. I started to learn about the investment methodology of hedge funds. So I did a few year hedge-style investing.

In June 2002 I sold my home in California and moved to Plano, Texas to look for a better environment for George to grow up. I met Tom through Pete. I learned how institutions manage their money. Tom works for the Texas Public Employee Retirement fund as one of the investment committee members (worked as Chairman for one period). So I paid more attentions to other pension funds or retirement funds. CalPer (California Public Employees Retirement Fund) is one of such funds. I started to see how these institutions allocate their money. Soon after, I started to manage personal money using this asset allocation methodology.

The Global Economic System

Global economy is the subject I am going to learn next semester from the University of Texas at Dallas. What do I know about the global economy now? I should summarize what I know already so that I could take my current view to compare with that of the professor.

The current global economy has three characteristics: one world, two modes, and three kinds of capital.

One world means that the political boundaries are reducing its roles to give path to the global economic exchanges. Each country strives to join the global economic systems. One of such systems is the WTO or the World Trade Organization. The WTO originally formed by the major economic powers such as the United States, European nations, and Japan. China joined it a few years ago. Now Vietnam and Russia are going to join it.

Two modes are the developing modes of the global economy. There are developed economies such as the United States, western European nations, Japan, and Australia. Developed means industrialization. Developing nations are those countries are still in the process of industrializing their economies. Brazil, China, India, and Russia are example of developing nations.

Three kinds of capital include the land, labors, and capital. Land is associated with agricultural production first. In the agrarian society, land and labor are the only resources needed for production. In industrial society, land, labor, and capital are needed for production in factories. In the current society, financial resources are the most critical resources for the smooth function of the global economy. Land, labor and capital are securitized for easy transaction. One can purchase and sell land, or labor, or capital within seconds. So one main characteristics of modern global economy is financial transactions.

History of Balanced Funds

The history of balanced funds is very interesting to me. Before the mutual funds, every investor tried his own lucks in selecting individual stocks. Although there are still many individual investors picking their own stocks, but mostly rely on mutual funds, exchange-traded funds, or closed-end funds for their investment needs.

Balanced funds or total return funds are those mutual funds with investments in equity and fixed income at the same time. One of the first such funds is the asset allocation funds. The weights between equity and fixed income are changing over time, depending on the views of the managing experts. When these experts think the equity markets are going to do well, then they allocate more capital in equity securities. If the experts think the fixed income securities are going to do well in the next period, they allocate more capital in the fixed income securities. However the experts have not done so well in predicting the proper weights between the equity and fixed income securities. So the financial institutions introduced the balanced funds with the fixed weights between equity securities and bonds. These settled the first chapter in balanced fund history.

When the one fixed weights of equity securities and bonds does not satisfy the need of all kinds of investors. The financial experts have believed that some people like growth funds (with more weights in equity securities) while the others like income funds (with more weights in bonds). So they introduced the style funds ranging from very aggressive growth, to aggressive growth, to moderate growth, and to conservative growth funds. These funds satisfied the investment community for a while.

Now the experts believe the people who should not be linked to a specific growth-category for his entire life. So they introduced a new type of funds – the target retirement funds. The weight of equity securities changes according the ages. The weights usually change from about 90% in equity securities for the young people to 10% in equity when people are close to their retirement ages.

Now what is the next wave for the balanced funds? I believe that they are the one-world funds. The history comes back to its original point but with higher technological flavors. The new round of balanced funds is the one-world funds which is mathematically optimized combinations among all investment asset classes ranging from equity, to bonds, to commodities, to real estates, to precious metals, and to long-life assets such as infrastructure facilities.

Target Retirement Funds & Balanced Funds

Should everyone have the same portfolio independent of his or her age? The answer to this question is academically not clear. However, in practice, people seem to understand the question perfectly. Several major mutual fund families have introduced the target retirement funds. One very interesting thing is that the target retirement funds have very different portfolios for people before entering the retirement age. After retirement, everyone has the same portfolio. In the case of Vanguard, there are now over 10 target retirement funds ranging from 2005 to 2050. But there is only one fund for after 2005.

Theoretically, the optimal portfolio should consider two independent variables: asset values and asset returns. Savors invest every year a fixed or variable amount of money to their retirement funds while retirees withdraw a fixed or variable amount of money from their retirement funds. So the optimal portfolio should consider both cases differently. In both cases, the optimal portfolio should maximize the product of asset values times asset returns. In the savors case, Asset value is composed of the sum of two terms, the asset value from the end of previous period and the new investment during the previous period. In the retiree case, Asset value is composed of the difference of two terms, the asset value from the end of previous period minuses the new withdrawal during the previous period.

So if the target retirement funds are programmed right, they should treat the retirees differently just as they treat the savors differently. I believe there is a flaw in this program. Actually, academic studies have concluded that the target retirement funds with equity weight varying from 80% for young people to 20% for retirees would have similar returns for portfolios with 50% equity and 50% bonds, which are just regular balanced funds.

Maximum Withdrawal & Terminal Lake

Flexibility is the game for all retirees. I have read several articles about the maximum sustainable withdrawal rate. Usually the rate is in dollars, sometimes adjusted for inflation. Since some of the basic living expenses are constant for the retired people, so the assumption for a relatively constant dollars term is reasonable. However, if flexibility in spending is incorporated in budgeting annual expenses, the retirement savings can last much longer.

We can learn from the nature about how to balance the evaporation from closed watersheds. A closed watershed is a basin where the river system drains itself to a terminal lake. The Owens River drains itself in to Owen Lake California is such a watershed. The Walker River terminates itself at Walker Lake is another example of such closed watersheds.

The amount of stream flow produced in Walker river basin is a variable. In wet years, there is a lot of water flowing into the Walker Lake, so the lake rises. When the lake rises, its surface water area increase, so does the evaporation from the lake. Since the annual evaporation rate has much less variation than the annual flow rate into the lake, so the lake size under natural conditions is relative stable. Over the last century, the economic activities in the Walker River basin have increased, so the amount of water diverted from the river has also increased. So the lake size has reduced tremendously.

In the Owens Valley case, since the amount of water diverted from the Owens River to outside the river basin (mostly to the Los Angeles Metropolitan Area) has increased so much. The Owens Lake is mostly dry now. Under natural conditions, Owens Lake was a perennial lake is a huge water surface.

For a terminal lake to keep its shape and size, the amount of water entering the lake should be balanced with the evaporation. If the amount of water entering the lake is reduced too much for extended period, then the lake goes dry.

If people learn from the natural system like the terminal lake basins, their retirement funds can last as long as they wish just like the nature had produced the beautiful Owens Lake and Walker Lake. However, human activities are so paramount to natural needs; the natural beauties of terminal lakes are replaced by the Hollywood stars.

What is the maximum sustainable withdrawal?

When we have a portfolio consisting of cash and risky assets, we need to know what the optimal combination for their respective weights is. One way to answer this question is to use the maximum sustainable withdrawal.

In general retirement accounts, the retirees have to find maximum sustainable withdrawals from their accounts. For an average account with a portfolio of 60% in stocks and 40% in bonds who takes our 7% a year has only a 30% chance of make that money last 25 years. That same retiree withdrawing 4% a year has a 94% chance of success. Experts say that the 4% is often the withdrawal rate that works best.

Actually, the MSWR (Maximum Sustainable Withdrawal Rate) might be able to increase when cash is added to the portfolio. Cash has two advantages. Cash can be used as cushion during the down-turn markets. Cash can also be used to purchase more securities at discounts when the market is down.

The problem of MSWR is similar to the problem in determine the reservoir size in water resources planning. In water resources planning, the reservoirs are built to sustain the longest droughts. During the drought years, the rive flow is low and not enough to sustain the aggregated water demands for agricultural, industrial, municipal, and environmental uses, water is taken out from the reservoirs to mitigate the low stream flow.

In planning for retirement, the market down-turns are just like the drought years in water resources planning. If we build cash reserves big enough for the market down-turn years, then we can achieve a much higher MSWR.

So the tools used for water resources planning can also be used for MSWR problem. One of the methods used in water resources planning is the mass-curve analysis. The mass-curve method of water-availability analysis is well-established and is extremely useful. Mass curves of available flow show cumulative flow and can be used to indicate cumulative utilization and storage requirements. Adjustments for evaporation and other losses must be made in determining the net volume available from accumulated stream flow. The mass curves of demands show the cumulative demands over time. The reservoir size can be determined by comparing the two curves.

Similarly, the mass-curves for cumulative investment incomes are compared with the mass-curves for cumulative withdrawals. We can determine the required cash reserves similarly as we determine the required reservoir sizes.

What is right # of funds in a portfolio

What is the right number of funds in an optimal portfolio? There are three major factors determine the right number, available investment assets (or portfolio size), Minimum initial investment size and additional investment size for each fund, and minimum exchange size or trading size relative to exchange fees or trading fees.

In elsewhere, I have estimated the expected trading return is a linear function of standard deviation over expected return of each fund. Sharpe has proposed that the portfolio risk-adjusted return can be measured by Sharpe Ratio which is the expected return divided by standard deviation. So an optimal portfolio should have the minimum risk-adjusted portfolio return and at the same time the maximum volatility for each fund.

Now we have a conflict of interest. On one side, for each fund, we are expecting high standard deviation. On another side, we are expecting low standard deviation for the entire portfolio. Solving this conflict of interests is the entire art of portfolio management.

Tobin once proposed a Tangent portfolio as the optimal portfolio. A balanced combination of risk-free asset with the risky tangent portfolio should lead us to a maximum Sharpe Ratio. What should be appropriate weights for the risk-free asset and the risky tangent portfolio?