Rich Dad Poor Dad

by Robert T. Kiyosaki

Introduction

The author has two “Dad”, one is his real dad, and the other is his friend’s dad. Both his dad and his friend dad are friends as well. For his two dads, one is rich and the other is poor, financially.

One work for bureau and as a professor at university. The other works for his own and strike before attending to college.

One dad had a habit of putting his brain to sleep when it came to finances, and the other had a habit of exercising his brain. For example, one says “I can’t afford it”, the brain stops working. The other ask a question “How can I afford it”, you brain is put to work.

One wanted the author to study hard, earn a degree, and get a good job to earn money, want the author to study to become a professional, an attorney or an accountant, and to go to business school for MBA. The other encouraged the author to study to be rich, to understand how money works, and make money works for you per se.

The rich dad is the one without even a college degree.

The book is not to compare the ideas from the rich and poor dad, but discuss how the rich dad’s insight affects the author.

Chapter 1: The Rich Don’t Work for Money

  • Life is difficult. Life pushes all of us around. Some people give up. A few learn the lesson and move on. They welcome life pushing them around. To these few people, it means they need and want to learn something. Learn and move one from the life, instead of blaming. Do not blame, you only are blaming or pushing back against the boss, the job, the wife. However, it is the life that pushing.

    Stop blaming the life, instead change yourself, learn something, and grow wiser.

  • The poor and the middle class work for money. The rich have money work for them.

  • Avoid one of life’s biggest trap. Some can see things most people never have the benefit of seeing because their vision is too narrow. Most people never see the trap they are in.

  • The Rat Race: The pattern of get up, go to work, pay bills; get up, go to work, pay bills. People’s lives are forever controlled by two emotion: fear and greed. Offer them more money and they continue the cycle by increasing their spending.

    However, do not get in trapped by the Rat Race, do not get trapped by those two emotions: fear and greed.

    Tell yourself the truth what you feel not the emotion.

    Do not be afraid of losing money.

    Avoid the trap caused by those two emotions, fear and desire. Use them in your favour, not against you.

Chapter 2: Why Teach Financial Literacy?

  • Rule #1: You must know the difference between an asset and a liability, and buy assets.

    Rich people acquire assets. The poor and middle class acquire liabilities that they think are assets.

    Asset put money in your pocket. Nice, simple, and usable.

    If you want to be rich, simply spend your life buying or building assets. For figures below, I/S of the Rich, Middle class, and Poor are shown.

    img

    For the Rich Dad, real estate is on the liability side. Money flow to expense, and run away.

    For the Poor Dad, real estate in on the asset side. Money flow as income, get into the I/S.

  • Why the Rich Get Richer?

    The asset column generates more than enough income to cover expenses, with the balance reinvested into the asset column. The asset column continues to grow and, therefore, the income it produces grows with it.

  • Why the Middle Class Struggle?

    Their primary income is through their salary. As their wages increase, so do their taxes. Their expenses tend to increase in proportion to their salary increase: hence, the phrase “the Rat Race”. They treat their home as their primary asset, instead of investing in income-producing assets.

  • Work for Your Own.

    • You work for the Company:

    Employees make their business owner or the shareholder rich, not themselves. Your efforts and success will help provide for the owner’s success and retirement.

    • You work for the Government:

    The government takes its share from your paycheck before you even see it. By working harder, you simply increase the amount of taxes taken by the government. Most people work from January to May just for the government.

    • Your work for the Bank:

    After taxes, your next largest expense is usually your mortgage and credit-card debt.

    Build an asset column that makes you financially independent. If you quit the job today, it still covers your monthly expenses with the cash flow from the asset.

  • Invest the excess cash flow from your assets reinvested into the asset column. The more money that goes into the asset column, the more asset column grows.

  • In short:

    • The rich buy assets
    • The poor only have expenses.
    • The middle class buy liabilities they think are assets.

Chapter 3: Mind You Own Business

Ray Kroc, the founder of McDonald’s, is not doing hamburger business. The real business behind it is the real estate.

  • Mind your own business. Your business resolves around your asset column, not your income column.

  • Keep expenses low, reduce liabilities, and diligently build a base of solid assets.

  • Categories of real assets the author mentioned: (in the view of the author)

    • Business that do not require my presence I own them, but they are managed or run by other people. If I have work there, it’s not a business. It becomes my job.
    • Stocks
    • Bonds
    • Income-generating real estate
    • Notes (IOUs)
    • Royalties from intellectual property such as music, scripts, and patents.
    • Anything else that has value, produces income or appreciates, and has a ready market.

    When the author is a boy, The educated dad (poor dad) encouraged the author to find a safe job. But, the rich dad encouraged him to begin acquiring assets that he love.

    Start a company, not run it. Stocks are the similar rationale.

    Minding your business doesn’t mean starting a company, though for some people it will. Instead, your business revolves around your asset column, not your income

  • Luxuries.

    An important distinction is that rich people buy luxuries last, while the poor and middle class tend to buy luxuries first. The poor and the middle class often buy luxury item like big houses, diamonds, furs, jewelry, or boats because they want to look rich. They look rich, but in reality they just get deeper in debt on credit.

    Buying a luxury on credit often causes a person to eventually resent that luxury because the debt becomes a financial burden.

Chapter 4: The History of Taxes and The Power of Corporations

Though the popular sentiment is that the rich should pay more in taxes and give to the poor, in reality it is the middle class that is heavily taxed, especially the educated upper-income middle class.

What historical dates fail to reveal is that both of taxes were initially levied against only the rich. That idea of taxes was made popular, and accepted by the majority, by telling the poor and the middle class that taxes were created only to punish the rich. This is how the masses voted for the law, and it became constitutionally legal.

Although it was intended to punish the rich, in reality it wound up punishing the very people who voted for it, the poor and middle class.

The poor dad is a government bureaucrat, the rich dad is a capitalist. They get paid, and the success is measured on opposite behaviour. The poor dad get paid to spend money and hire people. The more he spends and the more people he hires, the larger his organisation becomes. In the government, a large organisation is a respected organisation. And, as the government grows, more and more tax dollars are needed to support it.

On the other hand, with in the rich dad organisation, the fewer people he hire, and less money he spend, the more he is respected by the investors.

The rich dad said that government workers were a pack of lazy thieves. The poor dad said the rich were greedy crooks who should be made to pay more taxes.

  • Form a Company. A corporation is merely a legal document that creates a legal body without a soul. Using it, the wealth of the rich was once again protected. It was popular because the income-tax rate of a corporation is less than the individual income-tax rates. In addition, certain expenses could be paid by a corporation with pre-tax dollars.

    enter image description here

    In addition, even been a leader is still working for others. Why not own a company to let others work for you.

  • Financial IQ: get certain areas of expertise:

    1. Accounting
    2. Investing
    3. Understanding markets
    4. The laws:
    • Tax advantages: a corporation can do many things that an employee cannot, like pay expenses before paying taxes. A corporate earns, spends everything it can, and is taxed on anything that is left. It’s one of the biggest legal tax loopholes that the rich use. For example, by owning your own corporation, your vacations can be board meetings in Hawaii. Car payments, insurance, repairs, and health-club memberships are company expenses. Most restaurant meals are partial expenses. It’s done legally with pre-tax dollars.
    • Protection from lawsuits

In summary:

  • Business Owners with Corporations:
    1. Earn +
    2. Spend –
    3. Pay Taxes %
  • Employees Who Work for Corporations
    1. Earn +
    2. Pay Taxes %
    3. Spend –

Chapter 5: The Rich Invest Money

Once we leave school, most of us know that it is not so much a matter of college degrees or good grades that count. In the real world outside of academics, something more than just grades is required. That label decides one’s future much more than school grades do.

image-20240612125535619

image-20240612125553769

  • Financial Intelligence is made up of four main technical skills, again.
    1. Accounting
    2. Investing
    3. Understanding markets
    4. The law
  • The overall philosophy is to plant seeds inside my asset column. The author start small and plant seeds. Some grow; some don’t. The author use two main vehicles to achieve financial growth: real estate (including REIT) and small-cap stocks.
    • The real estate is stable and slow-moving. The cash flow is fairly steady and has a good chance, if properly managed, of increasing in value. The beauty of a solid base of real estate is that it allows to take greater risks of then investing in stocks.
    • Some people says, you cannot buy real estate cheap. That is not the author’s experience. Even in New York or Tokyo, or just outskirts of the city, prime bargains are overlooked by most people, or within a short driving distance.
  • However, gain is together with risks. It is not gambling if you know what you’re doing. It is gambling if you’re just throwing money into a deal an praying.

  • Most people never win because they’re more afraid of losing. That is why I found school so silly. In school we learn that mistakes are bad, and we are punished for making them. Yet if you look at the way humans are designed to learn, we learn by making mistakes. We learn to walk by falling down. If we never fell down, we would never walk. The same is true for learning to ride a bike. I still have scars on my knees, but today I can ride a bike without thinking. The same is true for getting rich. Unfortunately, the main reason most people are not rich is because they are terrified of losing. Winners are not afraid of losing. But losers are. Failure is part of the process of success. People who avoid failure also avoid success.

  • There are two types of investors:

    1. The first and most common type is a person who buys a packaged investment. They call a retail outlet, such as a real estate company, a stockbroker, or a financial planner, and they buy something. It could be a mutual fund, a REIT, a stock or a bond. It is a clean and simple way of investing. An analogy would be a shopper who goes to a computer store and buys a computer right off the shelf.
    2. The second type is an investor who creates investments. This investor usually assembles a deal in the same way a person who buys components builds a computer. I do not know the first thing about putting components of a computer together, but I do know how to put pieces of opportunities together, or know people who know how.

    Try to be the second type. And, if you want to be the second type of investor, you need to develop three main skills.

    1. Find an opportunity that everyone else missed. You see with your mind what others miss with their eyes. For example, a friend bought this rundown old house. It was spooky to look at. Everyone wondered why he bought it. What he saw that we did not was that the house came with four extra empty lots. He discovered that after going to the title company. After buying the house, he tore the house down and sold the five lots to a builder for three times what he paid for the entire package. He made $75,000 for two months of work. It’s not a lot of money, but it sure beats minimum wage. And it’s not technically difficult.

    2. Organize smart people. Intelligent people are those who work with or hire a person who is more intelligent than they are. When you need advice, make sure you choose your advisor wisely

If you do not want to learn those skills, then being a type-one investor is highly recommended.

There is always risk, so learn to manage risk instead of avoiding it

Chapter 6: Work to Learn – Don’t Work for Money

  • Financial intelligence is a synergy of accounting, investing, marketing, and law. Combine those four technical skills and making money with money is easier than most people would believe. However, when it comes to money, the only skill most people know is to work hard.

    Instead of simply working for money and security, take a second job to learn a second skill.

  • Start to do it. Life is much like going to the gym. The most painful part is deciding to go. Once you get past that, it’s easy. There have been many days I have dreaded going to the gym, but once I am there and in motion, it is a pleasure. After the workout is over, I am always glad I talked myself into going.

  • Get to learn the skill of sales and marketing. The world is filled with talented poor people. They focus on perfecting their skills at building a better hamburger rather than the skills of selling and delivering the hamburger. Maybe McDonald’s does not make the best hamburger, but they are the best at selling and delivering a basic average burger.

    The ability to sell – to communicate to another human being, be it a customer, employee, boss, spouse, or child – is the base skill of personal success.

    The skills of selling and marketing are difficult for most people, primarily due to their fear of rejection. The better you are at communicating, negotiating, and handling the fear of rejection, the easier life is.

  • Do not trapped by one skill. The author’s educated dad became more trapped the more specialised he got. Although his salary went up, his choices diminished. Sooner after he was locked out of government work, he found out how vulnerable he really was professionally. It is like professional athletes who suddenly are injured or are too old to play. Their once high-paying position is gone, and they have limited skills to fall back on. The negative example is that, when it comes to money, the only skill people knows is working hard.

  • Rich dad encourage one to know a little about a lot, to work with people smarter, and to bring smart people together to work as a team. This is called a synergy of professional specialties.

  • Job security meant everything to the author’s educated dad. Learning meant everything to the rich dad.

    If you are unwilling to work to learn something new and instead insist on becoming highly specialized within your field, make sure the company you work for is unionized.

  • The main management skills needed for success are (1) management of cash flow, (2) management of systems, and (3) management of people. The most important specialised skills are sales and marketing. Communication skills such as writing, speaking, and negotiating are crucial to a like of success. Attend courses or buy educational resources to expand the knowledge.

Chapter 7: Overcoming Obstacles

  • Overcome fear

    Failure inspires winners. Failure defeats losers. This is the biggest secret of winners.

    If you have little money and you want to be rich, you must first be focused, not balanced. To gamble, not to diversify, if you have little money.

    Do not do what poor and middle-class people do: put their few eggs in many baskets. Put a lot of your eggs in a few baskets and FOCUS: Follow One Course Until Successful.

    Think like a Texan. Win big, lose big – it’s the attitude toward that loss that matters.

  • Overcome Cynicism

    Doubts and cynicism keep most people poor. Rich dad liked to say “Cynics criticise, and winners analyse.” Winners keep their eyes open and see opportunities everyone else missed.

    When someone says, “I don’t want to fix toilets”, I want to fire back, “What makes you think I want to?”. Nobody want to fixed toilet, but what if you have to do? The real estate is the investment vehicle. however if you focus on the toilets, instead of the investment, it makes you poor.

    That is what rich dad meant by “I-don’t-wants hold the key to your success.” Because I do not want to fix toilets either, I figured out how to buy more real estate and expedite my getting out of the Rat Race. The people who continue to say “I don’t want to fix toilets” often deny themselves the use of this powerful investment vehicle. Toilets are more important than their freedom.

    So, how the author manage his real estate, he shop hard for a property manager who does fix toilets. And by finding a great property manager who runs houses or apartments, well, the cash flow goes up.

  • In the stock market, I often hear people say, “I don’t want to lose money.” Well, what makes them think I or anyone else likes losing money? They don’t make money because they choose to not lose money. They are keeping themselves from making money by closing their minds to that investment vehicle.

  • Overcome Laziness.

    One of the most common forms of laziness is staying busy. Too busy to take care of your wealth, or health, or relationship. To be a little greed to cure the problem.

    Change your mindset from “I can’t afford it” to “How can I afford it?”

    Today, I often meet people who are too busy to take care of their wealth. And there are people too busy to take care of their health. The cause is the same. They’re busy, and they stay busy as a way of avoiding something they do not want to face. Nobody has to tell them. Deep down they know. In fact, if you remind them, they often respond with anger or irritation.

    Yet deep down they know they are avoiding something important. That’s the most common form of laziness: laziness by staying busy. So what is the cure for laziness? The answer is—a little greed.

    When the spirit is screaming, “Come on. Let’s go to the gym and work out.” And the lazy mind says, “But I’m tired. I worked really hard today.” Or the human spirit says, “I’m sick and tired of being poor. Let’s get out there and get rich.” To which the lazy mind says, “Rich people are greedy. Besides it’s too much bother. It’s not safe. I might lose money. I’m working hard enough as it is. I’ve got too much to do at work anyway. Look at what I have to do tonight. My boss wants it finished by morning.”

    So how do you beat laziness? Once again, the answer is a little greed.

  • Overcoming Bad Habits

    To be successful, you must develop successful habits. Poor dad always paid everyone else first and himself last, but he rarely had left over. Rich dad always paid himself first, even if he was short of money.

    He knew that creditors and the government would make a big enough flap if he didn’t pay them that it would motivate him to seek other forms of income to pay them. If he paid himself last, he wouldn’t feel that kind of productive pressure. Forcing himself to think about how to come up with the extra income to pay the creditors made him fiscally stronger.

    “So you see, after paying myself, the pressure to pay my taxes and the other creditors is so great that it forces me to seek other forms of income. The pressure to pay becomes my motivation. I’ve worked extra jobs, started other companies, traded in the stock market, anything just to make sure those guys don’t start yelling at me. That pressure made me work harder, forced me to think, and all in all, made me smarter and more active when it comes to money. If I had paid myself last, I would have felt no pressure, but I’d be broke.”

  • Overcoming Arrogance

    Rich dad said every time he had been arrogant, he had lost money because he thought that what he didn’t know wasn’t important.

    Many people use arrogance to hide their own ignorance. Do not be ignorance, find an expert in the field to educate yourself.

    What I know makes me money. What I don’t know loses me money.

Chapter 8: Getting Started

You must awaken the financial genius sleeping within in order to find these great deals. The culture has told us that the love of money is the root of all evil, that we just need to find a profession and work hard and the government will take care of us when we’re old. The message is still to work hard, earn money, and spend it, and when we run short, we can always borrow more — and that is why, for so many of us, our financial genius within is asleep.

But we must awaken that financial genius in order to find million-dollar deals of a lifetime. It is far easier to simply find a job and work for money, but that is not the path to wealth.

There are 10 steps as a process to develop your god-given powers, powers over which only you have control.

  1. Find a reason greater than reality: the power of spirit

    The author interviews a athlete who has super-human ambition and sacrifice. The athlete said “I do it for myself and the people I love. It’s love that gets me over the hurdles and sacrifices.”

    Without a strong reason or purpose, anything in life is hard.

  2. Make daily choices: the power of choice

    Invest first in education. In reality, the only real asset you have is your mind, the most powerful tool we have dominion over. Each of us has the choice of what we put in our brain once we’re old enough. You can watch TV, read golf magazines, or go to ceramics class or a class on financial planning. You Choose. Most people simply buy investments rather than first investing in learning about investing.

    The author loves CDs and audio books. The reason is he can easily review what he just heard. Instead of becoming arrogant and critical, he simply listened to that five-minute stretch at least 20 times, maybe more. By keeping the mind open, he understood why he said what he said.

    Arrogant or critical people are often people with low self-esteem who are afraid of taking risks. That’s because, if you learn something new, you are then required to make mistakes in order to fully understand what you have learned.

    There are so many “intelligent” people who argue or defend when a new idea clashes with the way they think. In this case, their so-called intelligence combined with arrogance equals ignorance. Each of us knows people who are highly educated, or believe they are smart, but their balance sheet paints a different picture. A truly intelligent person welcomes new ideas, for new ideas can add to the synergy of other accumulated ideas. Listening is more important than talking. If that were not true, God would not have given us two ears and only one mouth. Too many people think with their mouth instead of listening in order to absorb new ideas and possibilities. They argue instead of asking questions.

    The author take a long view on my wealth. He do not subscribe to the get-rich-quick mentality most lottery players or casino gamblers have. He may go in and out of stocks, but he is long on education. If you want to fly an airplane, he advises taking lessons first. He is always shocked at people who buy stocks or real estate, but never invest in their greatest asset, their mind. Just because you bought a house or two does not make you an expert at real estate.

  3. Choose friends carefully: the power of association

    The author will admit that there are people he have actually sought out because they had money. But he was not after their money; he was seeking their knowledge.

    Don’t listen ti poor or frightened people.

    Keep your mind open, because both have valid points. Unfortunately, most poor people listen to Chicken Little.

    One of the hardest things about wealth-building is to be true to yourself and to be willing to not go along with the crowd. This is because, in the market, it is usually the crowd that shows up late that is slaughtered. If a great deal is on the front page, it’s too late in most instances. Look for a new deal. As we used to say as surfers: “There is always another wave.” People who hurry and catch a wave late usually are the ones who wipe out.

    Smart investors don’t time the markets. If they miss a wave, they search for the next one and get themselves in position. This is hard for most investors because buying what is not popular is frightening. Timid investors are like sheep going along with the crowd. Or their greed gets them in when wise investors have already taken their profits and moved on. Wise investors buy an investment when it’s not popular. They know their profits are made when they buy, not when they sell. They wait patiently. As I said, they do not time the market. Just like a surfer, they get in position for the next big swell.

    Regarding the “Insider Trading”. How far away from the inside are you? The reason you want to have rich friends is because that is where the money is made. It’s made on information. You want to hear about the next boom, get in, and get out before the next bust. I’m not saying do it illegally, but the sooner you know, the better your chances are for profits with minimal risk. That is what friends are for. And that is financial intelligence.

  4. Master a formula and then learn a new one: the power of learning quickly

    Learn a formula.

    Learned a lot that made you stock and real estate investing more meaningful and lucrative.

    In today’s fast-changing world, it’s not so much what you know anymore that counts, because often what you know is old. It is how fast you learn. That skill is priceless. It’s priceless in finding faster formulas—recipes, if you will—for making dough. Working hard for money is an old formula born in the day of cavemen.

  5. Pay yourself first: the power of self-discipline

    If you cannot get control of yourself, do not try to get rich.

    It is the lack of self-discipline that causes most lottery winners to go broke soon after winning millions.

    Simply put, people who have low self-esteem and low tolerance for financial pressure can never be rich. As I have said, a lesson learned from my rich dad was that the world will push you around. The world pushes people around, not because other people are bullies, but because the individual lacks internal control and discipline. People who lack internal fortitude often become victims of those who have self-discipline.

    The three most important management skills necessary to start your own business are management of:

    1. Cash Flow
    2. People
    3. Personal Time

    The skills to manage these three could apply to anything.

    image-20240614124158011

    Cash flows go to asset, can generate further cash flows. The above figure is when you pay yourself fits. However, the figure below is if salary goes to pay expenses.

    image-20240614124307982

    To successfully pay yourself first, keep the following in mind:

    1. Don’t get into large debt positions that you have to pay for. Keep your expenses low. Build up assets first. Then buy the big house or nice car. Being stuck in the Rat Race is not intelligent.
    2. When you come up short, let the pressure build and don’t dip into your savings or investments. Use the pressure to inspire your financial genius to come up with new ways of making more money, and then pay your bills. You will have increased your ability to make more money as well as your financial intelligence.
  6. Pay your brokers well: the power of good advice

    Today, the author has expensive attorneys, accountants, real estate brokers, and stockbrokers. Why? Because if, and the author do mean if, the people are professionals, their services should make you money. And the more money they make, the more money the author make.

    We live in the Information Age. Information is priceless. A good broker should provide you with information, as well as take the time to educate you.

    A good broker saves me time, in addition to making me money. A broker is my eyes and ears in the market.

    When the author interview any paid professional, he first find out how much property or stocks they personally own and what percentage they pay in taxes. And that applies to the author’s tax attorney as well as t the accountant. The author have an accountant who minds his own business. His profession is accounting, but his business is real estate.

    Find a broker who has your best interests at heart. Many brokers will spend the time educating you, and they could be the best asset you find. Just be fair, and most of them will be fair to you. If all you can think about is cutting their commissions, then why should they want to help you? It’s just simple logic.

  7. Be an Indian giver: the power of getting something for nothing

    When the first European settlers came to America, they were taken aback by a cultural practice some American Indians had. For example, if a settler was cold, the Indian would give the person a blanket. Mistaking it for a gift, the settler was often offended when the Indian asked for it back.

    The Indians also got upset when they realized the settlers did not want to give it back. That is where the term “Indian giver” came from, a simple cultural misunderstanding.

    The author pulls the initial dollar amount out, and stop worrying about the fluctuations of the market, because the initial money is back and ready to work on another asset.

    The author also lose. On an average 10 investments, he hit home runs on two or three, while five or six do nothing, and he lose on two or three

    Wise investors must look at more than ROI. They look at the assets they get for free once they get their money back. That is financial intelligence.

  8. Use assets to buy luxuries: the power of focus

    if a person cannot master the power of self discipline, it is best not to try to get rich. This is because, although the process of developing cash flow from an asset column is easy in theory, what’s hard is the mental fortitude to direct money to the correct use. Due to external temptations, it is much easier in today’s consumer world to simply blow money out the expense column. With weak mental fortitude, that money flows into the paths of least resistance. That is the cause of poverty and financial struggle.

    Developing cash flow from an asset column is easy in theory — what’s hard is the mental fortitude to direct money to the correct use. Borrowing money is easy in the short term but harder in the long run.

  9. Choose heroes: the power of myth

    By having heroes, we tap into a tremendous source of raw genius. Learn from someone.

  10. Teach and you shall receive: the power of giving

    “Teach and you shall receive”. The more the author teaches those who want to learn, the more he learn. If you want to learn about money, teach it to someone else. A torrent of new ideas and finer distinctions will come in

Chapter 9: Still Want More? Here Are Some To Do’s

The to-do list might be as the following:

  • Stop doing what you’re doing.

    Take a break and assess what is working and what is not working.

  • Look for new ideas.

    Go to bookstores and search for books on different and unique subjects. The book The 16 Percent Solution by Joel Moskowitz taught Robert something new and spurred him to action.

  • Find someone who has done what you want to do.

    Take them to lunch and ask them for tips and tricks of the trade.

  • Take classes, read, and attend seminars.

    Robert searches newspapers and the Internet for new and interesting classes.

And,

  • Make an offer, someone may say yes.

    You don’t know what the right price is until you have a second party who wants to deal. Most sellers ask too much. It is rare that a seller asks a price that is less than something is worth. It’s fun and only a game. Make offers. Someone might say yes. (And make offers with escape clauses)

    A friend wanted me to show her how to buy apartment houses. So one Saturday she, her agent, and I went and looked at six apartment houses. Four were dogs, but two were good. I said to write offers on all six, offering half of what the owners asked for. She and the agent nearly had heart attacks. They thought it was rude, and would offend the sellers, but I really don’t think the agent wanted to work that hard. So they did nothing and went on looking for a better deal.

    No offers were ever made, and that person is still looking for the right deal at the right price. Well, you don’t know what the right price is until you have a second party who wants to deal.

    Make an offer, someone may say yes.

    lol

    I always make offers with escape clauses. In real estate, I make an offer with language that details “subject-to” contingencies, such as the approval of a business partner. Never specify who the business partner is. Most people don’t know that my partner is my cat. If they accept the offer, and I don’t want the deal, I call home and speak to my cat. I make this ridiculous statement to illustrate how absurdly easy and simple the game is. So many people make things too difficult and take it too seriously.

And more hints:

  • Finding a good deal, the right business, the right people, the right investors, or whatever is just like dating. You must go to the market and talk to a lot of people, make a lot of offers, counteroffers, negotiate, reject, and accept.

  • Jog, walk, or drive a certain area once a month for 10 minutes.

    Robert has found some of his best real estate investments doing this. He will jog a certain neighborhood for a year and look for change. For there to be profit in a deal, there must be two elements: a bargain and change. There are lots of bargains, but it’s change that turns a bargain into a profitable opportunity.

  • Shop for bargains in all markets.

    Consumers will always be poor. When the supermarket has a sale, say on toilet paper, the consumer runs in and stocks up. But when the housing or stock market has a sale, most often called a crash or correction, the same consumer often runs away from it.

    Remember: Profits are made in the buying, not in the selling.

  • Look in the right places.

  • Look for people who want to buy first. Then look for someone who wants to sell.

    Buy a pie, and cut it in pieces. Most people look for what they can afford, so they look too small. They buy only a piece of the pie, so they end up paying more for less. Small people remain small because they think small, act alone, or don’t act all.

  • Learn from history.

    All the big companies on the stock exchange started out as small companies.

  • Action always beats inaction.

    Take action before you can receive the financial rewards. Act Now.

Never Split the Difference

by Chris Voss

A former FBI Top Hostage Negotiator’s Filed-Tested Tools for Talking

Chapter 1 The New Rules

One core assumption is that feeling is a form of thinking. Inspired by Daniel Kahneman and Amos Tversky, people are neither fully rational nor completely selfish, and that their tastes are anything but stable. Thus, do not assume people make rational decision especially when they are in negotiation.

  • Human suffers several behavioural phenomenons or theories, including Cognitive Bias, Framing Effect, Prospect Theory, Loss Aversion, etc.
  • System 1 (fast, instinctive, and emotional) and System 2 (slow, deliberative, and logical) are there to guide and steer the rational thoughts.
  • Tactical Empathy. When individuals feel listened to, they tend to listen to themselves more carefully and to openly evaluate and clarify their own thoughts and feelings. Listening is a martial art.
  • Negotiation servers to distinct (1) information gathering and (2) behaviour influencing

Chapter 2 Be A Mirror

Negotiator should engage the process with a mindset of discovery. The goal is to extract and observe as much information as possible. We start with we know nothing, and get to explore in the negotiation.

  • Don’t commit to assumptions; instead, view them as hypotheses and use the negotiation to test them rigorously. Negotiation is not an act of battle, it’s a process of discovery.

  • Slow Down, put together all the puzzle pieces.

  • Use the Late-Night, FM DJ Voice: deep, soft, slow, and reassuring. Clam the other side down. It’s the voice of an easygoing, good-natured person. The attitude is light and encouraging. Relax and smile. Smiling would have an impact tonally.

  • Mirroring, also called isopaxism, is essentially imitation. It’s another neuro-behaviour humans display in which we copy each other to comfort each other. Establish Trust. Use mirrors to encourage the other side to empathise and bond with you, keep people talking, buy your side time to regroup, and encourage your counterparts to reveal their strategy.

    • Repeat the last three words of what someone has just said.
    1. Start with “I’m sorry …”
    2. Mirror. Repeat the last three words (or the critical one to three words).
    3. Silence. At least four seconds, to let the mirror work its magic on your counterpart.
    4. Repeat

Chapter 3 Don’t Feel Their Pain, Label It

Negotiation is about emotional and feelings. How can one separate people from the problem when the emotions are the problem?

Instead of denying or ignoring emotions, good negotiators identify and influence them. Emotion is a tool.

  • Tactical Empathy. The ability to recognise the perspective of a counterpart, and of that recognition.
    • That’s an academic way of saying that empathy is paying attention to another human being, asking what they are feeling and making a commitment to understanding their world.
    • understand the feelings and mindset of another in the moment and also hearing what is behind those feelings so you increase your influence in all the moments that follow.
    • Labeling, by spotting their feelings, turned them into words, and then very calmly and respectfully repeated their emotions back to them.
    • Labeling is a way of validating someone’s emotion by acknowledging it. Give someone’s emotion a name and you show you identify with how the person feels.
    • use the wording with “roughly”: “it looks like you are …”, “it seems you don’t want to go back to jail”.
    • when you phrase a label as a neutral statement of understanding, it encourages your counterpart to be responsive.
    • The last rule of labeling is silence. Once thrown out a label, be quite and listen.
    • Label counterpart’s fears to diffuse their power. When deal with a person who wants to be appreciated and understood. So use labels to reinforce and encourage positive perceptions and dynamics.
    • when people are shown photos of faces expressing strong emotion, the brain shows greater activity in the amygdala, the part that generates fear. But when they are asked to label the emotion, the activity moves to the areas that govern rational thinking. In other words, labeling an emotion-applying rational words to a fear-disrupt its raw intensity.
    • list the worst things that the other party could say about you and say them before the other person can.

Chapter 4 Beware “Yes” – Master “No”

“Yes” is often a meaningless answer that hides deeper objection (and “Maybe” is even worse). Pushing hard for “Yes” doesn’t get a negotiator any closer to a win; it just angers the other side. “No” is pure gold. That negative provides a great opportunity for you and the other party to clarify what you really want by eliminating what you don’t want. ‘No’ is not failure, it lead to “Yes”, as the final goal. Don’t get to ‘Yes’ before the final. “No “make people feel safe, “Yes” make people guard.

  • “No” could be one of the alternative, i.e. I am not yet ready to agree;I don’t understand; I don’t think I can afford it.
  • After getting ‘No’, ask solution-based questions or simply label their effect, i.e. what about this doesn’t work for you? what would you need to make it work?
  • Every ‘No’ gets me closer to ‘Yes’. But how to lead to a ‘No’? Two ways as below.
    • Mislabel one’s emotions or desires. Say something that you know is totally wrong, i.e. “So it seems that you really are eager to leave your job”. That forces them to listen and makes them comfortable correcting you by saying ‘No’.
    • Ask the other party what they don’t want. People are comfortable saying ‘No’ because it feels like self-protection. And once you’ve gotten them to say ‘No’, people are much more open to moving forward to new options and ideas.
  • In Email, how ever to be ignored again. Provoke a “No” with a one-sentence email.

Chapter 5 Trigger The Two Words That Immediately Transform Any Negotiation

Never try to get “Yes” at the end point. “Yes” is nothing without “how”. In business negotiation, “that’s right” often leads to the best outcomes. “That’s right” is great, however if “You’re right”, nothing changes. Consider this: whenever someone is bothering you, and they just won’t let up, and they won’t listen to anything you have to say, what do you tell them to get them to shut up and go away? The answer is “You’re right”.

  • The more person feels understood, and positively affirmed in that understanding, the more likely that urge for constructive behaviour will take hold.
  • “That’s right” is better than “Yes”. Strive for it. Reaching “That’s right” in a negotiation creates breakthroughs.
  • Use a summary to trigger a “that’s right”. The building blocks of a good summary are a label combined with paraphrasing. Identify, reariculate, and emotionally affirm “the world according to…”

Chapter 6 Bend Their Reality

People are emotional, irrational beasts who are emotional and irrational in predictable, pattern-filled way. Using the knowledge and tools to bend the reality is rational, not cheating. Tools are:

  • Don’t let yourself be fooled by the surface.
  • Not not Compromise by a split difference.
    • The win-win mindset pushed by so many negotiation experts is usually ineffective and often disastrous.
    • Compromise is often a ‘bad deal’. No deal is better than a bad deal.
  • Approaching deadlines. Deadlines regularly make people say and do impulsive things that are against their best interest, because we all have a natural tendency to rush as a deadline approaches. Having a deadline pushes you to speed up your concessions, but the other side, thinking that it has time, will just hold out for more. So, reveal the deadline to the counterpart could reduce the risks of impasse, and lead to a quickest concession.
  • Page 120
  • The F-word, “Fair”, is an emotional term people usually exploit to put the other side on the defensive and gain concessions. When your counterpart drops the F-bomb, don’t get suckered into a concession. Instead, ask them to explain how you’re mistreating them.
  • Bend the counterpart’s reality by anchoring one’s starting point.
  • People will take more risks to avoid a loss than to realise a gain. Make sure your counterpart sees that there is more things to lose by inaction. (Prospect Theory)

Chapter 7 Create the Illusion of Control

Successful Negotiation involved getting your counterpart to do the work for you and suggest your solution himself. It involved giving him the illusion of control while you were the one defining the conversation.

A tool is provided in this chapter: Calibrated, or Open-ended, Question.

  • Don’t try to negotiate in the Fire-Fight.

  • There is always a team on the other side.

  • Suspend Unbelief. “Unbelief” is active resistance to what the other side is saying, complete rejection. That’s where the two parties in a negotiation usually start.

    If you can get the other side to drop their unbelief, you can slowly work them to your point of view on the back of their energy. You don’t directly persuade them to see your ideas. Instead, you ride them to your ideas. As the saying goes the best way to ride a horse is in the direction in which it is going.

    • Giving your counterpart the illusion of control by asking calibrated question is one of the most powerfull tools for suspending unbelief.
    • When you go into a store, instead of telling the salesclerk what you “need”, you can describe what you’re looking for and ask for suggestions. (give the counterpart the illusion of control).
    • As question such as “How am I supposed to do that?”. The critical party of this approach is that you really are asking for help and your delivery must convey that. Instead of bullying the clerk, you’re asking for their advice and giving them the illusion of control.
    • Asking for help in this manner is an incredibly powerful negotiating technique for transforming encounters from confrontational showdowns into joint problem-solving sessions. And Calibrated Questions are the best tool.
  • Calibrated Your Question.
    • The Rationale: Like the softening words and phrases “perhaps”, “maybe”, “I think”, and “it seems”, the calibrated open-ended question takes the aggression out of a confrontational statement or close-ended request that might otherwise anger your counterpart. What makes them work is that they are subject to interpretation by your counterpart instead of being rigidly defined. They allow you to introduce ideas and requests without sounding overbearing or pushy.

    • The real beauty of calibrated questions is that fact that they offer no target for attach like statements do. Calibrated questions have the power to educate your counterpart on what the problem is rather than causing conflict by telling them what the problem is.

    • Once you figure out where the conversation to go, you have to design the questions that will ease the conversation in that direction while letting the other guy think it’s his choice to take you there.

    • Rules:

    • Avoid Verbs or words like “can”, “is”, “are”, “do”, or “does”. There are closed-ended questions that can be answered with a simple “yes” or a “no”.

    • Instead, start with a list of words people know as reporter’s questions: “who”, “what”, “when”, “where”, “why”, and “how”. Those words inspire your counterpart to think and then speak expansively.
    • It’s best to start with “what”, “how”, and sometimes “why”. Not do “who”, “when”, and “where”, as the counterpart will share a fact without thinking.
    • “Why” can backfire. Regardless of what language the word “why” is translated into, it;s accusatory. Rarely rarely as “why”. The only time you can use “why” successfully is when the defensiveness that is created supports the change you are trying to get them to see. Treat “why” like a burner on a hot stove — don’t touch it.
    • Even something as harsh as “Why did you do it?” can be calibrated to “What caused you to do it?”, which takes away the emotion and makes the question less accusatory.
    • Questions like “What is the biggest challenge you face?” can get the other side to teach you something about themselves, which is critical to any negotiation because all negotiation is an information-gathering process.

    • Great Standbys:

    • What about this is important to you?

    • How can I help to make this better for us?

    • How would you like me to proceed?

    • What is it that brought us into this situation?

    • How can we solve this problem?

    • What’s the objective? / What are we trying to accomplish here?

    • How am I supposed to do that?

      The implication of any well-designed calibrated question is that you want what the other guy wants but you need his intelligence to overcome the problem. You’ve not only implicitly asked for help, but engineered a situation in which your formerly recalcitrant counterpart is now using his mental and emotional resources to overcome your challenges. That guides the other party toward designing a solution. – Your Solution.

    • Calibrated questions make your counterpart feel like they’re in charge, but it’s really you who are framing the conversation.

    • Avoid questions that can be answered with “Yes” or tiny pieces of information.

    • Ask “how” and “what” to give your counterpart an illusion of control, inspiring them to speak more, revealing more.

  • When you are attacked, Pause, Think. Let the passion dissipate. Keep your emotional cool. Lower the change of saying more than you want to. Every calibrated question and apology would lower his heart rate just a little bit. That’s how you get to a dynamic where solution can be found.

  • Be a listener, as talker is revealing information, while the listener is directing the conversation toward his own goals.

Chapter 8 Guarantee Execution

  • “Yes” is nothing without “No”.

    By making your counterparts articulate implementation in their own words, your carefully calibrated “How” questions will convince them that the final solution is their idea.

    Two key questions you can ask to push your counterparts to think they are defining success their way:

    • How will we know we’re on track?

    • How will we address things if we find we’re off track?

    When they answer, you summarise their answers until you get a “That’s right”

    No get to “I’ll try”, that means “I plan to fail”. When get that, dive back in with calibrated “How” questions until they define the terms of successful implementation.

    “Yes” is nothing without “How”. So keep asking “How?”

    Ask calibrated “How” questions, and ask them again and again. Ask “how” keeps your counterparts illusion of control. It will lead them to contemplate your problems when making their demands.

  • Influencing those behind the table.

  • Spotting liars, dealing with jerks, and charming everyone else. Learn how to spot and interpret the subtleties of communication – both verbal and nonverbal – that reveal the mental states of your counterparts.

    Tactics, Tools, and methods for using subtle verbal and nonverbal forms of communication to understand and modify the mental states of your counterpart: Tools are like:

    • The 7-38-55 percent rule: by studies, only 7 percent of a message is based on the words while 38 percent comes from the tone of voice and 55 percent from the speaker’s body language and face.

    Pay close attention to tone and body language to make sure they match up with the literal meaning of the words. If they don’t align, it’s quite possible that the speaker is lying for at least unconvinced. Then, use labels to discover the source of the incongruence. Label will make them feel respected.

    • The Rule of Three. There are three kinds of “Yes”: Commitment, Confirmation, and Counterfeit. We want to avoid the trap of Counterfeit “Yes”. The Rule is simply getting the other guy to agree to the same thing three times in the same conversation. In doing so, it uncovers problems before they happen, because it’s hard to repeatedly lie or fake conviction.

    The No. 1 yes if the counterpart agree to something to give a commitment.

    The No. 2 you might label or summarise what the counterpart said so they answer, “That’s right”.

    The No. 3 could be a calibrated “How” or “What” question about implementation that asks them to explain. Something like “What do we do if we get off track”

    Or, the three times might just be the same calibrated questions phrased three different ways, like “What’s the biggest challenge you faced? What are we up against here? What do you see as being the most difficult thing to get around?”

    • The Pinocchio Effect. On average, liars use more words than truth tellers and use far more third-person pronouns. They start talking about “him, her, it, one, they, their”, rather than “I”, in order to put more distance between themselves and the lie. Discover that liars tend to speak in more complex sentences in an attempt to win over their suspicious counterparts.

    • Pay attention to their usage of pronouns. The more in love they are with “I”, “me” and “my” the less important they are. Conversely, the harder it is to get a first person pronoun out of a negotiator’s mouth, the more important they are.

  • The Chris Discount. Remember and use your counterpart’s name in a negotiation. People are tired of being hammered with their own name. Also, use your own name. Humanise yourself. Use your name to introduce yourself. Say it in a fun, friendly way. Let them enjoy the interaction, too. That can get you a special price.

  • How to get the counterparts to bid against themselves.

    The best way to get your counterparts to lower their demands is to say “No” using “How” questions. These indirect ways of saying “No” using won’t shut down your counterpart the way a blunt, pride-piercing “No” would. So, Say “NO” in a Blunt way.

    Say “How am I suppose to do that?” – show empathy, request for help.

    Say “I’m sorry”, “I’m sorry but I’m afraid I just can’t do that”, “I’m sorry, No”

Chapter 9 Bargain Hard

There three categories of people in negotiation. (1) Accommodators, (2) Assertive, and (3) Data-Loving Analysts. Each styles can be effective. And to truly be effective you need elements from all three.

To be good, you have to learn to be yourself at the bargaining table. To be great you have to add to your strengths, not replace them.

  • Analyst
    • Characteristics:

    (Time = Preparation)

    (Silence makes Analysts think)

    The motto: As much time as it takes to get it right. The analysts need extensive preparation, and they hate surprises.

    Classic Analysts prefer to work on their own and rarely deviate from their goals. They rarely show emotion. Analysts often speak in a way that is distant and cold instead of soothing. This puts people off without them knowing it and actually limits them from putting their counterpart at ease and opening them up.

    They are reserved problem solvers, and information aggregators, and are hypersensitive to reciprocity.

    • As a counterpart:

    People like this are skeptical by nature. So asking too many questions to start is a bad idea, because they’re not going to want to answer until they understand all the implications. With them, it’s vital to be prepared.

    Silence to them is an opportunity to think. If you feel they don’t see things the way you do, give them a chance to think first.

    Apologies have little value to them since they see the negotiation and their relationship with you as a person largely as separate things. They are not quick to answer calibrated questions, or closed-ended questions when the answer is “Yes”. They may need a few days to respond.

    • If you’re this type:

    You should be worried about cutting yourself off from an essential source of data, your counterpart. The single biggest thing you can do is to smile when you speak. People will be more forthcoming with information to you as a result. Smiling can also become a habit that makes it easy for you to mask any moments you’ve been caught off guard.

  • Accommodator

    • Characteristics:

    (Time = Relationship)

    (Silence make accommodators anger)

    The most important thing to this type of negotiator is the time spent building the relationship.

    Accommodators want to remain friends with their counterpart even if they can’t reach an agreement.

    • As a counterpart:

    If your counterparts are sociable, peace-seeking, optimistic, distractible, and poor time managers, they’re probably Accommodators.

    If they’re your counterpart, be sociable and friendly. Listen to them talk about their ideas and use calibrated questions focused specifically on implementation to nudge them along and find ways to translate their talk into action.

    • If you’re this type:

    Stick to your ability to be very likable, but do not sacrifice your objections.

  • Assertive

    • Characteristics:

    (Time = Money)

    (Silence means nothing to say, lol)

    Assertives believe time is money.

    Assertives are fiery people who love winning above all else, often at the expense of others. They have aggressive communication style and they don’t worry about future interactions. Their view of business relationships is based on respect, nothing more and nothing less.

    Assertives want to be heard, and mostly do not have ability to listen, until they know that you’ve heard them. They focus on their own goals rather than people. And they tell rather than ask.

    • As a counterpart:

    It’s best to focus on what they have to say, because once they are convinced you understand them, then and only then will they listen for your point of view.

    Every silence is an opportunity to speak more. So, Mirrors are wonderful tool with this type. So are calibrated questions, labels, and summaries. The most important thing to get from an Assertive will be a “that’s right”.

    • If you’re this type:

    be particularly conscious of your tone.

    Use calibrated questions and labels with your counterpart since that will also make you more approachable and increase the changes for collaboration.

  • Why people often fail to identify their counterpart’s style?

    The great obstacle to accurately identifying someone else’s style is the “I am normal” paradox. This is, our hypothesis that the world should look to others as it looks to us. SO, do not project the counterpart the same as you.

  • Take a Punch.

    Set boundaries, and learn to take a punch or punch back, without anger. The guy across the table is not the problem, the situation is.

    Be prepared to withstand the hit and counter the panache, while taking a punch.

    1. Deflect the punch in a way that opens up your counterpart. Say “no”, or “How am I supposed to accept that?”, or “What are we trying to accomplish here?”
    2. When you feel you’re being dragged into a haggle, you can detour the conversation to the non-monetary issues that make any final price work. Says, “What else would you be able to offer to make that a good price for me.”
  • Punching Back: Using assertion without getting used by it.

    When a negotiation is far from resolution and going nowhere fast, you need to shake things up and get your counterpart out of their rigid mindset. There are tools:

    1. Use anger, but use anger under control, because anger reduces our cognitive ability. Researchers found that expressions of anger increase a negotiator’s advantage and final take. But there are different angers.

      When someone puts out a ridiculous offer, one that really pisses you off, take a deep breath, allow little anger, and channel it-at the proposal, not the person-and say, “I don’t see how that would ever work”

    2. “Why” question. Remember “Why” is usually defensive and might be less used. But while punching back, employ the defensiveness the question triggers to get your counterpart to defend your position.

    3. “I” messages:

      “I fell __ because __”

      Label + because to make it more convinced.

    4. Have the ready-to-walk mindset.

      Maintain the collaborative relationship even when you’re setting boundaries.

      Anger and other strong emotions can on rare occasions be effective. In any bare-knuckle bargaining session, the most vital principle to keep in mind is never to look at your counterpart as an enemy.

      The person across the table is never the problem. The unsolved issue is. So focus on the issue.

  • Ackerman Bargaining Model

    Steps are:

    1. Set your target price (your goal)
    2. Set your first offer at 65% of your target price
    3. Calculate three raises of decreasing increments (to 85, 95, and 100 percent)
    4. Use lots of empathy and different ways of saying “No” to get the other side to counter before you increase your offer.
    5. When calculating the final amount, use precise, non-round numbers like, say, USD 37,893, rather than USD 38,000. It gives the number credibility and weight.
    6. On your final number, throw in a non-monetary item (that they probably don’t want) to show you’re at your limit.

    Rationale: (1) knocking them off their game with an extreme anchor, (2) hitting them with calibrated question, (3) slowly give progressively smaller concession, (4) dropped the weired and accurate number that closed the deal.

Chapter 10 Find the Black Swan

Black Swan theory tells us that things happen that were previously thought to be impossible – or never thought of at all.

In every negotiating session, there are different kinds of information. Those are known knowns that are things we are certain that exist but we don’t know, like the possibility that the other side might get sick and leave us with another counterpart. And, known unknowns that you know they’re out there but you don’t know that we don’t know, pieces of information we’ve never imagined but that would be game changing if uncovered.

The Black Swan is unknown unknowns.

  • The key is to find unknown unknowns.

  • Three types of leverage.

    • Positive Leverage: the ability to provide things that your counterpart wants. If you can provide, then you have the positive leverage.

    • Negative Leverage: the ability to make the counterpart suffer. If you have negative leverage, you can tell the counterpart, “if you do not fulfill your commitment/pay your bill/etc, I will destroy your reputation.”

    However, threats can be like nuclear bombs. There will be a toxic residue that will be difficult to clean up. You have to handle the potential of negative consequences with care, or you will hurt yourself and poison or blow up the while process.

    May using “Label” to alleviate the attacking power of the negative leverage.

    Attention: The “Paradox of Power”, namely, the harder we push, the more likely we are to be met with resistance. That’s why you have to use negative leverage sparingly.

    • Normative Leverage: using the other party’s norms and standards to advance your position. If you can show inconsistencies between their beliefs and their actions, you have normative leverage.

    discover the Black Swan that give you normative valuation can be as easy as asking what your counterpart believes and listening openly.

  • Know their religion

    Access to this hidden space very often comes through understanding the other sides’ worldview, their reason for being, and their religion.

    Digging into your counterpart’s “religion” inherently implies moving beyond the negotiating table and into the life, emotional and otherwise, of your counterpart. – Know your counterpart.

    • Two Tips for reading religion correctly:
    1. Review everything you hear. Compare notes with your team members. Double-Check, and discover new information that helps your advance the negotiation.
    2. Use backup listeners whose only job is to listen between the lines. They will hear things you miss.
    • Listen, listen, and listen some more.
  • The Similarity Principle

    Social scientists find that we trust people more when we view them as being similar or familiar.

    When our counterpart displays attitudes, beliefs, ideas – even modes of dress – that are similar to our own, we tend to like and trust them more. Similarities as shallow as club memberships or college alumni status increase rapport.

  • Religion as a Reason

    Research studies have shown that people respond favorably to requests made in a reasonable tone of vice and followed with a “because” reason. And it didn’t matter if the reason made sense. People just responded positively to the framework.

    So, if there is not reasoning, using religion as a reason.

  • Mistakes:

    1. They are ill-informed.

      Often the other side is acting on bad information, and when people have bad information they make bad choices. GIGO.

      People operating with incomplete information appear crazy to those who have different information. Your job when faced with someone like this in a negotiation is to discover what they do not know and supply that information.

    2. They are constrained.

      The other side might not be able to do something because of legal advice, or because of promises already made, or even to avoid setting a precedent. Or they may just not have the power to close the deal.

    3. They have other interests.

      The presence of hidden interests isn’t as rare as you might think. Your counterpart will often reject offers for reasons that have nothing to do with their merits.

  • Get Face Time. Try getting face time, because it can avoid using email that gives counterpart too much time to think and re-center themselves to avoid revealing too much. Pay special attention to your counterpart’s verbal and non-verbal communication at unguarded moments.

  • Overcoming fear and learning to get what you want out of life.

    Pushing hard for what you believe is not selfish. It’s not bullying. It’s not just helping you. Your amygdala, the part of the brain that processes fear, will try to convince you to give up, to flee, because the other guy is right, or you’re being cruel.

Club de Paris

The Paris Club (Club de Paris, 巴黎俱乐部) has reached 478 agreements with 102 different debtor countries. Since 1956, the debt treated in the framework of Paris Club agreements amounts to $ 614 billion.

Low-income countries generally do not have access to these markets. The assistance from bilateral and multilateral donors remains vital for them. Non-Paris Club creditors are becoming an increasingly important source of financing for these countries. Yet despite the fact that Paris Club creditors now have to deal with far more complex and diverse debt situations than in 1956, their original principles still stand.

Members

Duty of Members

Ad Hoc Participants & 6 principles

Permanent Members

The 22 Paris Club permanent members are countries with large exposure to other States woldwide and that agree on the main principles and rules of the Paris Club. The claims may be held directly by the government or through its appropriate institutions, especially Export credit agencies. These creditor countries have constantly applied the terms defined in the Paris Club Agreed Minutes to their bilateral claims and have settled any bilateral disputes or arrears with Paris Club countries, if any. The following countries are permanent Paris Club members:

AUSTRALIA
AUSTRIA
BELGIUM
BRAZIL
CANADA
DENMARK
FINLAND
FRANCE
GERMANY
IRELAND
ISRAEL
ITALY
JAPAN
KOREA
NETHERLANDS
NORWAY
RUSSIAN FEDERATION
SPAIN
SWEDEN
SWITZERLAND
UNITED KINGDOM
UNITED STATES OF AMERICA

Ad Hoc Members

Other official creditors can also actively participate in negotiation sessions or in monthly “Tours d’Horizon” discussions, subject to the agreement of permanent members and of the debtor country. When participating in Paris Club discussions, invited creditors act in good faith and abide by the practices described in the table below. The following creditors have participated as creditors in some Paris Club agreements or Tours d’Horizon in an ad hoc manner:

Abu Dhabi
Argentina
China
Czech Republic
India
Kuwait
Mexico
Morocco
New Zealand
Portugal
Saudi Arabia
South Africa * prospective member on 8 July 2022
Trinidad and Tobago
Turkey

Development and History of Paris Club

Early Stage

In 1956, the world economy was emerging from the aftermath of the Second World War. The Bretton Woods institutions were in the early stages of their existence, international capital flows were scarce, and exchange rates were fixed. Few African countries were independent and the world was divided along Cold War lines. Yet there was a strong spirit of international cooperation in the Western world and, when Argentina voiced the need to meet its sovereign creditors to prevent a default, France offered to host an exceptional three-day meeting in Paris that took place from 14 to 16 May 1956.

Dealing with the Debt Crisis (1981-1996)

1981 marked a turning point in Paris Club activity. The number of agreements concluded per year rose to more than ten and even to 24 in 1989. This was the famous “debt crisis” of the 1980s, triggered by Mexico defaulting on its sovereign debt in 1982 and followed by a long period during which many countries negotiated multiple debt agreements with the Paris Club, mainly in sub-Saharan Africa and Latin America, but also in Asia (the Philippines), the Middle East (Egypt and Jordan) and Eastern Europe (Poland, Yugoslavia and Bulgaria). Following the collapse of the Soviet Union in 1992, Russia joined the list of countries that have concluded an agreement with the Paris Club. So by the 1990s, Paris Club activity had become truly international.

Debt Burden Enlarges for some Countries

In 1996, the international financial community realized that the external debt situation of a number of mostly African low-income countries had become extremely difficult. This was the starting point of the Heavily Indebted Poor Countries (HIPC) Initiative.

The HIPC Initiative demonstrated the need for creditors to take a more tailored approach when deciding on debt treatment for debtor countries. Hence in October 2003, Paris Club creditors adopted a new approach to non-HIPCs: the “Evian Approach”.

Evian Approach

General frame of the Evian approach

  1. Analysis the sustability

    When a country approaches the Paris Club, the sustainability of its debt would be examined, before the financing assurances are requested, in coordination with the IMF according to its standard debt sustainability analysis to see whether there might be a sustainability concern in addition to financing needs. Specific attention would be paid to the evolution of debt ratios over time as well as to the debtor country’s economic potential; its efforts to adjust fiscal policy; the existence, durability and magnitude of an external shock; the assumptions and variables underlying the IMF baseline scenario; the debtor’s previous recourse to Paris Club and the likelihood of future recourse. If a sustainability issue is identified, Paris Club creditors will develop their own view on the debt sustainability analysis in close coordination with the IMF.

  2. if face liquidity problem

    For countries who face a liquidity problem but are considered to have sustainable debt going forward, the Paris Club would design debt treatments on the basis of the existing terms. However, Paris Club creditors agreed that the rationale for the eligibility to these terms would be carefully examined, and that all the range built-into the terms including through shorter grace period and maturities, would be used to adapt the debt treatment to the financial situation of the debtor country. Countries with the most serious debt problems will be dealt with more effectively under the new options for debt treatments. For other countries, the most generous implementation of existing terms would only be used when justified.

  3. if not sustainable or need special treatment

    For countries whose debt has been agreed by the IMF and the Paris Club creditor countries to be unsustainable, who are committed to policies that will secure an exit from the Paris Club in the framework of their IMF arrangements, and who will seek comparable treatment from their other external creditors, including the private sector, Paris Club creditors agreed that they would participate in a comprehensive debt treatment. However, according to usual Paris Club practices, eligibility to a comprehensive debt treatment is to be decided on a case-by-case basis.

    In such cases, debt treatment would be delivered according to a specific process designed to maintain a strong link with economic performance and public debt management. The process could have three stages. In the first stage, the country would have a first IMF arrangement and the Paris Club would grant a flow treatment. This stage, whose length could range from one to three years according to the past performance of the debtor country, would enable the debtor country to establish a satisfactory track record in implementing an IMF program and in paying Paris Club creditors. In the second stage, the country would have a second arrangement with the IMF and could receive the first phase of an exit treatment granted by the Paris Club. In the third stage, the Paris Club could complete the exit treatment based on the full implementation of the successor IMF program and a satisfactory payment record with the Paris Club. The country would thus only fully benefit from the exit treatment if it maintains its track record over time.

Data

There data in the website yoy.

Insights

Refer to Horn et al., (2021) figure 9 in page 13, Paris Club seems played important role during 2010s.

tbc

Reference

https://clubdeparis.org/en

About Gold

About Gold ?

There seems some “irrational” movements of gold price since the end of 2023.

How gold should be priced? What factors affect the pricing of gold. Here below are some of my reading and insights.

Typical Determinants

Typically, the gold price is considered to be correlated with a list of factors:

  1. Inflation

    In counter with the inflation.

  2. Long-term Real Interest Rate

    TIPS, the Treasury Inflation-Protected Securities, is considered to be the real-interest rate, as the inflation rate is counter-deducted. The long-term rate, specifically 10-yr rate, is preferred as we generally assume holding the Gold in a long-term investment horizon. The long-term Real Interest Rate is considered as the opportunity of holding gold. Therefore, the higher rate, the greater the cost of holding golds, and less demand of gold. Price decrease thereafter.

  3. US Dollar

    The Brandon Wood System links the gold price with US Dollar, with 35USD = 1 ounce Gold. Since the collapse of Brandon Wood System, there is not a fixed exchange rate between USD and Gold anymore. However, USD is still the most important determinant of gold price in that the unit of Gold price is still USD/ounce. It is also like an exchange rate, the more per ounce value of gold is, the more USD/ounce should be. Or, contrastively, the weak USD is, the more USD/ounce shall be.

  • US Dollar Index

    The US Dollar Index might be consider an proxy of the strength and weakness of US dollar. However, as US dollar is the weighted geometric mean of the exchange rates of six major currencies compared to the US dollar:

    • Euro (EUR) – 57.6% weight
    • Japanese yen (JPY) – 13.6% weight
    • British pound (GBP) – 11.9% weight
    • Canadian dollar (CAD) – 9.1% weight
    • Swedish krona (SEK) – 4.2% weight
    • Swiss franc (CHF) – 3.6% weight

      The USD Index is actually a composite of weighted average of above listed currency. The increase of US dollar index means USD is appreciated w.r.t. above currencies. I.E. if USD appreciates w.r.t. EURO, then USDX is likely to increase.

      Therefore, an increase in USDX means appreciation of USD, and then USD/ounce shall decrease, gold price decrease.

  1. Risks / Uncertainty

  2. Demand and Supply from Central Banks.

    We ignore the impact of demand and supply from individuals and industries, but focus on the demand of Central Banks. Like what those CB did during February and March 2024 would increase the demand of gold price.

Empirical Research

Refer to the research report from CICC, a four-factor model is established. The authors specified the relationship between gold and those four factors, one by one.

  • The dependent variable: Gold Price. (Also, attention that they focus on the gold price, not the return as machine learning usually do)

  • Explanatory Variables:

    • US Real Interest rate

    ​ Capture the Opportunity Cost of holding gold. Similar as the explanation in the above section.

    • US Dollar Index,

    ​ Similar as the explanation in the above section.

    • Central Bank Net Gold Purchasing,

    ​ The supply side is limited, demand is mainly driven by the Central Banks of US, China, EU, JP, etc.

    • US Gov Debt Level.

    ​ This factor represents the credibility of US dollar or US government. The greater US Debt level, the less credit-worthy the US gov is. Then, the more desire of holding gold as the counter party of US Dollar credibility.

    The Statistic table is shown below.

image-20240401133442117

​ The author argue that people do not need to consider the spurious regression though the R-squared is incredibly high. They state that the reason is that they are only considering the model like a co-integration model. They have tested the integration of the residual term, and find that the residual is stationary. High R-squared means there are less left in the residual.

​ Their explanation is like the Bull Shit. However, we just ignore the bull shit econometric modeling and statistic figure in the above table, as we are not doing academic. Let consider the predictable power and the implication of the model.

​ Here below is their simulated result and the real gold price movement. Let’s investigate is their model perform as good as stated in their report. Also, let’s see how ML way could perform.

image-20240402120333385


Code Example

Gold_Price_Analysis.html

CFA Learning Notes and Materials

11th April 2024

I have passed the CFA III level exam, and been granted the chart.

For any errates and insights, please free to contact to me.


Here below are my learning footprints for CFA level III. All files are converted to .html as you will find in the following . If you need the raw markdown codes, please move to my Github Repo.

P.S. there are typos and miswritten parts in the notes. Welcome to find me and help me update those mistakes. Or, probably I will update them if I fail the level III exam (in that I would review those notes). 🙂

Best Wishes
FZ

  1. CME
    P.S. BehaviouralFinance
  2. AssetAllocation
  3. Derivatives&Exchange
  4. Fixed-Income
  5. Equity
    P.S. Equity-Active
  6. Fixed-Income
  7. Alternatives
  8. PrivateWealthManagement
  9. InstitutionalInvestors
  10. TradingEvaluationManagerSelection
    P.S. TradingAdditional
  11. Ethics
    P.S. Ethics_from_Level_II_Code_n_Standards

Two Approaches for Forecasting Exchange Rate

The first approach is that analysts focus on flows of export and imports to establish what the net trade flows are and how large they are relative to the economy and other, potentially larger financing and investment flows. The approach also considers differences between domestic and foreign inflation rates that relate to the concept of purchasing power parity. Under PPP, the expected percentage change in the exchange rate should equal the difference between inflation rates. The approach also considers the sustainability of current account imbalances, reflecting the difference between national saving and investment.

The second approach is that the analysis focuses on capital flows and the degree of capital mobility. It assumes that capital seeks the highest risk-adjusted return. The expected changes in the exchange rate will reflect the differences in the respective countries’ assets’ characteristics such as relative short-term interest rates, term, credit, equity and liquidity premiums. The approach also considers hot money flows and the fact that exchange rates provide an across the board mechanism for adjusting the relative sizes of each country’s portfolio of assets.

Source by CFA reading materials

Least Squares Method – Intro to Kalman Filter

Consider a Linear Equation,

$$ y_i = \sum_{j=1}^n C_{i,j} x_j +v_i,\quad i=1,2,…$$

, where C_{i,j} are scalars and v_i\in \mathbb{R} is the measurement noise. The noise is unknown, while we assume it follows certain patterns (the assumptions are due to some statistical properties of the noise). We assume v_i, v_j are independent for i\neq j. Properties are mean of zero, and variance equals sigma squared.

$$\mathbb{E}(v_i)=0$$

$$\mathbb{E}(v_i^2) = \sigma_i^2$$


We can rewrite y_i = \sum_{j=1}^n C_{i,j} x_j +v_i as,

$$ \begin{pmatrix} y_1 \ y_2 \ \vdots\ y_s\end{pmatrix} = \begin{pmatrix} C_{11} & C_{12} & \cdots & C_{1n} \ C_{21} & C_{22}& \cdots & C_{2n} \ \vdots & \vdots & \cdots & \vdots \ C_{s1} & C_{s2} & \cdots & C_{sn}\end{pmatrix} \begin{pmatrix} x_1 \ x_2 \ \vdots\ x_n\end{pmatrix} + \begin{pmatrix} v_1 \ v_2 \ \vdots\ v_s\end{pmatrix} $$

, in a matrix form,

$$ \vec{y} = C \vec{x} + \vec{v} $$

, but I would write in a short form,

$$ y= C x +v$$

We solve for the least squared estimator from the optimisation problem, (there is a squared L2 norm)

$$ \min_x || y-Cx ||_2^2 $$

Recursive Least Squared Method

The classic least squared estimator might not work well when data evolving. So, there emerges a Recursive Least Squared Method to deal with the discrete-time instance. Let’s say, for a discrete-time instance k, y_k \in \mathbb{R}’ is within a set of measurements group follows,

$$y_k = C_k x + v_k$$

, where C_k \in \mathbb{R}^{l\times n}, and v_k \in \mathbb{R}^l is the measurement noise vector. We assume that the covariance of the measurement noise is given by,

$$ \mathbb{E}[v_k v_k^T] = R_k$$

, and

$$\mathbb{E}[v_k]=0$$

The recursive least squared method has the following form in this section,

$$\hat{x}k = \hat{x}{k-1} + K_k (y_k – C_k \hat{x}_{k-1})$$

, where \hat{x}k and \hat{x}{k-1} are the estimates of the vector x at the discrete-time instants k and k-1, and K_k \in \mathbb{R}^{n\times l} is the gain matrix that we need to determine. K_k is coined the ‘Gain Matrix’

The above equation updates the estimate of x at the time instant k on the basis of the estimate \hat{x}_{k-1} at the previous time instant k-1 and on the basis of the measurement y_k obtained at the time instant k, as well as on the basis of the gain matrix K_k computed at the time instant k.

Notation

$\hat{x}$ is the estimate.

$$ \hat{x}k = \begin{pmatrix} \hat{x}{1,k} \ \hat{x}{2,k} \ \vdots \\hat{x}{n,k} \end{pmatrix} $$

, which is corresponding with the true vector x.

$$x = \begin{pmatrix} x_1 \ x_2 \ \vdots \ x_n \end{pmatrix}$$

The estimation error, \epsilon_{i,k} = x_i – \hat{x}_{i,k} \quad i=1,2,…,n.

$$\epsilon_k = \begin{pmatrix} \epsilon_{1,k} \ \epsilon_{2,k} \ \vdots \\epsilon_{n,k} \end{pmatrix} = x – \hat{x}_k = \begin{pmatrix} x_1-\hat{x}_{1,k} \ x_2 – \hat{x}_{2,k} \ \vdots \x_n-\hat{x}_{n,k} \end{pmatrix} $$

The gain K_k is computed by minimising the sum of variances of the estimation errors,

$$ W_k = \mathbb{E}(\epsilon_{1,k}^2) + \mathbb{E}(\epsilon_{2,k}^2) + \cdots + \mathbb{E}(\epsilon_{n,k}^2) $$

Next, let’s show the cost function could be represented as follows, (tr(.) is the trace of a matrix)

$$ W_k = tr(P_k) $$

, and P_k is the estimation error covariance matrix defined by

$$ P_k = \mathbb{E}(\epsilon_k \epsilon_k^T )$$

Or, says,

$$ K_k = arg\min_{K_k} W_k = tr\bigg( \mathbb{E}(\epsilon_k \epsilon_k^T ) \bigg)$$

Why is that?

$$\epsilon_k \epsilon_k^T = \begin{pmatrix} \epsilon_{1,k} \ \epsilon_{2,k} \\vdots \ \epsilon_{n,k} \end{pmatrix} \begin{pmatrix} \epsilon_{1,k} & \epsilon_{2,k} & \cdots & \epsilon_{n,k} \end{pmatrix}$$

$$ = \begin{pmatrix} \epsilon_{1,k}^2 & \cdots & \epsilon_{1,k}\epsilon_{n,k} \ \vdots & \epsilon_{i,k}^2 & \vdots \ \epsilon_{1,k}\epsilon_{n,k} & \cdots & \epsilon_{n,k}^2\end{pmatrix} $$

So,

$$ P_k = \mathbb{E}[\epsilon_k \epsilon_k^T] $$

$$tr(P_k) = \mathbb{E}(\epsilon_{1,k}^2) + \mathbb{E}(\epsilon_{2,k}^2) + \cdots + \mathbb{E}(\epsilon_{n,k}^2)$$


Optimisation

$$ K_k = arg\min_{K_k} W_k = tr\bigg( \mathbb{E}(\epsilon_k \epsilon_k^T ) \bigg) = tr(P_k)$$

Let’s derive the optimisation problem.

$$\epsilon_k = x-\hat{x}_k$$

$$ =x-\hat{x}{k-1} – K_k(y_k – C_k \hat{x}{k-1}) $$

$$ = x- \hat{x}{k-1} – K_k (C_k x + v_k – C_k \hat{x}{k-1}) $$

$$ = (I – K_k C_k)(x-\hat{x}_{k-1}) – K_k v_k $$

$$ =(I-K_k C_k )\epsilon_{k-1} – K_k v_k $$

Recall y_k = C_k x + v_k and \hat{x}k = \hat{x}{k-1} + K_k (y_k – C_k \hat{x}_{k-1})

So, \epsilon_k \epsilon_k^T would be,

$$\epsilon_k \epsilon_k^T = \bigg((I-K_k C_k )\epsilon_{k-1} – K_k v_k\bigg)\bigg((I-K_k C_k )\epsilon_{k-1} – K_k v_k\bigg)^T$$

$P_k = \mathbb{E}(\epsilon_k \epsilon_k^T)$, and $P_{k-1} = \mathbb{E}(\epsilon_{k-1} \epsilon_{k-1}^T)$.

$\mathbb{E}(\epsilon_{k-1} v_k^T) = \mathbb{E}(\epsilon_{k-1}) \mathbb{E}(v_k^T) =0$ by the white noise property of $\epsilon$ and $v$. However, $\mathbb{E}(v_k v_k^T) = R_k$. Substituting all those into $P_k$, we would get,

$$P_k = (I – K_k C_k)P_{k-1}(I – K_k C_k)^T + K_k R_k K_k^T$$

$$ P_k = P_{k-1} – P_{k-1} C_k^T K_k^T – K_k C_k P_{k-1} + K_k C_k P_{k-1}C_k^T K_k^T + K_k R_k K_k^T $$

$$W = tr(P_k)= tr(P_{k-1}) – tr(P_{k-1} C_k^T K_k^T) – tr(K_k C_k P_{k-1}) + tr(K_k C_k P_{k-1}C_k^T K_k^T) + tr(K_k R_k K_k^T) $$

We take F.O.C. to solve for K_k = arg\min_{K_k} W_k = tr\bigg( \mathbb{E}(\epsilon_k \epsilon_k^T ) \bigg) = tr(P_k), by letting \frac{\partial W_k}{\partial K_k} = 0. See the Matrix Cookbook and find how to do derivatives w.r.t. K_k.

$$\frac{\partial W_k}{\partial K_k} = -2P_{k-1} C_k^T + 2K_k C_k P_{k-1} C_k^T + 2K_k R_k = 0$$

We solve for K_k,

$$ K_k = P_{k-1} C_k^T (R_k + C_k P_{k-1} C_k^T)^{-1}$$

, we let L_k = R_k + C_k P_{k-1} C_k^T, and L_k has the following property L_k = L_k^T and L_k^{-1} = (L_k^{-1})^T

$$ K_k = P_{k-1} C_k^T L_k^{-1} $$

Plug K_k = P_{k-1} C_k^T K_k^{-1} back into P_k.

$$ P_k = P_{k-1} – K_kC_k P_{k-1} = (I-K_k C_k)P_{k-1} $$


Summary

In the end, the Recursive Least Squared Method could be summarised as the following three equations.

  • 1. Update the Gain Matrix.

$$ K_k = P_{k-1} C_k^T (R_k + C_k P_{k-1} C_k^T)^{-1}$$

  • 2. Update the Estimate.

$$\hat{x}_k = \hat{x}_{k-1} + K_k (y_k – C_k \hat{x}_{k-1})$$

  • 3. Propagation of the estimation error covariance matrix by using this equation.

(I-K_k C_k)P_{k-1}

Reference

Sigmoid & Logistic

Sigmoid function is largely used for the binary classification, in either machine learning algorithm or econometrics.

Why the Sigmoid Function shapes in this form?

Firstly, let’s introduce the odds.

Odds provide a measure of the likelihood of a particular outcome. They are calculated as the ratio of the number of outcomes that produce that outcome to the number that do not.

Odds also have a simple relation with probability: the odds of an outcome are the ratio of the probability that the outcome occurs to the probability that the outcome does not occur. In mathematical terms, p is the probability of the outcome, and 1-p is the probability of not occurring.

$$ odds = \frac{p}{1-p} $$

Odd and Probability

Let’s find some insights behind the probability and the odd. Probability links with the outcomes in that for each outcomes, the probability give its specific corresponding probability. Pr(Y), where Y is the outcome, and Pr(\cdot) is the probability density function that project outcomes to it’s prob.

What about the odds? Odds is more like a ratio that is calculated by the probability as the formula says.

Implication: Compared to the probability, odds provide more about how the binary classification is balanced or not, but the probability distribution.

Example

Rolling a six-side die. The probability of rolling 6 is 1/6, but the odd is $1/5.

Formula

$$ odd = \frac{Pr(Y)}{1-Pr(Y)} $$

, where Y is the outcomes.

Logit

As the probability Pr(Y) is always between [0,1], the odds must be non-negative, odd \in [0,\infty]. We may want to apply a monotonic transformation to re-gauge that range of odds. We will apply on the logarithm.

$$ Sigmoid/Logistic := log(odds) =log\bigg( \frac{Pr(Y)}{1-Pr(Y)} \bigg) $$

We then get the Sigmoid function.

As the transformation we apply on is monotonic, the Sigmoid function remains the similar properties as the odd. The Sigmoid function keeps the similar implication, representing the balance of the binary outcomes.

Then, we bridge Y = f(X), the outcome Y is a function of events X. Here, we assume a linear form as Y = X\beta. The sigmoid function would then become a function of X.

$$g(X) = log\bigg( \frac{Pr(X\beta)}{1-Pr(X\beta)} \bigg) $$

$$ e^g = \frac{p}{1-p} $$

$$ p = \frac{e^g}{e^g+1}=\frac{1}{1+e^{-g}}$$

$$ p = \frac{1}{1+e^{-X\beta}}$$

We finally get out logistic sigmoid function as above.

Dirac Delta Function

The Dirac Delta Function could be applied to simplify the differential equation. There are three main properties of Dirac Delta Function.

$$\delta (x-x’) =\lim_{\tau\to0}\delta (x-x’)$$

such that,

$$ \delta (x-x’) = \begin{cases} \infty & x= x’ \ 0 & x\neq x’ \end{cases} $$

$$\int_{-\infty}^{\infty} \delta (x-x’)\ dx =1$$

Three Properties:

  • Property 1:

$$\delta(x-x’)=0 \quad \quad ,x\neq x’ $$

  • Property 2:

$$ \int_{x’-\epsilon}^{x’+\epsilon} \delta (x-x’)dx =1\quad \quad ,\epsilon >0 $$

  • Property 3:

$$\int_{x’-\epsilon}^{x’+\epsilon} f(x)\ \delta (x-x’)dx = f(x’)$$

At x=x’ the Dirac Delta function is sometimes thought of has having an “infinite” value. So, the Dirac Delta function is a function that is zero everywhere except one point and at that point it can be thought of as either undefined or as having an “infinite” value.