Sunday, September 26, 2010

Problem Solving III (10 Habits of Mind for Investors)

This material was originally posted by a mathematics teacher.

Barry Ritholtz author of the Big Picture was so impressed with its potential application for investors he posted it on his blog without any changes.

I think it is the best list of problem solving tips I have seen.

1. Pattern Sniff
. . .A. On the lookout for patterns
. . .B. On the lookout for shortcuts

2. Experiment, Guess and Conjecture
. . .A. Can begin to work on a problem independently
. . .B. Estimates
. . .C. Conjectures
. . .D. Healthy skepticism of experimental results
. . .E. Determines lower and upper bounds
. . .F. Looks at small or large cases to find and test conjectures
. . .G. Is thoughtful and purposeful about which case(s) to explore
. . .H. Keeps all but one variable fixed
. . .I. Varies parameters in regular and useful ways
. . .J. Works backwards (guesses at a solution and see if it makes sense)

3. Organize and Simplify
. . .A. Records results in a useful way
. . .B. Process, solutions and answers are detailed and easy to follow
. . .C. Looks at information about the problem or solution in different ways
. . .D. Determine whether the problem can be broken up into simpler pieces
. . .E. Considers the form of data (deciding when, e.g., 1+2 is more helpful than 3)
. . .F. Uses parity and other methods to simplify and classify cases

4. Describe
. . .A. Verbal/visual articulation of thoughts, results, conjectures, arguments, etc.
. . .B. Written articulation of arguments, process, proofs, questions, opinions, etc.
. . .C. Can explain both how and why
. . .D. Creates precise problems
. . .E. Invents notation and language when helpful
. . .F. Ensures that this invented notation and language is precise

5. Tinker and Invent
. . .A. Creates variations
. . .B. Looks at simpler examples when necessary (change variables to numbers, change values, reduce or increase the number of conditions, etc)
. . .C. Looks at more complicated examples when necessary
. . .D. Creates extensions and generalizations
. . .E. Creates algorithms for doing things
. . .F. Looks at statements that are generally false to see when they are true
. . .G. Creates and alters rules of a game
. . .H. Creates axioms for a mathematical structure
. . .I. Invents new mathematical systems that are innovative, but not arbitrary

6. Visualize
. . .A. Uses pictures to describe and solve problems
. . .B. Uses manipulatives to describe and solve problems
. . .C. Reasons about shapes
. . .D. Visualizes data
. . .E. Looks for symmetry
. . .F. Visualizes relationships (using tools such as Venn diagrams and graphs)
. . .G. Vizualizes processes (using tools such as graphic organizers)
. . .H. Visualizes changes
. . .I. Visualizes calculations (such as doing arithmetic mentally)

7. Strategize, Reason and Prove
. . .A. Moves from data driven conjectures to theory based conjectures
. . .B. Tests conjectures using thoughtful cases
. . .C. Proves conjectures using reasoning
. . .E. Looks for mistakes or holes in proofs
. . .F. Uses indirect reasoning or a counter-example (Park School)
. . .E. Uses inductive proof

8. Connect
. . .A. Articulates how different skills and concepts are related
. . .B. Applies old skills and concepts to new material
. . .C. Describes problems and solutions using multiple representations
. . .D. Finds and exploits similarities between problems (invariants, isomorphisms)

9. Listen and Collaborate
. . .A. Respectful to others when they are talking
. . .B. Asks for clarification when necessary
. . .C. Challenges others in a respectful way when there is disagreement
. . .D. Participates
. . .E. Ensures that everyone else has the chance to participate
. . .F. Willing to ask questions when needed
. . .G. Willing to help others when needed
. . .H. Shares work in an equitable way
. . .I. Gives others the opportunity to have “aha” moments

10. Contextualize, Reflect and Persevere
. . .A. Determines givens
. . .B. Eliminates unimportant information
. . .C. Makes and articulates reasonable assumptions
. . .D. Determines if answer is reasonable by looking at units, magnitudes, shape, limiting cases, etc.
. . .E. Determines if there are additional or easier explanations
. . .F. Continuously reflects on process
. . .G. Works on one problem for greater and greater lengths of time
. . .H. Spends more and more time stuck without giving up

Saturday, September 25, 2010

Problem Solving II (Vision Motivation Persistence)

This is a little bit of Tony Robbins,, a kung fu story, and a tip of the hat to Dave Ramsey.

I have never been completely comfortable with Dave Ramsey’s theory that financial security and peace is 20% knowledge and 80% behavior. This kind of assumes that people are stupid rather than ignorant. As the t-shirt says, ignorance can be fixed. Stupid is forever. I have always had good money management skills (thanks to my parents). As I grew older, I have tried to learn how to create wealth, as well as manage the money that comes my way. It is hard for me to realize anyone else would be any different. But then there is my problem with weight. I know I should eat celery sticks and drink water. Instead, I eat hot pastrami sandwiches and drink beer, so what should I expect?

This approach to problem solving begins with vision, a clear picture with the way things should be. It collapses step 1 and step 2 of the spiral method into a detailed mental image rather than spending a lot of time understanding the problem and developing something like a project management plan. Really this is probably OK. Most of us know where our goal lies and where we are currently located. I know that to get to Florida from Maryland, I need to head south. When I start out I may not know whether to take US-1 or I-95. I may not even have a map, but if I keep heading south and asking questions, I will get to Florida. (the pf stands for Personal Finance) calls the second step in this approach, “Getting Mad, Zealous, and Passionate.” There is nothing in the spiral method about emotional commitment, nothing to blast you from step 2 to step 3, implementing the solution. In my own personal experience, I needed that kind of energy to get me into a house. At that time my rent was already approaching the price of a house payment. One year, my rent jumped over 10% when my lease ended. That was it. Even though I didn’t quite have enough money to buy a house, I did it anyway. At the time 10% down was standard and there were about $7,000 in closing costs. We had saved the required $17,000 with a few hundred to spare, but there was not really enough left to be able to pay all our regular bills with certainty. I borrowed $3,000 from my father-in-law until I had the cash flow situation under control.

The last step is persistence. Losing weight, getting out of debt, or saving enough money to pay for a house is hard work. There will be setbacks along the way, weeks when your weight goes up even when you are staying on your diet, unexpected expenses that wipe out several months of effort. Continuing to do the right thing day after day, week after week, without much positive feedback is a wretched business.

A White Crane master, Dr. Yang, Jwing-Ming tells this story. “I felt so depressed after comparing myself with one of my most talented classmates. I always felt awkward compared to him. I told my master about this. He again looked at me and said, “Little Yang! The reason you want to train is because you want to train. It is the same as plowing a field. When you plow, you simply do it for your harvest. Why do you look around? If you are ahead of others, you will be proud of yourself, you will be satisfied, and you will become lazy. If you are behind, you will become depressed and despise yourself. Why don’t you just bow your head and keep plowing? Do not look around. Just keep plowing. Until one day…He pointed his finger towards my face…when you get tired and take a break, suddenly you realize that there is nobody around you. You have left all the others far far behind and you cannot even be seen.”

Friday, September 24, 2010

A $1,000 Car

$1000 car's life was through,
'bought 50,000 miles 'fore it got to you.
Oh why did I ever buy,
A $1000 car.

Sometimes I come across something that is so good, I just can’t stand it. I heard a song on the radio, titled “A Thousand Dollar Car” by the Bottle Rockets. It made me think of some the more extreme advice I have read in “get out of debt” financial discussions. Authors have suggested selling your current vehicle to get out from under car payments and buying a thousand dollar car. The principle is sound but where to draw the line.

A $1000 car ain't even gonna roll,
til you throw at least another thousand in the hole.
Sink your money in it, and there you are
the owner of a 2,000 dollar 1,000 dollar car.

In 1973 I bought a 1967 Chevrolet for $600. It had about 90,000 miles on the odometer. In those days a car was lucky to make it to 100,000 miles. It seemed to be in pretty good shape and the owner promised me he had prayed frequently for that car (really). I wrote out the check and bought a $600 car. The window frames rusted out, allowing water to leak into the car and the trunk. The inside door handle broke, so I had to open the door for my wife when we took that car. That was funny. Women would sigh and give me romantic looks, as I chivalrously opened the door for my wife.

$1000 car is gonna let you down,
More than it's ever gonna get you around.
Replace your gaskets and paint over your rust,
You'll still end up with something that you'll never trust.

I named that Chevrolet Betty Lou. She continued to run for about 7 years. It certainly wasn’t reliable by modern standards, but it never left me stranded. At one point, I had 3 cars, so I lent her to a friend who needed a second car for his wife. Once I received a call from a wrecker. One of wheels broke off that car and it had been abandoned on one of the main streets in Columbia, SC. Of course I discovered my friend was in the process of taking care of the problem. Over the course of the next year or so he put over $500 into that car. At that point I told him to keep it. He insisted that he give me something, so I sold him the car for $50 dollars. Later, he sold it to a man who wanted to turn it into a hot rod. The new owner went to prison. After that, I don’t know what became of Betty Lou.

Just for grins, I went to value of a dollar by year calculator. One 1973 dollar had the buying power of $5.08 2010 dollars. That sounds a little low. I would have guessed $6.00, but let’s go with the lower number. My $600 dollar car would cost $3,048 today. That sounds just about right. I have seen $3,000 cars that would be fine for someone trying to get out of debt, but I have to agree with song’s composer.

If you've only got a $1000.
You ought to just buy a good guitar.
Learn how to play it it'll take you farther,
than any old $1000 car.

Listen to the song at

Problem Solving I (The Spiral Method)

I would like to share at least three methods for problem solving. As is often the case in this blog, they will not contain material that you will find all that shocking or original, but maybe revisiting something you already know might prove of value in times of trouble.

The Basic Engineering Method – Sometimes Called the Spiral Development Model

Step 1- Understand the Problem

This is not nearly a simple as it sounds. Understanding a problem is a complex layered process. For example, “I don’t have enough money,” is not really the problem. If you don’t have any expenses, money is not a problem. Ask yourself why is not having enough money a problem. Perhaps the answer is, I have too many debts. Why do you have too many debts? Perhaps the answer is, “I bought things I didn’t need with money I didn’t have and then I got sick and lost my job.” There are at least four dimensions to this particular problem, spending habits, existing debt, health, and unemployment. Ask how have my spending habits contributed to this problem. Perhaps there is a psychological dimension to this problem called compulsive shopping. I think you get the idea.

Step 2- Propose a Solution

Once you have enough information, begin to construct a solution. It does not have to be perfect, complete, or address all the issues in step 1. In this particular example, visiting a free clinic, calling all creditors in an attempt to negotiate reduced payments, and contacting anyone you might know who could help you find a new job might be a proposed solution.

Step 3- Implement the Solution

Many people with problems spend a great deal of time on steps 1 and 2 (particularly Step 1), but never get to step 3. Talking to others about your problems is necessary but it is not an end in itself. At some point a proposed solution has to be implemented.

Step 4- Examine the Results

Once you are implementing your planned solution, examine the results you are getting. Generally, life is a pretty quick feedback mechanism. It usually does not take all that long to determine if your efforts are producing the results you desire. If your initial solution is working, great, keep on working that solution. If you are not getting everything you want as quickly as you want, return to step 1. Did I really understand the problem? Begin over again or continue to uncover layers in the Understand the Problem step. Perhaps you have not been able to find a job in your hometown, because there are no jobs in your hometown. That might lead to a proposal to expand your job search horizon.

I think you get the idea. Wikipedia observes, “The spiral model was defined by Barry Boehm in his 1980 article "A Spiral Model of Software Development and Enhancement." This model was not the first model to discuss iterative development, but it was the first model to explain why the iteration matters.”

Friday, September 10, 2010

When the Student is Ready, The Teacher Will Appear

A certain man caught a bird in a trap.

The bird says, “Sir you have eaten many cows and sheep in your life and you are still hungry. The little bit of meat on my bones won’t satisfy you either. If you let me go, I will give you three pieces of wisdom. One I’ll say standing on your hand. One on your roof. And one I’ll speak from the limb of that tree.

The man was interested. He freed the bird and let it stand on his hand.

“Number one: Do not believe in absurdity, no matter who says it.

The bird flew and lit on the man’s roof. “Number two: Do not grieve over what is past. It’s over. Never regret what has happened.

“By the way,” the bird continued, “In my body there is a huge pearl weighing as much as ten copper coins. It was meant to be an inheritance for you and your children. But now you have lost it. You could have owned the largest pearl in existence, but evidently it was not meant to be.”

The man started wailing like a woman in childbirth. The bird said, “Didn’t I just say, don’t grieve for what’s in the past, and also, don’t believe in absurdity. My entire body does not weigh as much as ten copper coins. How could I have a pearl that heavy inside me?”

The man came to his senses, “Alright. Tell me number three.”

“Yes, you’ve made such good use of the first two!”

“Don’t give advice to someone who is groggy and falling asleep. Don’t throw seeds on the sand.”

The story was written by Rumi, the 13th century Persian poet, jurist, theologian, and mystic.

Once again, I have been thinking about how difficult it can be to find teachers who are willing to actually educate others on how to use money and create wealth, without enriching themselves at their student’s expense. This would be OK if it represented a fair exchange of value, but often the slick self promoting scoundrels on the infomercials are just this side of what the law allows. Sometimes they are criminals and end up in prison where they belong.

My church is finally considering the possibility of offering one of the basic financial literacy courses to the congregation and the community, a no brainer I have been promoting for many years. In this particular case, I have been asked to look into Dave Ramsey’s Financial Peace University. Of course I am somewhat acquainted with Dave Ramsey and his ideas. They are pretty typical of most Christian financial teachers. These courses teach common sense ideas like avoiding debt, budgeting, thrift, deferring gratification, and long range financial planning. The box costs $93 per family unit. That would include husband, wife, and teenaged children. It contains 13 lessons on CD, a book, some budgeting paraphernalia, and some “bonus” material. The “university” itself consists of 13 weekly meetings featuring Dave lecturing on DVD followed by small group meetings (to be coordinated by yours truly if our church decides to offer this course) that explore what has just been taught in the lecture. I expect it will be well worth $93 especially if the students are willing to learn and to apply what they learn to their lives.

In financial matters as in all areas of life, be alert, always ready to learn something new from someone who knows something you do not know. Seek wisdom wherever she can be found. It is OK for a teacher to make a living, but beware of the coyotes who ask you to believe absurd nonsense like their $3,000 trading software will allow you to become an instant millionaire. Don’t spend too much time regretting missed opportunities, more will come along, and this time you will be ready to recognize it. If you are really lucky you might find a teacher who understands that wisdom is the only commodity he can give away without becoming any poorer. For in the end, it is what we can give to our community that makes us truly happy. Perhaps the day may come when you can help someone with their first step out of debt or their first fearful attempt to begin an investment program.

Proverbs 13:20

He who walks with the wise grows wise, but a companion of fools suffers harm.

Monday, September 6, 2010

I Gotta' Win the Lottery and Move to Hawaii

From the news of the extremely weird:

The Italian towns of Ficara in Messina and Anguillara in Lazio, faced with growing budget shortfalls have decided to balance their budgets, fund public projects now brought to a standstill by the economy, and lower their tax rates with winnings from the lottery. Really! Governments have become so desperate; they are not only selling lottery tickets. They are buying lottery tickets. To be fair the city fathers of these two municipalities, the sums to be invested in lottery tickets are 5 and 15 Euros a week. These sums of money are not enough to really matter, but are things really that bad in Ficara and Anguillara?

One of my go to lines after a particularly bad day is, “I’ve gotta’ win the lottery and move to Hawaii.”

I used this line recently on the owner of the local wine and beer store. He replied, “You never buy any tickets. You can’t win, if you don’t play.” I laughed. It is pretty close to the truth. I buy about two tickets a year (maybe).

When the prize gets really big, I think, “Ah, Why not?” Sadly, at local stores I see regulars playing the lottery with money they can not afford to lose. It has been my observation that most lottery tickets are sold to desperate or discouraged individuals who believe that any efforts they can make to improve their situation are pointless. Instead of taking arms against a sea of troubles and, by opposing, end them, these unhappy souls buy lottery tickets, lots of lottery tickets.

Laura Rowley recently reported on some findings by researchers a several universities. Evidently, a surprisingly large number of lottery winners (5.5%) declare bankruptcy within five years of winning. Small winners tended to go bankrupt more quickly than big winners. In this particular sample $65,000 in cash was the median big prize. Laura observes, “That would be enough, on average, to pay off all unsecured debt or boost the equity in new or existing assets. Instead, the big jackpots simply evaporated.”

Apparently there are two reasons that explain this phenomenon. First, they winners are not use to handling large sums of money and make mistakes. They are not financially literate. Hence, they do not use the money wisely. The authors of the study believe the more important reason can be termed “mental accounting.” One of the authors, Mark Hoekstra observes, "We treat 'found money' differently than money we earn. So if you find $20 on the sidewalk, you may decide to blow it on a nice dinner, whereas if you earned it you wouldn't have done that."

The authors of this study believe that their findings have policy implications for governments dealing with heavily indebted consumers and homeowners with upside down mortgages. Mark Hoekstra says, “It appears the simplest solution-giving them cash-doesn’t enhance longer term financial stability and only postpones, rather than avoids bankruptcy.”

Laura Rowley adds, “The lottery findings are consistent with a 2007 research paper that showed consumers initially used their 2001 federal rebate checks to reduce debt, but eventually debt returned to its pre-rebate level.”

Hoekstra concludes, “Our research suggests that perhaps there is something more systematic about the types of people who get themselves into financial trouble -- and the appropriate policy prescription for helping them out is going to be considerably more complex than giving them additional resources.”

Even though I don’t think Solomon would have much good to say about lottery tickets, I will probably continue to buy one or two a year and dream of retirement in Hawaii.

Here is a sample of king’s thoughts on such matters.

Proverbs 13 11

Dishonest money dwindles away, but he who gathers money little by little makes it grow.

Proverbs 28 19-20

He who works his land will have abundant food, but the one who chases fantasies will have his fill of poverty.

A faithful man will be richly blessed, but one eager to get rich will not go unpunished.

Labor Day 2010

When I attended college the first time around (1969-1973) I learned about something called, theoretical full employment. At that time theoretical full employment allowed for a 3% unemployment rate. Academic economists noted that there is always some churn in the economy. People get fired or quit their jobs in disgust. Sometimes people just want to leave wherever they live and find someplace better to start over. I wondered what economists might consider theoretical full employment in 2010. I didn’t find much except a book titled, “Full Employment Abandoned: Shifting Sands and Policy Failures” published in 2008. Evidently the concept of theoretical full employment, once given at 2% I discovered, has been replaced by a new concept, structural unemployment. The definition of structural unemployment is given as, “Joblessness caused not by lack of demand, but by changes in demand patterns or obsolescence of technology, and requiring retraining of workers and large investment in new capital equipment,” ( In recent decades, structural unemployment was expected to run at about 5% as technology and regulation destroyed old jobs and created new jobs. In this model, a constant level of unemployment is primarily generated by a mismatch in workers who lack skills required for new jobs.

In “9% is Now Full Employment in America,” an extremely disturbing article written by Michael James McDonald, the author contends that 20,000,000 U.S. jobs have been exported to foreign countries. Most of these jobs were relatively stable, high paying, wealth producing jobs that provided men and women of average ability a middle class life style. They are gone.

In January of 2006 Warren Buffett said, “The U.S. trade deficit is a bigger threat to the domestic economy than either the federal budget deficit or consumer debt and could lead to ‘political turmoil.’ Pretty soon, I think there will be a big adjustment.”

One year ago on Labor Day, U-3 unemployment stood at 9.7%. Today that measure is 9.6%. The more realistic measure U-6 was 16.8% in 2009. Today it is 16.7%. Approximately 26.3 million Americans are unemployed, marginally attached to the work force, or working less than full time because no full time work is available. These numbers are low because they only include individuals actively seeking employment who are reporting their efforts to a government agency. It does not include many young people who have yet to find their first job, older workers who were forced into early retirement, or the plain discouraged who have just given up.

It isn’t that the government hasn’t tried. Trillions of dollars of borrowed money have been spent on corporate bailouts, stimulus programs, mortgage modifications, and ideas like cash for clunkers and an $8,000 tax credit for first time home buyers. It hasn’t worked. McDonald observes, “Global conditions and factors now control the American economy more than what is happening internally. It also puts in doubt the tried and true, standard solutions the government uses. Stimulation packages no longer work because there is now little to stimulate. They are using old internal solutions to fix an economy now controlled by external conditions. Until the government faces this and begins to solve the real issue – the long term detrimental effects of globalization on the American economy – nothing significant can occur.”

Today, over 26 million Americans are unemployed. 41,275,411 Americans are receiving food stamps, now called the Supplemental Nutrition Assistance Program. As a country, we are facing a very bad situation with no easy solutions. On this Labor Day, let us take at least a moment, look into our own hearts, confess our sins, and ask God to extend his hands in mercy to our Nation. Let us try and understand that when we stand with Christ we can not separate ourselves from our neighbors.

Psalm 70

[1] Make haste, O God, to deliver me; make haste to help me, O LORD.
[2] Let them be ashamed and confounded that seek after my soul: let them be turned backward, and put to confusion, that desire my hurt.
[3] Let them be turned back for a reward of their shame that say, Aha, aha.
[4] Let all those that seek thee rejoice and be glad in thee: and let such as love thy salvation say continually, Let God be magnified.
[5] But I am poor and needy: make haste unto me, O God: thou art my help and my deliverer; O LORD, make no tarrying.

Sunday, September 5, 2010

You Got To Know When to Hold 'em

“You got to know when to hold ’em, know when to fold ’em,”
The Gambler

Recently, Calculated Risk, an excellent financial blog that often focuses on Real Estate told the story of an accidental landlord. In a market rapidly heading South, he couldn’t sell his house at the price he wanted, so he decided to rent the house until the market recovered. Earlier this year, he put the house back on the market, at a substantially lower price. It didn’t work. Nobody wanted to pay that price. Once again he rented the property and hoped for a better day. Currently, he dropped the price again and put his home back on the market. It isn’t selling. The owner believes he will pull it back off the market and hope for a better day. Real Estate investors call the phenomenon, “chasing the market down.” It doesn’t work.

People do this because they fall in love with their homes, believing that the market must value such a wonderful property as much as the owner. They get a price stuck in their head, and continue holding on to that price even as the market tanks. I have seen this happen a couple of times in my neighborhood. Once, after several years of frustration, the owners finally sold at $100,000 less they wanted. The second example ended in a successful short sale, if a short sale can ever be considered successful.

People who buy and sell stocks can fall into the same trap. I have a pretty good idea when to buy a stock but sometimes I exhibit the tendency to hold on, hoping for a better day, when I should just take a tax loss and walk away. Sometimes there is more than a little ego involved. Sometimes I just fall in love with a stock. Neither ego nor love should ever be a factor in an investment decision. With General Electric, I bought the stock after it had dropped, at $34.79. General Electric was a dividend aristocrat. Under Neutron Jack Welch, GE developed the most ruthlessly efficient management this side of the Waffen SS. Ah the technology, I just loved their turbines, locomotives, and big box medical equipment.

What I didn’t realize was I did not own an industrial/technological conglomerate. I owned a finance company with many dubious loans and questionable customers. As GE continued to head down, I bought a little more at $28.75 and then a little more at $24.25. I was certain that given their AAA credit rating, superior management, and impregnable dividend things would get better. Things didn’t get any better. In fact GE lost their coveted AAA credit rating and management was forced to cut the dividend. The price tanked. Finally, I bought a little more at $12.49. Today GE sells for $15.39 and pays a 3.12% dividend. Clearly, my handling of this investment is the worst performance of my career.

For the record, today GE is rated B by Schwab, Outperform by Credit Suisse, Buy by Ned Davis, Hold by Argus, Four Stars by Standard and Poor’s, Outperform by Reuters, and Neutral by Market Edge. I continue to hold. I am also comforted that Warren Buffet, the genius, bought $3 billion worth of GE preferred near the bottom. I also must admit he got a much better deal than is available to the average investor.

I bought more shares in a number of companies during the great debacle of 2008-2009. In the other instances, it paid off. But there was a difference, I wasn’t in love with any of those stocks and I didn’t feel as though my ego was tied up in owning them. Earlier, I made the same mistake with a small holding of Corning. After watching the stock go up and down for several years, I finally grew disgusted, gave up, and sold my shares at a loss. I held on to Corning for longer than I should, because I was in love with their technology. I should have learned something about myself from that inexpensive lesson. Hopefully, I have finally learned my lesson.

From an article by Harry Domash, entitled, Nobel winner unearths 5 common investing mistakes; the author reports, “Daniel Kahneman, a psychology professor at Princeton University, won the Nobel Prize in economics for his attempts to explain the quirkiness that governs our financial decisions…. The truth is that investors don’t like to recognize a loss. I know I don’t. One strategy they use is to wait for a stock or a mutual fund to get back to even, reasoning that they haven’t lost anything. This shortsighted approach ignores the opportunity cost, or what else they might have done with their money in the meantime. And the reluctance to recognize losses affects professional managers as well as amateur investors, Kahneman says. Accepting a loss and moving on is very difficult.”

“Now ev’ry gambler knows that the secret to survivin’
Is knowin’ what to throw away and knowing what to keep.
’cause ev’ry hand’s a winner and ev’ry hand’s a loser,
And the best that you can hope for is to die in your sleep.”