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How Warren Buffett Makes Decisions – The Secret to His Investing Success.

By Michael Lewis.

Warren Buffett is considered by many to be the most successful stock investor ever. Despite the occasional mistake, Buffett’s investing strategies are unrivaled. In 1956, at age 26, his net worth was estimated at $140,000. MarketWatch estimated his net worth at the end of 2016 to be $73.1 billion, an astounding compound annual growth rate of 24.5%. By contrast, the S&P 500 has grown at an average rate of 6.79% and most mutual funds have failed to equal the annual S&P 500 return consistently.

Buffett has achieved these returns while most of his competition failed. According to John Bogle, one of the founders and former Chairman of The Vanguard Group, “The evidence is compelling that equity fund returns lag the stock market by a substantial amount, largely accounted for by cost, and that fund investor returns lag fund returns by a substantial amount, largely accounted for by counterproductive market timing and fund selection.”

Since the evidence shows that Buffet has been an exceptional investor, market observers and psychologists have searched for an explanation to his success. Why has Warren Buffett achieved extraordinary gains compared to his peers? What is his secret?

A Long-Term Perspective. Why Some People Are More Successful Than Others.
Philosophers and scientists have long sought to determine why some people are more successful than others at building wealth. Their findings are varied and often contradictory.

For centuries, people believed their fate, including wealth and status, depended upon the capricious favor of pagan gods – more specifically, the favor of Tyche (Greek) or Fortuna (Roman). Expansion of the Judeo-Christian-Islamic religions and their concepts of “free will” led to the general belief that individuals could control their destiny through their actions, or lack thereof.

Modern science, specifically psychology and neuroscience, advanced a theory of biological determinants that control human decisions and actions. This theory suggests that free will might not be as “free” as previously thought. In other words, we may be predisposed to certain behaviors that affect the ways we process information and make decisions.

Evolutionary biologists and psychologists have developed a variety of different theories to explain human decision-making. Some claim that the ability to make superior decisions with favorable outcomes is the result of eons of natural selection, which favors individuals with exceptional genetics, such as those with high IQs.

Despite the perception that a high IQ is necessary for building wealth, study after study indicates that the link between super-intelligence and financial success is dubious at best:

Dr. Jay Zagorsky’s study in the Intelligence Journal found no strong relationship between total wealth and intelligence: “People don’t become rich just because they are smart.”
Mensa members rank in the top 2% of the brightest people on earth, but most are not rich and are “certainly not the top 1% financially,” according to an organization spokesperson. A study by Eleanor Laise of the Mensa Investment Club noted that the fund averaged 2.5% per annum for a 15-year period, while the S&P 500 averaged 15.3% during the same time. One member admitted that “we can screw up faster than anyone,” while another described their investment strategy as “buy low, sell lower.”
Buffett has never claimed to be a genius. When asked what he would teach the next generation of investors at the 2009 Berkshire Hathaway annual meeting, he replied, “In the investing business, if you have an IQ of 150, sell 30 points to someone else. You do not need to be a genius . . . It’s not a complicated game; you don’t need to understand math. It’s simple, but not easy.”

He later expanded the thought: “If calculus or algebra were required to be a great investor, I’d have to go back to delivering newspapers.”

Economists’ Rational Man.
Economists have historically based their models upon the presumption that humans make logical decisions. In other words, a person faced with a choice balances certainties against risks. The theory of expected value presumes that people facing choices will choose the one that has the largest combination of expected success (probability) and value (impact).

A rational person would always model the industrious ant in Aesop’s fable, not the insouciant grasshopper. The idea that people would make decisions contrary to their interests is inconceivable to economists.

To be fair, most economists recognize the flaws in their models. Swedish economist Lars Syll notes that “a theoretical model is nothing more than an argument that a set of conclusions follows from a fixed set of assumptions.”

Economists presume stable systems and simple assumptions, while the real world is in constant flux. Paraphrasing H.L Mencken’s famous quote, there is always a simple economic model [well-known solution] for every human problem. This notion is neat, plausible, and wrong.

Psychologists’ Natural Man.
According to Harvard professor Daniel Lieberman, humans are naturally inclined to seek the solutions that require the least expenditure of energy.

In the real world, we have difficulty deferring immediate gratification for future security, selecting investments best suited to our long-term goals and risk profile, and acting in our best financial interests. Psychological research suggests that the difficulty is rooted in our brains – how we think and make decisions.

Researchers Susan Fiske and Shelley Taylor postulate that humans are “cognitive misers,” preferring to do as little thinking as possible. The brain uses more energy than any other human organ, accounting for up to 20% of the body’s total intake.

When decisions involve issues more remote from our current state in distance or time, there is a tendency to defer making a choice. This impulse accounts for the failure of people to save in the present since the payoff is years in the future.

As far as we know, Mr. Buffett’ brain is similar to other investors and he experiences the same impulses and anxieties as others. While he experiences the tensions that arise in everyone when making decisions, he has learned to control impulses and make reasoned, rational decisions.

Our Two-Brain System.
The studies by Daniel Kahneman and Amos Tversky provide new insight into decision-making, perhaps the key to Buffett’s success. They theorize that each human uses two systems of mental processing (System 1 and System 2) that work together seamlessly most of the time. Khaneman’s book, “Thinking, Fast and Slow,” outlines these two systems.

System 1 – Think Fast.
System 1, also referred to as the “emotional brain,” developed as the limbic system in the brain of early humans. Sometimes called the “mammalian brain,” it includes the amygdala, the organ where emotions and memories arise.

Neuroscientist Paul MacLean hypothesized that the limbic system was one of the first steps in the evolution of the human brain, developed as part of its fight or flight circuitry. Through necessity, our primitive ancestors had to react quickly to danger when seconds could mean escape or death.

The emotional brain is always active, capable of making quick decisions with scant information and conscious effort. It continuously makes and remakes models – heuristic frames – of the world around it, relying on the senses and memories of past events.

For example, an experienced driver coordinates steering and speed of an automobile on an empty highway almost effortlessly, even casually. The driver can simultaneously carry on conversations with passengers or listen to the radio without losing control of the vehicle. The driver is relying on the decisions of System 1.

The emotional brain is also the source of intuition, that “inner voice” or gut feeling we sometimes get without being consciously aware of the underlying reasons for its occurrence. We rely primarily on this system for the hundreds of everyday decisions we make – what to wear, where to sit, identifying a friend. Paradoxically, System 1 is a source of creativity as well as habits.

System 2 – Think Slow.
System 2, also called the “logical brain,” is slower, more deliberate, and analytical, rationally balancing the benefits and costs of each choice using all the available information.

System 2 decisions take place in the latest evolutionary addition to the brain – the neocortex. It is believed to be the center of humans’ extraordinary cognitive activity. System 2 was slower to evolve in humans and requires more energy to exercise, indicating the old saw “Thinking is hard” is a fact.

Kahneman characterizes System 2 as “the conscious, reasoning self that has beliefs, makes choices, and decides what to think about and do.” It is in charge of decisions about the future, while System 1 is more active in the moment. While our emotional brain can generate complex patterns of ideas, it is also freewheeling, impulsive, and often inappropriate.

Fortunately, System 1 works well most of the time; its models of everyday situations are accurate, its short-term predictions are usually correct, and its initial reactions to challenges are swift and mostly appropriate.

System 2 is more controlled, rule-based, and analytical, continuously monitoring the quality of the answers provided by System 1. Our logical brain becomes active when it needs to override an automatic judgment of System 1.

For example, the earlier driver proceeding casually down the road is more focused when passing a semi-truck on a narrow two-lane road or in heavy traffic, actively processing the changing conditions and responding with deliberate actions. His or her mental effort is accompanied by detectable physical changes, such as tensed muscles, increased heart rate, and dilated pupils. In these circumstances, System 2 is in charge.

The logical brain normally functions in low-effort mode, always in reserve until System 1 encounters a problem it cannot solve or is required to act in a way that doesn’t come naturally. Solving for the product of 37 x 82 requires the deliberate processes of System 2, while the answer to a simple addition problem, such as the sum of 2 + 2, is a System 1 function. The answer is not calculated, but summoned from memory.

Neuropsychologists Abigail Baird and Jonathan Fugelsang’s 2004 study indicates that System 2 does not fully develop until adulthood. Their findings suggest the reason that adolescents are more likely to engage in risky behavior is because they lack the mental hardware to weigh decisions rationally. For most people, the two systems work together seamlessly, transitioning from one to the other as needed.

The Buffett Style.
The Oracle of Omaha’s key to investing is understanding and coordinating the two systems of decision-making. Buffett relies upon System 1 to intuitively seek out investments he finds attractive and understands.

When deciding on a possible investment, he recommends, “If you need a computer or a calculator to decide whether to invest, then don’t do it – invest in something that shouts at you – if it is not obvious, walk away . . . If you don’t know the business, the financials won’t help at all.”

Avoid the Traps of Thinking Fast.
Master investors like Buffett simplify their decisions by relying upon System 1, and it serves them well in most cases. However, they recognize that their emotional decision-making system is also prone to biases and errors, including:

Mental Framing.
Our brains, equipped with millions of sensory inputs, create interpretive mental “frames” or filters to make sense of data. These mental filters help us understand and respond to the events around us. Framing is a heuristic – a mental shortcut – that provides a quick, easy way to process information. Unfortunately, framing can also provide a limited, simplistic view of reality that can lead to flawed decisions.

The choices we make depend on our perspective, or the frames surrounding the problem. For example, research shows that people are likely to proceed with a decision if the outcome is presented with a 50% chance of success and decline if the consequence is expressed with a 50% chance of failure, even though the probability is the same in either case.

Most investors incorrectly frame stock investments by thinking of the stock market as a stream of electronic bits of data independent of the underlying businesses the data represents. The constant flow of information about prices, economies, and expert opinions triggers our emotional brains and stimulates quick decisions to reap profits (pleasure) or prevent loss (pain).

Buffett recommends investors not think of an investment in stock as “a piece of paper whose price wiggles around daily” and is a candidate for sale whenever you get nervous.

Short-term thinking – System 1 – often leads to trading stocks, not investing in companies. Day traders – those who buy and sell stocks within a single market session – are unusually unsuccessful, according to day trading studies by the University of California-Berkeley:

80% of all day traders quit within the first two years.
Active traders underperform the stock market average by 6.5% annually.
Only 1.6% of day traders make a net profit each year.
Financial data is especially susceptible to framing. Companies always express earnings and losses positively, either as an increase compared to past results or a smaller loss than previous periods. Trends can be manipulated based upon the comparison point and time interval.

Even the words we use to describe a choice establish a frame for assessing value. Characterizations like “high growth,” “turnaround,” or “cyclical” trigger the subconscious stereotypes we have for such terms without regard to the underlying financial data.

Framing can lead rational people to make irrational decisions based upon their projections of the outcome. This accounts for the difference between economics’ rational man and psychology’s natural man.

Buffett has learned to frame his investment opportunities appropriately to avoid short-term, arbitrary outcomes:

“We [Berkshire Hathaway] select such investments on a long-term basis, weighing the same factors as would be involved in the purchase of 100% of an operating business.”
“When we own portions of outstanding businesses with outstanding managements, our favorite holding period is forever.”
“If you aren’t willing to own a stock for 10 years, don’t even think about owning it 10 minutes.”
Loss Aversion.
Kahneman and Tversky determined that in human decision-making, losses loom larger than gains. Their experiments suggest that the pain of loss is twice as a great as the pleasure from gain. This feeling arises in the amygdala, which is responsible for generating fearful emotions and memories of painful associations.

The fact that investors are more likely to sell stocks with profit than those with a loss, when the converse strategy would be more logical, is evidence of the power of loss aversion.

While Buffett sells his positions infrequently, he cuts his losses when he realizes he has made a judgment error. In 2016, Buffett substantially reduced or liquidated his position in three companies, because he believed they had lost their competitive edge:

Wal-Mart: Despite his regrets that he had not purchased more shares earlier, he has been a long-time investor in the company. The rationale for the recent sales is thought to be due to the transition of the retail market from bricks-and-mortar stores to online. A Pew Research Center study found almost 80% of Americans today are online shoppers versus 22% in 2000.
Deere & Co: Buffett’s initial purchases of the agricultural equipment manufacturer began in the third quarter of 2012. By 2016, he owned almost 22-million shares with an average cost of less than $80 per share. He liquidated his shares during the last two quarters of 2016 when prices were more than $100 per share. Buffett may have felt that farm income, having fallen by half since 2013 due to worldwide bumper crops, was unlikely to improve, leaving the premier provider of agricultural equipment unable to continue to expand its profits.
Verizon: Having owned the stock since 2014, he liquidated his entire position in 2016, due to a loss of confidence in management after the company’s questionable acquisition of Yahoo and the continued turmoil in the wireless carrier market.
Our distaste for losses can create anxiety and trick us into acting prematurely because we fear being left out in a rising market or staying too long in a bear market. Buffett and Munger practice “assiduity – the ability to sit on your ass and do nothing until a great opportunity presents itself.”

Representativeness.
People tend to ignore statistics and focus on stereotypes. An example in the Association of Psychological Science Journal illustrates this common bias. When asked to select the proper occupation of a shy, withdrawn man who takes little interest in the real world from a list including farmer, salesman, pilot, doctor, and librarian, most people incorrectly chose librarian. Their decision ignores the obvious: there are many more farmers in the world than librarians.

Buffett focuses on finding the “inevitables” – great companies with insurmountable advantages – rather than following conventional wisdom and accepted patterns of thinking favored by System 1’s decision-making process. In his 1996 letter to investors, he defines Coca-Cola and Gillette as two companies that “will dominate their fields worldwide for an investment lifetime.”

He is especially wary of “imposters” – those companies that seem invincible but lack real competitive advantage. For every inevitable, there are dozens of imposters. According to Buffett, General Motors, IBM, and Sears lost their seemingly insurmountable advantages when values declined in “the presence of hubris or of boredom that caused the attention of the managers to wander.”

Buffett recognizes that companies in high-tech or embryonic industries capture our imaginations – and excite our emotional brains – with their promise of extraordinary gains. However, he prefers investments where he is “certain of a good result [rather] than hopeful of a great one” – an example of the logical brain at work.

Anchoring.
Evolution is the reason humans rely too heavily on the first or a single bit of information they receive – their “first impression.” In a world of deadly perils, delaying action can lead to pain or death. Therefore, first impressions linger in our minds and affect subsequent decisions. We subconsciously believe that what happened in the past will happen in the future, leading us to exaggerate the importance of the initial purchase price in subsequent decisions to sell a security.

Investors unknowingly make decisions based on anchoring data, such as previous stock prices, past years’ earnings, consensus analyst projections or expert opinions, and prevailing attitudes about the direction of stock prices, whether in a bear or bull market. While some characterize this effect as following a trend, it is a System 1 shortcut based on partial information, rather than the result of System 2 analysis.

Buffett often goes against the trend of popular opinion, recognizing that “most people get interested in stocks when everyone else is. The time to get interested is when no one else is. You can’t buy what is popular and do well.” When making a decision based on historical data, he notes, “If past history was all that is needed to play the game of money, the richest people would be librarians.”

Buffett’s approach is neither to follow the herd nor purposely do the opposite of the consensus. Whether people concur with his analysis isn’t important. His goal is simple: acquire, at a reasonable price, a business with excellent economics and able, honest management.

Despite considering IBM an “imposter” in 1996, Berkshire Hathaway began acquiring the stock in 2011, consistently adding to Buffett’s position over the years. By the end of the first quarter in 2017, Berkshire owned more than 8% of the outstanding shares with a value greater than $14 billion.

While his analysis remains confidential, Buffett believes that the investors have discounted the future of IBM too severely and failed to note its transition to a cloud-based business might lead to brighter growth prospects and a high degree of customer retention. Also, the company pays a dividend almost twice the level of the S&P 500 and actively repurchases shares on the open market.

The growing IBM position – quadrupling since the initial purchase – is evidence that Buffett isn’t afraid to take action when he is comfortable with his analysis: “Opportunities come infrequently. When it rains gold, put out the bucket, not the thimble.”

Availability.
Humans tend to estimate the likelihood of an event occurring based on the ease with which it comes to mind. For example, a 2008 study of State lottery sales showed that stores that sell a publicized, winning lottery ticket experience a 12% to 38% increase in sales for up to 40 weeks following the announcement of the winner.

People visit stores selling a winning ticket more often due to the easy recall of the win, and a bias that the location is “lucky” and more likely to produce another winning ticket than a more convenient store down the street.

This bias frequently affects decisions about stock investments. In other words, investor perceptions lag reality. Momentum, whether upward or downward, continues well past the emergence of new facts. Investors with losses are slow to reinvest, often sitting on the sidelines until prices have recovered most of their decline (irrational pessimism).

Conversely, reinforcement from a bull market encourages continued purchasing even after the economic cycle turns down (irrational optimism). Therefore, investors tend to buy when prices are high and sell when they are low.

The S&P 500 fell 57% between late 2007 and March 2009, devastating investor portfolios and liquidating stocks and mutual funds. Even though the index had recovered its losses by mid-2012, individual investors had not returned to equity investments, either staying in cash or purchasing less risky bonds.

At the time, Liz Ann Sonders, Chief Investment Strategist at Charles Schwab & Co., noted, “Even three-and-a-half years into this bull market and the gains we’ve seen since June [2012], it has not turned this psychology [of fear] around.” In other words, many individuals took the loss but did not participate in the subsequent recovery.

Buffett has always tried to follow the advice of his mentor, Benjamin Graham, who said, “Buy not on optimism [or sell due to pessimism], but on arithmetic.” Graham advocated objective analysis, not emotions, when buying or selling stocks: “In the short run, the market is a voting machine [emotional], but in the long run it is a weighing machine [logical].”

Affect.
We tend to assess probabilities based on our feelings about the options. In other words, we judge an option less risky solely because we favor it and vice versa. This bias can lead people to buy stock in their employer when other investments would be more appropriate for their goals. Overconfidence in one’s ability magnifies the negative impact of affect.

For example, Buffett invested $350 million in preferred stock of U.S. Airways in 1989, despite his belief that airlines and airline manufacturers had historically been a death trap for investors. The investment followed a dinner with Ed Colodny, the CEO of the airline, who impressed Buffett. Certain that the preferred stock was safe and the airline had a competitive seat cost (around 12 cents per mile), he made the investment.

Buffett later admitted his analysis “was superficial and wrong,” perhaps due to hubris and his like for Colodny. An upstart Texas airline (Southwest Airlines) subsequently upset the competitive balance in the industry with seat costs of 8 cents per mile, causing Berkshire Hathaway to write down its investment by 75%.

Buffett was lucky to make a significant profit on the investment ($216 million), primarily because the airline subsequently and unexpectedly returned to profitability and was able to pay the accrued dividends and redeem its preferred stock.

Final Word.
Mr. Buffett’s investment style has been criticized by many over the decades. Trend followers and traders are especially critical of his record and philosophy, claiming that his results are the result of “luck, given the relatively few trades that made him so wealthy.”

Hedge fund manager Michael Steinhardt, who Forbes called “Wall Street’s Greatest Trader,” said during a CNBC interview that Buffett is “the greatest PR person of all time. And he has managed to achieve a snow job that has conned virtually everyone in the press to my knowledge.”

Before following the advice of those who are quick to condemn Buffett’s investment style, it should be noted that no investment manager has come close to rivaling Buffet’s record over the past 60 years. While Steinhardt’s returns are similar to those of Buffett, his were for a period of 28 years – less than one-half of Buffett’s cycle.

Despite their antipathy, both men would agree that System 2 decision-making is critical to investment success. Steinhardt, in his autobiography “No Bull: My Life In and Out of Markets,” said that his results required “knowing more and perceiving the situation better than others did . . . Reaching a level of understanding that allows one to feel competitively informed well ahead of changes in ‘street’ views, even anticipating minor stock price changes, may justify at times making unpopular investments.”

Buffett appears to agree, insisting on taking the time for introspection and thought. “I insist on a lot of time being spent, almost every day, to just sit and think. That is very uncommon in American business. I read and think. So I do more reading and thinking, and make fewer impulsive decisions than most people in business.”

Do you take the time to gather facts and make carefully analyzed investment decisions? Perhaps you are more comfortable going with the flow. What is your decision-making preference and how has it worked out for you thus far?
Do you know anyone who has owned the same stock for 20 years? Warren Buffett has held three stocks – Coca-Cola, Wells Fargo, and American Express – for more than 20 years. He has owned one stock – Moody’s – for 15 years, and three other stocks – Proctor & Gamble, Wal-Mart, and U.S. Bancorp – for over a decade.

To be sure, Mr. Buffett’s 50-year track record is not perfect, as he has pointed out from time to time:

Berkshire Hathaway: Pique at CEO Seabird Stanton motivated his takeover of the failing textile company. Buffett later admitted the purchase was “the dumbest stock I ever bought.”
Energy Future Holding: Buffett lost a billion dollars in bonds of the bankrupt Texas electric utility. He admitted he made a huge mistake not consulting his long-term business partner Charlie Munger before closing the purchase: “I would be unwilling to share the credit for my decision to invest with anyone else. That was just a mistake – a significant mistake.”
Wal-Mart: At the 2003 Berkshire Hathaway shareholder meeting, Buffet admitted his attempt to time the market had backfired: “We bought a little, and it moved up a little, and I thought maybe it would come back. That thumb-sucking has cost us in the current area of $10 billion.”
Even with these mistakes, Buffett has focused on making big bets that he intends to hold for decades to come. A longer time horizon has allowed him to take advantage of opportunities few others have the patience for. But how has he been able to make these successful bets in the first place?

source : https://www.moneycrashers.com/warren-buffett-decisions-secret-investing-success.
August 14, 2020

How to Use the Rule of 72.

The Rule of 72 is a handy tool used in finance to estimate the number of years it would take to double a sum of money through interest payments, given a particular interest rate. The rule can also estimate the annual interest rate required to double a sum of money in a specified number of years. The rule states that the interest rate multiplied by the time period required to double an amount of money is approximately equal to 72.
The Rule of 72 is applicable in cases of exponential growth, (as in compound interest) or in exponential "decay," as in the loss of purchasing power caused by monetary inflation.

Method 1 Estimating "Doubling" Time.
1. Let R x T = 72. R is the rate of growth (the annual interest rate), and T is the time (in years) it takes for the amount of money to double.
2. Insert a value for R. For example, how long does it take to turn $100 into $200 at a yearly interest rate of 5%? Letting R = 5, we get 5 x T = 72.
3. Solve for the unknown variable. In this example, divide both sides of the above equation by R (that is, 5) to get T = 72 ÷ 5 = 14.4. So it takes 14.4 years for $100 to double at an interest rate of 5% per annum. (The initial amount of money doesn't matter. It will take the same amount of time to double no matter what the beginning amount is.)
4. Study these additional examples:
How long does it take to double an amount of money at a rate of 10% per annum? 10 x T = 72. Divide both sides of the equation by 10, so that T = 7.2 years.
How long does it take to turn $100 into $1600 at a rate of 7.2% per annum? Recognize that 100 must double four times to reach 1600 ($100 → $200, $200 → $400, $400 → $800, $800 → $1600). For each doubling, 7.2 x T = 72, so T = 10. So, as each doubling takes ten years, the total time required (to change $100 into $1,600) is 40 years.

Method 2 Estimating the Growth Rate.
1. Let R x T = 72. R is the rate of growth (the interest rate), and T is the time (in years) it takes to double any amount of money.
2. Enter the value of T. For example, let's say you want to double your money in ten years. What interest rate would you need in order to do that? Enter 10 for T in the equation. R x 10 = 72.
3. Solve for R. Divide both sides by 10 to get R = 72 ÷ 10 = 7.2. So you will need an annual interest rate of 7.2% in order to double your money in ten years.

Method 3 Estimating Exponential "Decay" (Loss).
1. Estimate the time it would take to lose half of your money (or its purchasing power in the wake of inflation). Let T = 72 ÷ R. This is the same equation as above, just slightly rearranged. Now enter a value for R. An example.
How long will it take for $100 to assume the purchasing power of $50, given an inflation rate of 5% per year?
Let 5 x T = 72, so that T = 72 ÷ 5 = 14.4. That's how many years it would take for money to lose half its buying power in a period of 5% inflation. (If the inflation rate were to change from year to year, you would have to use the average inflation rate that existed over the full time period.)
2. Estimate the rate of decay (R) over a given time span: R = 72 ÷ T. Enter a value for T, and solve for R. For example.
If the buying power of $100 becomes $50 in ten years, what is the inflation rate during that time?
R x 10 = 72, where T = 10. Then R = 72 ÷ 10 = 7.2%.
3. Ignore any unusual data. If you can detect a general trend, don't worry about temporary numbers that are wildly out of range. Drop them from consideration.

Method 4 Derivation.
1. Understand how the derivation works for periodic compounding.
For periodic compounding, FV = PV (1 + r)^T, where FV = future value, PV = present value, r = growth rate, T = time.
If money has doubled, FV = 2*PV, so 2PV = PV (1 + r)^T, or 2 = (1 + r)^T, assuming the present value is not zero.
Solve for T by taking the natural logs on both sides, and rearranging, to get T = ln(2) / ln(1 + r).
The Taylor series for ln(1 + r) around 0 is r - r2/2 + r3/3 - ... For low values of r, the contributions from the higher power terms are small, and the expression approximates r, so that t = ln(2) / r.
Note that ln(2) ~ 0.693, so that T ~ 0.693 / r (or T = 69.3 / R, expressing the interest rate as a percentage R from 0-100%), which is the rule of 69.3. Other numbers such as 69, 70, and 72 are used for easier calculations.
2. Understand how the derivation works for continuous compounding. For periodic compounding with multiple compounding per year, the future value is given by FV = PV (1 + r/n)^nT, where FV = future value, PV = present value, r = growth rate, T = time, and n = number of compounding periods per year. For continuous compounding, n approaches infinity. Using the definition of e = lim (1 + 1/n)^n as n approaches infinity, the expression becomes FV = PV e^(rT).
If money has doubled, FV = 2*PV, so 2PV = PV e^(rT), or 2 = e^(rT), assuming the present value is not zero.
Solve for T by taking natural logs on both sides, and rearranging, to get T = ln(2)/r = 69.3/R (where R = 100r to express the growth rate as a percentage). This is the rule of 69.3.
For continuous compounding, 69.3 (or approximately 69) gives more accurate results, since ln(2) is approximately 69.3%, and R * T = ln(2), where R = growth (or decay) rate, T = the doubling (or halving) time, and ln(2) is the natural log of 2. 70 may also be used as an approximation for continuous or daily (which is close to continuous) compounding, for ease of calculation. These variations are known as rule of 69.3, rule of 69, or rule of 70.
A similar accuracy adjustment for the rule of 69.3 is used for high rates with daily compounding: T = (69.3 + R/3) / R.
The Eckart-McHale second order rule, or E-M rule, gives a multiplicative correction to the Rule of 69.3 or 70 (but not 72), for better accuracy for higher interest rate ranges. To compute the E-M approximation, multiply the Rule of 69.3 (or 70) result by 200/(200-R), i.e., T = (69.3/R) * (200/(200-R)). For example, if the interest rate is 18%, the Rule of 69.3 says t = 3.85 years. The E-M Rule multiplies this by 200/(200-18), giving a doubling time of 4.23 years, which better approximates the actual doubling time 4.19 years at this rate.
The third-order Padé approximant gives even better approximation, using the correction factor (600 + 4R) / (600 + R), i.e., T = (69.3/R) * ((600 + 4R) / (600 + R)). If the interest rate is 18%, the third-order Padé approximant gives T = 4.19 years.
To estimate doubling time for higher rates, adjust 72 by adding 1 for every 3 percentages greater than 8%. That is, T = [72 + (R - 8%)/3] / R. For example, if the interest rate is 32%, the time it takes to double a given amount of money is T = [72 + (32 - 8)/3] / 32 = 2.5 years. Note that 80 is used here instead of 72, which would have given 2.25 years for the doubling time.


FAQ.
Question : When would I need to use the rule of 72?
Answer : It's a handy shortcut when considering compounded, monetary gains or losses. For example, you might want to know how long it would take for invested money to double in value, given a specific rate of interest.
Question : How do I calculate compound interest?
Answer : The formula for annual compound interest (A) is: P [1 + (r / n)]^(nt), where P=principal amount, r = the annual interest rate as a decimal, n = the number of times the interest is compounded per year, and t = the number of years of the loan or investment.
Question : What is APY for an APR of 3.5% compounded?
Answer : It depends on how often the interest compounds: annually, semi-annually, quarterly, monthly or daily.

Tips.

Let the Rule of 72 work for you by starting to save now. At a growth rate of 8% a year (the approximate rate of return in the stock market), you would double your money in nine years (72 ÷ 8 = 9), quadruple your money in 18 years, and have 16 times your money in 36 years.
The value of 72 was chosen as a convenient numerator in the above equation. 72 is easily divisible by several small numbers: 1,2,3,4,6,8,9, and 12. It provides a good approximation for annual compounding at typical rates (from 6% to 10%). The approximations are less exact at higher interest rates.
You can use Felix's Corollary to the Rule of 72 to calculate the "future value" of an annuity (that is, what the annuity's face value will be at a specified future time). You can read about the corollary on various financial and investing websites.

Warnings.
Let the rule of 72 convince you not to take on high-interest debt (as is typical with credit cards). At an average interest rate of 18%, semiretired credit card debt doubles in just four years (72 ÷ 18 = 4), quadruples in eight years, and becomes completely unmanageable after that.
April 10, 2020

Ray Dalio: 3 pieces of advice for how to manage your savings in a coronavirus recession.

By Tom Huddleston Jr.

Though the stock market is on the rebound of late as more and more states reopen, hedge fund billionaire Ray Dalio has made it clear that he expects the ongoing coronavirus pandemic to leave behind an economic downturn that could be the worst since the Great Depression.

“We’re not going to go back to normal” once the pandemic subsides, Dalio previously told CNBC Make It, arguing against the idea of a “v-shaped recovery” where the economy would rebound quickly once the country fully reopens.

“Think of the virus as like a tsunami that comes in,” Dalio said. “And if it goes away completely and we never see it again, it still will produce damage, the financial damage ... incomes that are lost, balance sheets that are hurt, restructurings that need to take place. So that will impede the recovery.”

With that in mind, Dalio has advice for Americans worrying about whether or not their savings will keep them afloat should the economy truly take a historic turn for the worse that lasts well beyond 2020.

Though 21% of Americans do not save any of their annual income, according to a 2019 Bankrate survey, for those who do, Dalio offers up three pieces of advice on relatively safe investment strategies to carry you through.

Determine how far your savings will go
First, you need to take a hard look at your savings and calculate how much you need to be “safe and free,” Dalio says.

″[Determine] how many months or years can you get by” based on your current savings and what it would take to ensure you can still have the type of life you’re comfortable leading, he says.

In other words, you should calculate your average, basic expenses — from rent or mortgage payments to food costs and other essential bills that cannot be trimmed or cut out completely — in order to figure out how much money you would need to survive losing a major source of income.

Dalio suggests saving enough to make sure “you’re okay for ‘X’ amount of time,” he says, whether that’s several months, or even a year.

Remember, “you don’t have to have a world of luxury to cover the basics,” he says.

And “when you’ve [calculated] that savings ... cut it in half, just to be conservative,” Dalio says. “Because between taxes, inflation and possible losses in your portfolio, maybe they can add up to half.”

“That’s No. 1. Do those calculations so that you know, if everything is bad, you and your family [are] still good,” Dalio says.

Once you have that amount of your portfolio set aside to feel safe, Dalio says you can start planning how to put the rest of your money to work for you by investing any money that is not part of what you’ve set aside from your expenses.

“I want you to visualize your acceptable worst case scenario and secure that, because once you do, everything else changes and you can have peace of mind that you can take more risk,” Dalio says. “But if you haven’t secured that acceptable picture, you have to make doing that your top priority.”

Diversify your investments
Which brings on Dalio’s second piece of money advice, which is to take the money that you feel comfortable building on and “diversify that portfolio well.” That means spreading your money across different asset classes that can typically be counted on to perform relatively well no matter the economic environment.

“You need to diversify by holding assets that will do well in either a rising or a falling growth environment, or a rising or falling inflation environment, and [you] should diversify by holding international as well as domestic asset classes,” Dalio says.

For instance, the billionaire has been adamant that investors should back “both horses in the race” in terms of the U.S.-China trade war and the two superpowers’ increasing competition for economic growth in recent years.

“I believe Chinese businesses are competitors of American businesses or other business around the world, and that therefore you want to be, if you’re diversified, having bets on both horses in the race,” Dalio said in 2019.

Dalio has also argued against holding onto cash or government bonds at the moment, due to fears that currency inflation could hurt their value over time. “Cash is not going to be a good investment,” he says, adding: “In relation to inflation, it’ll probably lose 2% a year and maybe more.”

Dalio does see gold as a more attractive asset, he says, echoing his sentiments from January, when he said: “I think you have to have a little bit of gold in your portfolio.” Many investors, including billionaire Warren Buffett, tend to look at gold as a relatively safe and steady investment in times of crisis.

Don’t try to time the market
Lastly, Dalio says never try to time the market.

That is “going to be really important.”

In the past, Dalio has said that the “biggest mistake that most people make is to judge what will be good by what has been good lately” in terms of looking at how the stock market has performed recently and when is the best time to buy.

Trying to perfectly time the market is something that even professionals can’t always manage, and the average person will find it extremely difficult to do successfully, Dalio says.

“To do that well you have to beat the pros, who themselves typically can’t do that well.”

Instead, it’s probably a better idea for non-professional investors to take long-term positions in a diversified portfolio that can pay off over time. Otherwise, all investors need to keep in mind the historical cycles and patterns of the economy and stock market.

From bubbles leading into busts, and vice versa, Dalio has always been adamant that those economic cycles tend to repeat themselves and that investors need to learn to avoid thinking along the lines of: ”‘That’s a bad market, and I don’t want any of it,’” Dalio previously told CNBC Make It. That’s because a bear market might actually be the best time to get bargain prices on certain stocks.

After all, a company like Amazon once saw its stock price lost most of its value after the tech bubble burst in the early 2000s, but many of the company’s long-term investors (those who held onto the stock through rough times, or bought it at a nadir) have seen huge gains because they ignored the most recent market trends at the time and took a long-term approach that’s paid off as Amazon is now worth several times what it was even just a decade ago.

August 11, 2020