Kelly Criterion For Stock Trading Size

I’m sure some people know about Efficient Frontier, but I’m guessing that there are less investors that know about Kelly Criterion. So what is Kelly Criterion and who is Kelly? Kelly worked at AT&T, and published the original paper back in 1956. Its math is quite involved with communication and information theory, mostly dealing with probabilities. However, behind all the maths, there lies an astonishing result: by placing bet amounts according to Kelly Criterion (originally applied to horserace gambling), one can maximize the returns in the long term. Here is the betting formula which has been tailored to stock trading:

K% = ( (b+1) * p – 1) / b = ( b*p – (1-p) ) / b

Win probability (p): The probability that any given trade you make will return a positive amount.
Win/loss ratio (b) or odds: The total positive trade amounts divided by the total negative trade amounts.

If you think of b as the odds of b-to-1, payout of b when betting 1 unit of money, the numerator is simply the mean value of expected payout, or the so-called “edge”. Therefore, K% can be expressed as edge/odd. For obvious reason, you don’t want to bet in any game where the expected payout is 0 or negative.

If Kelly Criterion is so great, why is that this is not heard or used very often in the investing world. There are a couple of reasons that prevent it to be used practically:

  1. The volatility of strictly using Kelly Criterion is quite big. Despite that in the long term, probabilistically speaking your portfolio will have the maximum return possible, the ups and downs are too big to be digested by most people. Therefore, people talk about using “half Kelly” or half of the bet amount calculated from Kelly Criterion in attempt to reduce the portfolio volatility.
  2. To use Kelly Criterion, it requires knowing how good you trade stocks (in terms of p & b). Obviously, if you don’t know exactly how much your “edge” is, the Kelly betting amount will probably be off from the correct amount. Estimating and knowing your edge will be a much harder task than calculating the Kelly betting amount.

Despite the mathematical correctness of Kelly Criterion, it is much harder to invest such in practice. Aren’t there anything that we can walk away from such a terrific investing formula? Indeed, there is. Here is what I personally learned after investing stocks for almost 10 years now. The riskier the stock/or entry point is, the less amount that you should put in; the safer the stock/or entry point is, the more amount that you should put in. This is exactly the spirit of Kelly Criterion that bet should be proportional to your edge or your supposed advantage. I have been burned by stupid bets so many times that I finally learned to carefully size each of my stock transaction. In fact, sizing of your transaction is equally important if not more than what stocks you pick. While most of the investment world talks about what to buy, much less attention is spent on how much one should buy. But for every transaction, it always consists of the following elements: what (stock) to buy/sell, when to buy/sell, and how much to buy/sell. For successful investing, all three elements must be carefully chosen. And Kelly Criterion helps you on deciding the last element: how much.

For more related articles, one can check out the article from Businessweek, and investopedia. Tom Weideman also has an excellent article using simple calculus for deriving Kelly Criterion with less math from information theory.

Saving On My Car Insurance

I’m paying $529.60 a year for car insurance on my two cars. It’s probably not easy to pay a lower amount than this. I think there are four major reasons for this low rate:

  1. Both my wife and I have a clean driving record and zero claim history.
  2. Our cars are modest and not very new (year 2000 and year 1995 Toyotas). Their values are less than $10K in Kelly’s blue book, and so it doesn’t cost a fortune to insure them.
  3. We only have liability insurance ($100K/$300K/$100K), and a high deductible of theft/comprehensive coverage. Obviously, I won’t recommend anyone to have liability only, unless the cars are not very new, and also you can afford to lose the cars in an accident. It means that you are financially capable of replacing a lost car, without causing hardship to your life.
  4. The fact that we don’t drive or commute a lot of miles helps lowering the rate. If you get online quotes, one of the advantages is that you can play with your annual mileage and see what’s the range of mileage that will put you to the next bracket of insurance rate. The lowest rate bracket at most insurance companies seem to be at 0 to 7500 miles. But you don’t want to have your claims denied only because you put down some out-of-whack mileage numbers on the insurance policy.
  5. I shop for a good deal on my car insurance. I got very competitve quotes from, but I ended up using Costco’s.

If your car insurance rate on a per car basis is cheaper than mine, please leave a short comment. I would be thrilled to hear from you.

The Importance Of Knowing How To Budget

How can you keep the money in your pocket, if you don’t know how it comes in and how it goes out? Granted, the most painful part about saving money is not to spend it. Deferring immediate gratification for the future takes some real discipline. Having a realistic financial goal in sight with a proper plan and budget will help one to succeed on this difficult saving path.

The most important things about making a good budget is that you must be truthful, realistic, and comprehensive. A budget is a detailed plan that you and your family can achieve, not some math exercises on additions and subtractions on paper. You can make up a balanced budget, with wrong or unrealistic numbers in them, or leaving out certain spending items. Or you can make a budget with some 5% to 10% head room on every item, plus a line for miscellaneous spending for general breathing room on the entire budget, or to account for little things that are not accounted for.

Budgeting is essentially the time to be honest with yourself and your family. Try not to persuade yourself either into believing that vacation or the morning StarBucks coffee is a one-time event that you don’t need to budget it for. Once you have a budget on paper, you should re-visit and refine your budgets every once in a while to check if all the numbers are realistic, and see if your budget still truly reflects on the ways that you spend your money. Go over your old utility and credit card bills, and see if your budget is correct. Also go over your bank statements to see if your projected savings have gone into your piggy bank accounts. If not, you should check and see why your budget plan has gone wrong. In fact, this self-discovery process can take a couple of years to get everything right. Quite often, you may over-spend your annual budget for Christmas gifts or vacation travels, and still don’t know how the money disappears.

In summary, making a good budget involves the following:

  1. Be comprehensive. Don’t leave out any items that are more than about 3% of your total spending. Budget monthly by dividing 12 for those annual one-time events.
  2. Be realistic and at ease. Don’t try to be 100% accurate on every item. You can either leave some room for every item or add a misc item for your total head room.
  3. Negotiate and compromise with you & your family member to make financial sacrifices for the long term well being.
  4. Verify the correctness of your budget, and make modifications if necessary.

Leverage: The Secret of Making Big Money

Have you wondered how some people get so incredibly rich? There is a saying: “you need money to make more money.” If you hear that from a poor person, it may sound a little sour-graped. But underlying it, there is probably some grain of salt, not well-understood by the person who says it, but a good observation nevertheless.

What happens usually is that you need money or asset to borrow a lot more money, using which you can make even more money out of it. It is a game of leverage. The money-making potential is always proportional to the total amount of money involved. Whether it’s borrowed or not, it doesn’t matter. So when a business owner is successful in his or her venture, he or she will be handsomely rewarded. But if he or she fails, the leverage works in the reverse gear and may lead to substantial loss or even bankruptcy, depending on the company structure and amount of risk and leverage that is undertaken.

In fact, leverage comes in many forms, and in each case, you can see its multiplicative power.

  1. Leverage of employee’s time: As long as each employee can bring in more money than his or her wage, then the money left or the net profit goes into the employer’s pocket. The employer or the business owner is leveraging on employee’s time to make money. Multiplying by more employees is multiplying the profits.
  2. Leverage of the machinery: As an example, for an internet retail business, it leverages on computer equipments to take purchase orders. Equipments have a fixed cost. As long as the equipment brings in more money before its utility is fully depreciated, then it’s good business. Multiplying by more equipments for machinery is multiplying the profits.
  3. Leverage of copies or copyright or franchise: This is leverage in the purest form of multiplication. More copies of songs or CDs, more copies of software, more copies of books or DVDs, will all result in more profits for the owner of copyright or franchise.

These are the reasons that in Robert Kiyosaki’s four quadrant of E/S/B/I, B (business owner) is a better money-making model than S (self-employed) because of the multiplicative power, while S relies solely on the available time of oneself, to be multiplied by a very high per hour rate to reach a good income level. However, using leverage is not risk-free at all even when you control your own business.

The other forms of leverage are financial leverages:

  1. Margin: Margin power in stock is usually 2X of your cash. Margin in forex trading can go upto 400X.
  2. Asset-back loan: mortgage debt.
  3. Other loans that are not back by assets: Credit card debt falls into this category.
  4. Marketable options: These are call & put contract in the stock or futures market.
  5. Employer’s granted stock options: It’s essentially a long term call option on the given stock.

The only leverages that I recommend of pursuing are mortgage debt and stock options. The other ones like #1 and #4 are better for professionals. And the interest rate on #3 is usually too high to be worthwhile carrying, unless it’s for very short timeframe. The advantage of carrying a mortgage is explained in my post: “Why is your home the best investment?“ #5, the stock options are very good if you are fortunate have them. Under non-bubble conditions, value of stocks tend to go up along with inflation, and one should be rewarded with certain gain.

My Hunting Trip For A Money Manager

A couple of years ago, with my idle cash piling up, and my time dwindling down for a newborn in my family, I decided that I wanted to give up the control of some of my money to someone else, and see how well it would turn out. Since I did and still do most of my investment decisions on my own, I wanted to find someone or some firm that was hopefully at least as good as I was (or else, what is the point of getting an advisor).

The first one I spoke to was from Bank of America. She asked me about my current investment, and had me filled out a profile survey on my risk tolerance and investment goals. Sensing that I was quite competent in doing my own investing, which at that time included selling covered call options and short-sellings, she actually didn’t call me back for further in-depth appointments. Sounds a little rude, but I was glad that she didn’t waste her or my time.

The second one I spoke to was from UBS Financial. This advisor was relatively new in this business, probably less than 3 years, and was more willing to win my business. Again, she asked my current investment, and walked me through some standard talks on those large cap/small cap, US/foreign, stock/bond, income/growth portfolio diversification. And then, later she came back with some selection of funds and allocation for what she would recommend for me. She worked hard, but I was not impressed. I could have done exactly the same thing utilizing ETFs or mutual funds to achieve the same purpose, but without the 1% fee (which is usually the minimum money management fee in this industry).

The third one I spoke to was from Smith Barney. This advisor was knowledgeable, and was trying to sell various kinds of financial services such as 529 college saving account, and even mortgage financing. Again, I went through this standard talk about age to stock/bond allocation, and diversification among large cap/small cap, income/growth, US/foreign sectors. He even touted on one of his energy investment recommendation which had a return exceeding 50%. However, I gave him an ETF holding of mine which practically tracked his recommendation in chart exactly, and yet I got in even earlier than his recommendation call.

By this time, I was totally unimpressed with the standard asset allocation and diversification talk. So when I met the fourth advisor from Ameriprise (formerly American Express), I decided to quiz this poor guy, before I wasted more of his and my time. I devised a set of four simple binary choice questions, such that randomly guessing would only have 1/16 chance of getting all of them right:

  1. Shall I invest in a foreign utility or domestic utility company, if $US is going down, and all other factors remain the same?
  2. Shall I invest in a domestic producer or foreign producer of a certain commodity, if $US is going down, and all other factors remain the same?
  3. Shall I buy or sell more of the commodity producer stock, if interest rate is going up, and all other factors remain the same?
  4. Shall I buy domestic stocks or foreign stocks, if $US interest rate is going up?

Despite my persistence on having him answer my quiz before the appointment, this guy from Ameriprise refused to answer my short quiz. Instead, he told me that he couldn’t give out any investment advices when I was not his client, even though I protested that the quiz was only testing his general knowledge on economics. I guessed he knew that he couldn’t answer all of my questions correctly, and chose to refuse my trial instead of embarassing himself.

Want to try answer my questionaire yourself by posting to the comment? I will post the answer in the comment after a week. After these meetings with financial advisors from investment banks and brokerage houses, I have concluded that unless it’s an actively investing firm like a hedge fund, you are probably better off using ETF and low fee mutual funds to construct your own customized portfolio with regular rebalancing. Of course, whether active investing is better than indexing is highly debatable. But if I’m paying for 1% (or more) management fee, I would want my money manager to actively work for above average performance, rather than plain indexing for an average performance (minus his fees).

How I Bank: Online Banking

I actually started online banking back in 1998/1999 when I first read an article on online banking in BusinessWeek. The article was comparing two internet banks, and I chose to give NetBank a try. NetBank was one of the highest yielding banks in the nation at that time according to, and has been so until recent last 2 to 3 years. I made sure that NetBank was listed at FDIC database, and then I started my online banking.

In the beginning, I didn’t have a lot of trust. So I started by depositing some small amount of money, and tried to withdraw money from my account by checks & ATMs. After everything seemed to work fine without any problems, I started to move majority of my cash holdings to NetBank.

Because of the inconvenience of online banking, mainly due to very few free ATMs, I keep accounts at two local banks. In one local bank, I only have saving account to reduce the amount of money that I need to keep for minimum balance to avoid fee, since checking account usually has a higher minimum balance. In another local bank, I have both checking and saving accounts, so that I have at least a checking account locally. And my rationale to have two local banks is to simply increase the total number of free ATMs that I could use in a short distance from wherever I was. Of course, if you don’t have enough cash reserve, you probably want to limit the number of banks you have.

This strategy of having an online bank and two local banks have served me well. I can easily access my small cash need, while I can keep the majority of my cash in a higher yielding online account. Depending on your comfort level for accessible cash, you can put that amount in local banks, and put the rest in online accounts. Since I conduct most of my purchases through credit cards, my need for cash is low. I usually only keep about one thousand dollar in local banks, but it could vary from a few hundreds to just less than two thousands. And to avoid all kinds of ATM & bank fees, I define my accessible cash as any amount over the minimum balance that is required to avoid monthly fee. And I always use the ATMs of my banks.

I also take full advantages of (free) online payment offered by NetBank. Every month or quarterly, depending on the bill frequency, I pay my electricity, gas, water, trash, home owner association dues, and two of my credit cards automatically. My phone bill and auto-insurance is paid automatically through credit card instead of NetBank, since I can get the 1% cash rebate on credit card charges. Having all the bill paying arrangements, I spend probably less than 10 minutes for viewing or paying all of my bills, excluding credit card bills. And I make sure that there is sufficient amount of money for payments by setting up an automatic transfer of an upper estimate of the total bill from my major high-yielding money market account to the checking account that allows unlimited withdrawals.

In summary, I try to achieve the followings for my banking needs:

  1. Easily accessible cash by having two local banks.
  2. Higher yields for most cash in accounts at my online banks.
  3. Avoid any bank or ATM fees by using ATMs of my banks.
  4. Take full advantage for online bill payments to save time & stamps.

By the way, I opened accounts at INGdirect a few years ago, and now I’m still debating whether it is worth my time and trouble to move my INGdirect accounts to EmigrantDirect for their exceptionally high yields currently at 4.50% 4.65%.

Steps To Wealth: Saving and Networth

Saving = Income – Expense
Networth = Asset – Liability
Accumulating networth is a process by which one controls the expenses and trickle down the savings into growable assets, while reducing liability.

Sounds simple? Yes, it’s easier said than done. But that’s how it always is. If you don’t get a lottery income, or don’t inherit a substantial asset base like most people, then accumulating networth is a fairly slow process most of the time. Definitely it requires lots of patience and fiscal disciplines.

Now let’s look at the two equations more closely. The first equation describes the fruits of your daily activities. By earning your income and controlling your expenses through budgeting, you can have savings. These savings are the very first step to your wealth. However small the savings may be, without it, one simply cannot get ahead financially.

In the second equation, it describes more of the passive side of money. The liability or debt should remain fixed or paid down. When acquiring new debt, you must have very good reasons, such as helping to increase your curent income or grow your asset faster. Unless there is an extraordinary reason, you should always pay down at least the interest on the debt so that it doesn’t increase as time goes on.

The Asset term in the second equation is the most tricky and difficult one to handle among the four input terms on the right hand side. How to invest your money in the right assets is an aged old question. Your return on investment or ROI must exceed the general inflation rate, or else you will be losing purchasing power. Investing can be active, but preferably be a passive activity. How to invest is another topic all by itself. However, both Saving and Investing are equally important to reaching wealth.

In a nutshell, save to increase your networth; invest to maintain (or increase) your existing wealth.

Why Is Your Home The Best Investment

Well, I should really qualify the title of this, by not buying the home in a bubble. Whether our current housing market is a bubble or not is debatable. Under normal circumstances however, buying a home is usually your best investment. And the reason is inflation. Historically, housing price tracks inflation fairly well. Since inflation is seldom zero, or negative, buying a home is a financial transaction that has two very big advantages, assuming that you acquire the home with some amount of mortgage.

  1. Leverage: A leveraged transaction means that your return (or loss) is magnified by the amount of leverage that you use. In a leveraged transaction, you use less amount of cash to take control of a much bigger amount of asset with debt. If the asset goes up in value, then you are rewarded with extra returns.
  2. Inflation: Your home value is almost guaranteed to go up in value in a very long term perspective (I’m talking about 10+ years) because of inflation. Since you repay your mortgage debt by cash gradually, the debt burden actually goes down as your wage gets inflationary increase. $100K owed now will be less burdensome 10 years later, even if you have not paid down a cent in principal. Inflation is the best for debtors, but worst for creditors.
  3. Tax: At least in the United States, federal tax laws clearly have a preferential treatment for homeowners. You can deduct mortgage interest which is also AMT-deductible. Possibly you can deduct your usage of home as home office. The property tax is deductible too. And the best thing is that the capital gain on the home is usually tax-free under $250K for singles, and $500K for couples.

That is why real estate is often touted as a good investment because it is really true, with the following assumptions:

  1. You didn’t buy it in a bubble.
  2. You have sufficient positive cash flow to carry you through enough years for inflation to increase your return.
  3. You can take good care of the home or property.

I have constructed a Rent vs Buy calculator for you to experiment the outcomes of the two choices.

Stages In Life: Retirement Planning

Most people when they finally get out of school and start their first job, are so happy with their financial independence and the first paycheck, that they splurge the entire paycheck, if not more.  Few people think so far ahead about the next stages in life, of getting married, having a family, and eventually retiring from work.  If one doesn’t plan to have children, then they have plenty of time to save for their retirement.  But if they plan to have children, the best time for saving money is really right after schooling is over, and before having any children.

For the ease of this discussion, I’m going to assume some simplistic scenario.  Let’s assume that a person named Kevin graduates from college at the age of 22.  For the next two years, Kevin either spends another 2 years for graduate school studies, or simply lives from paycheck to paycheck because of little work experience which leads to lower salary.  And after age of 24, to age of 30, Kevin develops the career, and gets married.  At about the age of 30, Kevin has his first child.  The first child goes to all the levels of schooling, and graduate from high school after 18 years.  At that time, college expenses will start to kick in when Kevin is age of 48.  Assuming that Kevin has two kids, separate by 3 years in age.  So for the next 7 years, Kevin will need to help out college expenses for his kids.  Once it’s over, Kevin is 55, and has another 10 years of working & saving money until his planned age of retirement at 65.

Now, let’s look back at the timeline of Kevin’s life in regards to earning and saving potential:

  1. From 0 to 24: it’s pretty much zero.  At the end of 24, Kevin may have some or a lot of college debt.
  2. From 24 to 30: this is a time that he can potentially save some money (either towards paying down college debt, or just simply saving).
  3. From 30 to 48: Kevin’s earning may grow with experiences, but his expenses probably go up as kids grow up.  Let’s assume that the increase in earning is offset by the increase in expenses.  Actually in reality, expenses are a lot higher for the beginning years because the wife cannot go out to work.  If the wife goes out working, the preschooling or daycare expenses may take up all of her paycheck.  Either way, you end up with less (retirement) savings per husband and wife.
  4. From 48 to 55: I think we can safely assume that the saving will be zero or negative if Kevin decides to pay the majority of the college expenses for his children.
  5. From 55 to 65: This is another good 10 years of earning and saving, especially with Kevin’s long time work experiences.
  6. From 65 to 90: That’s 25 years of living expenses that need to be saved up (for both husband and wife).

So you want to tell me when Kevin can save for his retirement?  To err on the conservative side, and for simple discussion, let’s assume that Kevin’s investment return is only on-par with inflation rate.  So in terms of buying power, what he save every year will simply be what he can spend later.  Depending on the ratio of Kevin’s annual saving to Kevin’s annual retirement expense, the entire retirement picture can look very different.  If we assume that the sum of Kevin & his wife saving is about the same as their retirement expenses which will probably be more than $30000 every year, we can simply count the number of years of savings to find out how many years they can retire.  And that’s 6 years from 24 to 30, 18 (or probably less) years of savings from 30 to 48, and 10 years from 55 to 65.  That’s total of 34 years of savings for 25 years of retirement.  Boy, I haven’t counted the college debt at the time of graduation, and I forgot about buying a house to live.  But for the house, I would also count the housing equity as part of your saving, more in terms of the mortgage that you have paid down, and less in terms of equity due to the current high housing price.  So you can “keep” part of your saving in the house, and reverse mortgaging your equity at the end.  It’s almost like another bank account.

So with ratio of 1, that’s 34-25 = 9 years extra savings, either for your heir, or for your margin of errors, such as discounting the first 5 year savings when the kids are 0 to 5, or discounting for negative saving years when they’re in college.  Now, if you have spent thru your paycheck from 24 to 30, you have just made your margin of errors to be pretty close to zero.

For singles, the scenario is much better.  There are no kids to raise, nor kids’ college expenses to pay.  All the increase in salary earning can go towards extra saving (& inflation), not counting the extra 7 prime years of age 48 to 55.

As for myself, my current saving rate is about $45K, and my estimated retirement expenses are about $31K, summing from my current budget, plus doubling the travel expenses and tripling the medical insurance and doubling the car insurance, and subtracting out any direct kids’ related expenses.  I also add in property tax.  My saving to retirement expense ratio is slightly better than 1, at almost 1.5.

If you want to put in all the details of your retirement planning, including the inflation rate and investment return, existing asset and liability, you can use my retirement calculator.  You can use it to estimate when you can retire.  It’s what I use personally, and it’s very comprehensive, yet simple.

Bottom line, it’s never too late to start saving now.  It is far better to have some savings set aside already, then to worry about whether you can hit your retirement saving goal in time.

All About Inflation

Modern money is paper money since the world came off from the gold standard in early 1900. One problem with paper money is that it is based upon confidence and trust, which can be fickle and fleeting sometimes. When the confidence is suddenly gone, then you have an Asian currency crisis or Mexican Peso crisis. The other serious problem with paper money is that government can print it in unlimited quantity. Pretty much with any forms of government human can conceive of, all forms of government leads to monetary inflation. The basic reason is that money can translate into power, and all forms of government are power-hungry. With more money, politicians can please their voters in various ways they choose. And so they either choose to print more, or borrow more, and both ways are inflationary. The cycle of more money more power, and then more power more money is self-perpetual. In this process, paper money gets debased constantly, and therefore you have inflation.Monetary inflation complicates the savers’ goal. Without inflation, the savers can simply save and store his or her wealth in whatever form he or she chooses. He or she does not need to worry about losing purchasing power of his or her dollars in cash. However, with constant inflation even when it’s gradual, over time government dilutes the value of the dollar and steals from savers.

With inflation, the price of everything goes up, including the wage of the labor. The lower class people who have minimal savings don’t have much to lose. (Forgive me to use this political incorrect word “class”. ) Their wage is usually behind the curve of inflation, and therefore, their lives are a constant struggle to catch up with the last payment that is due. The middle class people who have some savings face similar situation as the lower class people. In a low inflationary environment, they can try to maintain their purchasing power with the limited venues of investment choices that they have. But the most distinct advantage of middle class compared to lower class is that their major asset is their home which goes up in value via inflation. Since their mortgage debt gets devalued relatively speaking versus the prevailing wage, servicing the debt gets easier over time. The upper middle and upper class people, because of their more plentiful resources, usually have substantial wealth invested in assets and/or owning business that will go up in value in an inflationary environment. Inflation always benefits more to the people who get their money first, such as businesses or government, while the inflationary effects propagates last to the wage earners.

From the calculator provided from US Federal Reserve, you can see that from 1913 to 2006, the value of US$1 is equivalent to $20.45 today’s dollar, an astounding 95.1% loss in purchasing power, but only about 3.3% inflation rate compounded annually. Is your bank account yielding more than 3.3%? And government does not forget to tax you on this imaginary inflated value, be it the capital gain or interest or dividends. At a marginal tax bracket of 35%, you need to have a return of 5.07% before tax to beat this gradual inflation rate. That is why if you don’t put your money in some inflation-hedged assets, you can seldom get ahead.