Five Secrets To Buffett’s Success.

Five Secrets To Buffett’s Success.

By John P. Reese.

Warren Buffett has made enough money by investing over the decades to warrant the attention he gets.
But why haven't others been able to generate the billions of dollars of personal wealth he has amassed using the same techniques? At Validea, I study and extract the stock selection methods of great investors and my strategies have come nowhere near Buffett’s incredible long-term results.
It could be that Buffett, and his Berkshire Hathaway (BRK.A) conglomerate, follow some simple investment rules that others find difficult to follow.
Patience and discipline over the long-term—and we're talking decades, here, not quarters, months or weeks—isn't the hallmark of the typical investor. It is one of Buffett's strong suits.
Having a process and sticking with it through thick and thin is also difficult for the average investor, so much so that Buffett himself has advised those who can't do it to stick to low-cost funds that track market indexes. But there is also Buffett's willingness to not follow the crowd when stocks are hot and being brave when others aren't and grabbing those unique opportunities.

Here are five secrets to Buffett's success.

Dividend stocks.
Companies that pay dividends tend to have characteristics Buffett likes, such as a good market share and steady and reliable growth and profitability. Otherwise, management wouldn't feel comfortable giving a set portion of the cash flow every quarter back to investors. Dividend-paying companies historically outperform those that don't pay one.
Of course, for investors, dividends are a source of income, and Berkshire's $182 billion portfolio has certainly delivered on that score.
The payout on Berkshire's Bank of America (BAC) shares alone is more than $526 million. And Apple (AAPL) shares will pay about $737 million. Kraft Heinz pays $814 million and Coca Cola (KO) pays $624 million. Wells Fargo $760 million.
By one calculation, according to Motley Fool, Berkshire could collect more than $4.6 billion in dividend payments for 2019, based on the company's reported holdings. Berkshire's portfolio changes slightly from quarter to quarter, so that might not be an exact number, but the message is clear. Berkshire is making a lot of money from dividend investing.

Buy-and-hold strategy.
The portfolio also highlights Buffett's other secret: invest for the long term rather than attempting to time the market. This is a lesson he learned from Benjamin Graham, the so-called father of the value investing style, Buffett embraced decades ago. The underpinning of the strategy is to buy stocks, for less than they are worth fundamentally and hold on to them.
Someone who is frequently trading in and out of a stock is merely speculating on the direction of the market and various events that may affect it. That is a speculator, not an investor.
Truly value-oriented investors would be more concerned with a company's measurable value, including profitability and assets, not with the short-term events that create near-term price swings in the stock.
Berkshire's portfolio reflects Buffett's buy-and-hold philosophy. American Express (AXP) is a holding dating back to the mid-1960s. Coke (KO) shares have been in Berkshire's hands since the 1980s. So have shares of Wells Fargo (WFC).
Moody's Corporation (MCO) is another long-term holding going back more than a decade, as are U.S. Bancorp (USB) and Proctor & Gamble (PG).
Among Berkshire's biggest holdings, Apple is the newest entry, first appearing in 2017.

Don't be afraid to let go.
That is not to say Buffett hasn't made some mistakes, and he is open about them when he does. Shares of IBM (IBM) are the perfect example.
Berkshire had long shied away from technology stocks, but in 2011 began building a stake in IBM…..just as the company would begin an agonizing six-year stretch of declining revenue and shrinking market value. Berkshire finally tossed in the towel in 2018, admitting its investment thesis was flawed.
Buffett has also talked about famous misses, including Google, which has surged to over $1 trillion in market value in the last few years. He told shareholders at the annual meeting last year that he considered it and then passed. "I blew it."

Seize opportunities.
If Buffett's success is owed to anything, though, it's to being brave when others are afraid. This means taking a chance on a stock when the rest of the investing world is fleeing for the sidelines.
During the 2008-2009 financial crisis, when investors were panicking about the markets and banks were reeling from losses on mortgage-backed securities, Berkshire swooped in with a $5 billion deal to back Goldman Sachs. The deal included high-yielding preferred stock and the chance to buy more common stock down the road, which Berkshire did, netting billions when Goldman and the rest of the financial sector recovered.
Buffett stuck a similar deal in 2011 to help Bank of America, which was reeling from lawsuits dating back to the mortgage bond crisis. Berkshire swapped the preferred stock for common stock in 2017 and continued to increase his stake in the bank, collecting billions of dollars in dividends and capital gains along the way.

Don't follow the crowd.
Finally, Buffett avoids participating in a hot market. While the S&P 500 reached multiple records last year, Berkshire's pile of cash available to invest grew to $128 billion. This has baffled analysts but probably reflects Buffett's view that there isn't much out there that is valued to his liking, so the best solution is to avoid making a costly mistake and just wait it out.
Instead, Berkshire is doing something it hasn't done in the past: It's buying back its own stock, to the tune of $700 million in the third quarter and probably more for the final three months of last year. That reflects Buffett's belief that Berkshire is undervalued.
He told the Financial Times in an interview last year that the time Berkshire is finally trading at a fair price and the stock market also looks expensive would be his "nightmare."
For investors, you may not be able to achieve the performance Buffett has but these are timeless investing principles that can go a long way to helping you achieve good results in the stock market over time. Learning from successful investors like Buffett can go a long way for many investors.

August 04, 2020

Value Investing Strategies. PART 1

Value Investing.

By ADAM HAYES.

What Is Value Investing?
Value investing is an investment strategy that involves picking stocks that appear to be trading for less than their intrinsic or book value. Value investors actively ferret out stocks they think the stock market is underestimating. They believe the market overreacts to good and bad news, resulting in stock price movements that do not correspond to a company's long-term fundamentals. The overreaction offers an opportunity to profit by buying stocks at discounted prices—on sale.


Warren Buffett is probably the best-known value investor today, but there are many others, including Benjamin Graham (Buffet's professor and mentor), David Dodd, Charlie Munger, Christopher Browne (another Graham student), and billionaire hedge-fund manager, Seth Klarman.


KEY TAKEAWAYS.
Value investing is an investment strategy that involves picking stocks that appear to be trading for less than their intrinsic or book value.
Value investors actively ferret out stocks they think the stock market is underestimating.
Value investors use financial analysis, don't follow the herd, and are long-term investors of quality companies.
How Value Investing Works
The basic concept behind every-day value investing is straightforward: If you know the true value of something, you can save a lot of money when you buy it on sale. Most folks would agree that whether you buy a new TV on sale, or at full price, you’re getting the same TV with the same screen size and picture quality.


Stocks work in a similar manner, meaning the company’s stock price can change even when the company’s value or valuation has remained the same. Stocks, like TVs, go through periods of higher and lower demand leading to price fluctuations—but that doesn't change what you’re getting for your money.

Just like savvy shoppers would argue that it makes no sense to pay full price for a TV since TVs go on sale several times a year, savvy value investors believe stocks work the same way. Of course, unlike TVs, stocks won't go on sale at predictable times of the year such as Black Friday, and their sale prices won’t be advertised.

Value investing is the process of doing detective work to find these secret sales on stocks and buying them at a discount compared to how the market values them. In return for buying and holding these value stocks for the long-term, investors can be rewarded handsomely.


 Value investing developed from a concept by Columbia Business School professors Benjamin Graham and David Dodd in 1934 and was popularized in Graham's 1949 book, The Intelligent Investor.
Intrinsic Value and Value Investing
In the stock market, the equivalent of a stock being cheap or discounted is when its shares are undervalued. Value investors hope to profit from shares they perceive to be deeply discounted.


Investors use various metrics to attempt to find the valuation or intrinsic value of a stock. Intrinsic value is a combination of using financial analysis such as studying a company's financial performance, revenue, earnings, cash flow, and profit as well as fundamental factors, including the company's brand, business model, target market, and competitive advantage. Some metrics used to value a company's stock include:

Price-to-book (P/B) or book value or, which measures the value of a company's assets and compares them to the stock price. If the price is lower than the value of the assets, the stock is undervalued, assuming the company is not in financial hardship.

Price-to-earnings (P/E), which shows the company's track record for earnings to determine if the stock price is not reflecting all of the earnings or undervalued.

Free cash flow, which is the cash generated from a company's revenue or operations after the costs of expenditures have been subtracted. Free cash flow is the cash remaining after expenses have been paid, including operating expenses and large purchases called capital expenditures, which is the purchase of assets like equipment or upgrading a manufacturing plant. If a company is generating free cash flow, it'll have money left over to invest in the future of the business, pay off debt, pay dividends or rewards to shareholders, and issue share buybacks.

Of course, there are many other metrics used in the analysis, including analyzing debt, equity, sales, and revenue growth. After reviewing these metrics, the value investor can decide to purchase shares if the comparative value—the stock's current price vis-a-vis its company's intrinsic worth—is attractive enough.

Margin of Safety.
Value investors require some room for error in their estimation of value, and they often set their own "margin of safety," based on their particular risk tolerance. The margin of safety principle, one of the keys to successful value investing, is based on the premise that buying stocks at bargain prices gives you a better chance at earning a profit later when you sell them. The margin of safety also makes you less likely to lose money if the stock doesn’t perform as you had expected.

Value investors use the same sort of reasoning. If a stock is worth $100 and you buy it for $66, you’ll make a profit of $34 simply by waiting for the stock’s price to rise to the $100 true value. On top of that, the company might grow and become more valuable, giving you a chance to make even more money. If the stock’s price rises to $110, you’ll make $44 since you bought the stock on sale. If you had purchased it at its full price of $100, you would only make a $10 profit. Benjamin Graham, the father of value investing, only bought stocks when they were priced at two-thirds or less of their intrinsic value. This was the margin of safety he felt was necessary to earn the best returns while minimizing investment downside.

Markets are not Efficient.
Value investors don’t believe in the efficient-market hypothesis, which says that stock prices already take all information about a company into account, so their price always reflects their value. Instead, value investors believe that stocks may be over- or underpriced for a variety of reasons.

For example, a stock might be underpriced because the economy is performing poorly and investors are panicking and selling (as was the case during the Great Recession). Or a stock might be overpriced because investors have gotten too excited about an unproven new technology (as was the case of the dot-com bubble). Psychological biases can push a stock price up or down based on news, such as disappointing or unexpected earnings announcements, product recalls, or litigation. Stocks may also be undervalued because they trade under the radar, meaning they're inadequately covered by analysts and the media.

Don't Follow the Herd.
Value investors possess many characteristics of contrarians —they don’t follow the herd. Not only do they reject the efficient-market hypothesis, but when everyone else is buying, they’re often selling or standing back. When everyone else is selling, they’re buying or holding. Value investors don’t buy trendy stocks (because they’re typically overpriced). Instead, they invest in companies that aren’t household names if the financials check out. They also take a second look at stocks that are household names when those stocks’ prices have plummeted, believing such companies can recover from setbacks if their fundamentals remain strong and their products and services still have quality.

Value investors only care about a stock’s intrinsic value. They think about buying a stock for what it actually is: a percentage of ownership in a company. They want to own companies that they know have sound principles and sound financials, regardless of what everyone else is saying or doing.

Value Investing Requires Diligence & Patience.
Estimating the true intrinsic value of a stock involves some financial analysis but also involves a fair amount of subjectivity—meaning at times, it can be more of an art than a science. Two different investors can analyze the exact same valuation data on a company and arrive at different decisions.

Some investors, who look only at existing financials, don't put much faith in estimating future growth. Other value investors focus primarily on a company's future growth potential and estimated cash flows. And some do both: Noted value investment gurus Warren Buffett and Peter Lynch, who ran Fidelity Investment's Magellan Fund for several years are both known for analyzing financial statements and looking at valuation multiples, in order to identify cases where the market has mispriced stocks.

Despite different approaches, the underlying logic of value investing is to purchase assets for less than they are currently worth, hold them for the long-term, and profit when they return to the intrinsic value or above. It doesn't provide instant gratification. You can’t expect to buy a stock for $50 on Tuesday and sell it for $100 on Thursday. Instead, you may have to wait years before your stock investments pay off, and you will occasionally lose money. The good news is that, for most investors, long-term capital gains are taxed at a lower rate than short-term investment gains.

Like all investment strategies, you must have the patience and diligence to stick with your investment philosophy. Some stocks you might want to buy because the fundamentals are sound, but you’ll have to wait if it’s overpriced. You’ll want to buy the stock that is most attractively priced at that moment, and if no stocks meet your criteria, you'll have to sit and wait and let your cash sit idle until an opportunity arises.

One-Third.
Value investing guru Benjamin Graham argued that an undervalued stock is priced at least a third below its intrinsic value.

Why Stocks Become Undervalued.
If you don’t believe in the efficient market hypothesis, you can identify reasons why stocks might be trading below their intrinsic value. Here are a few factors that can drag a stock’s price down and make it undervalued.

Market Moves and Herd Mentality.
Sometimes people invest irrationally based on psychological biases rather than market fundamentals. When a specific stock’s price is rising or when the overall market is rising, they buy. They see that if they had invested 12 weeks ago, they could have earned 15% by now, and they develop a fear of missing out. Conversely, when a stock’s price is falling or when the overall market is declining, loss aversion compels people to sell their stocks. So instead of keeping their losses on paper and waiting for the market to change directions, they accept a certain loss by selling. Such investor behavior is so widespread that it affects the prices of individual stocks, exacerbating both upward and downward market movements creating excessive moves.

Market Crashes.
When the market reaches an unbelievable high, it usually results in a bubble. But because the levels are unsustainable, investors end up panicking, leading to a massive selloff. This results in a market crash. That's what happened in the early 2000s with the dotcom bubble, when the values of tech stocks shot up beyond what the companies were worth. We saw the same thing happened when the housing bubble burst and the market crashed in the mid-2000s.

Unnoticed and Unglamorous Stocks.
Look beyond what you're hearing in the news. You may find really great investment opportunities in undervalued stocks that may not be on people's radars like small caps or even foreign stocks. Most investors want in on the next big thing such as a technology startup instead of a boring, established consumer durables manufacturer. For example, stocks like Facebook, Apple, and Google are more likely to be affected by herd-mentality investing than conglomerates like Proctor & Gamble or Johnson & Johnson.

Bad News.
Even good companies face setbacks, such as litigation and recalls. However, just because a company experiences one negative event doesn’t mean that the company isn’t still fundamentally valuable or that its stock won’t bounce back. In other cases, there may be a segment or division that puts a dent in a company's profitability. But that can change if the company decides to dispose of or close that arm of the business.

Analysts do not have a great track record for predicting the future, and yet investors often panic and sell when a company announces earnings that are lower than analysts’ expectations. But value investors who can see beyond the downgrades and negative news can buy stock at deeper discounts because they are able to recognize a company's long-term value.

Cyclicality​.
Cyclicality is defined as the fluctuations that affect a business. Companies are not immune to ups and downs in the economic cycle, whether that's seasonality and the time of year, or consumer attitudes and moods. All of this can affect profit levels and the price of a company's stock, but it doesn't affect the company's value in the long term.

July 25, 2020

Strategies of Legendary Value Investors

Strategies of Legendary Value Investors.

By ANDREW BEATTIE.

Value investing is a strategy where investors actively look to add stocks they believe have been undervalued by the market, and/or trade for less than their intrinsic values. Like any type of investing, value investing varies in execution with each person. There are, however, some general principles that are shared by all value investors.

These principles have been spelled out by famed investors like Peter Lynch, Kenneth Fisher, Warren Buffett, Bill Miller and others. By reading through financial statements, they seek out mispriced stocks and look to capitalize on a possible reversion to the mean.

In this article, we will look at some of the more well-known value investing principles.

Buy Businesses, Not Stocks.
If there is one thing that all value investors can agree on, it's that investors should buy businesses, not stocks. This means ignoring trends in stock prices and other market noise. Instead, investors should look at the fundamentals of the company that the stock represents. Investors can make money following trending stocks, but it involves a lot more activity than value investing. Searching for good businesses selling at a good price based on probable future performance requires a larger time commitment for research, but the payoffs include less time spent buying and selling, as well as fewer commission payments.

Love the Business You Buy Into.
You wouldn't pick a spouse based solely on his or her shoes, and you shouldn't pick a stock based on cursory research. You have to love the business you are buying, and that means being passionate about knowing everything about that company. You need to strip the attractive covering from a company's financials and get down to the naked truth. Many companies look far better when you judge them beyond the basic price to earnings (P/E), price to book (P/B) and earnings per share (EPS) ratios and look into the quality of the numbers that make up those figures.

If you keep your standards high and make sure the company's financials look as good naked as they do dressed up, you're much more likely to keep it in your portfolio for a long time. If things change, you'll notice it early. If you like the business you buy, paying attention to its ongoing trials and successes becomes more of a hobby than a chore.

Invest in Companies You Understand.
If you don't understand what a company does or how, then you probably shouldn't be buying shares. Critics of value investing like to focus on this main limitation. You are stuck looking for businesses that you can easily understand because you have to be able to make an educated guess about the future earnings of the business. The more complex a business is, the more uncertain your projections will likely be. This moves the emphasis from "educated" to "guess."

You can buy businesses you like but don't completely understand, but you have to factor in uncertainty as added risk. Any time a value investor has to factor in more risk, they have to look for a larger margin of safety – that is, more of a discount from the calculated true value of the company. There can be no margin of safety if the company is already trading at many multiples of its earnings, which is a strong sign that however exciting and new the idea is, the business is not a value play. Simple businesses also have an advantage, as it's harder for incompetent management to hurt the company.

Find Well-Managed Companies.
Management can make a huge difference in a company. Good management adds value beyond a company's hard assets. Bad management can destroy even the most solid financials. There have been investors who have based their entire investing strategies on finding managers that are honest and able.

Warren Buffett advises that investors should look for three qualities of good management: integrity, intelligence, and energy. He adds that "if they don't have the first, the other two will kill you." You can get a sense of management's honesty through reading several years' worth of financials. How well did they deliver on past promises? If they failed, did they take responsibility, or gloss it over?

Value investors want managers who act like owners. The best managers ignore the market value of the company and focus on growing the business, thus creating long-term shareholder value. Managers who act like employees often focus on short-term earnings in order to secure a bonus or other performance perk, sometimes to the long-term detriment of the company. Again, there are many ways to judge this, but the size and reporting of compensation is often a dead giveaway. If you're thinking like an owner, then you pay yourself a reasonable wage and depend on gains in your stock holdings for a bonus. At the very least, you want a company that expenses its stock options.

Don't Stress Over Diversification.
One of the areas where value investing runs contrary to commonly accepted investing principles is on diversification. There are long stretches where a value investor will be idle. This is because of the exacting standards of value investing as well as overall market forces. Towards the end of a bull market, everything gets expensive, even the dogs. So, a value investor may have to sit on the sidelines waiting for the inevitable correction.

Time — an important factor in compounding — is lost while waiting to invest. So, when you do find undervalued stocks, you should buy as much as you can. Be warned, this will lead to a portfolio that is high-risk according to traditional measures like beta. Investors are encouraged to avoid concentrating on only a few stocks, but value investors generally feel that they can only keep proper track of a few stocks at a time.

One obvious exception is Peter Lynch, who kept almost all of his funds in stocks at all times. Lynch broke stocks into categories and then cycled his funds through companies in each category. He also spent upwards of 12 hours every day checking and rechecking the many stocks held by his fund. However, as an individual value investor with a different day job, it's better to go with a few stocks for which you've done the homework and feel good about holding long term.

Your Best Investment Is Your Guide.
Anytime you have more investment capital, your aim for investing should not be diversity, but finding an investment that is better than the ones you already own. If the opportunities don't beat what you already have in your portfolio, you may as well buy more of the companies you know and love, or simply wait for better times.

During idle times, a value investor can identify the stocks he or she wants and the price at which they'll be worth buying. By keeping a wish list like this, you'll be able to make decisions quickly in a correction.

Ignore the Market 99% of the Time.
The market only matters when you enter or exit a position — the rest of the time, it should be ignored. If you approach buying stocks like buying a business, you'll want to hold onto them as long as the fundamentals are strong. During the time you hold an investment, there will be spots where you could sell for a large profit and others where you're holding an unrealized loss. This is the nature of market volatility.

The reasons for selling a stock are numerous, but a value investor should be as slow to sell as he or she is to buy. When you sell an investment, you expose your portfolio to capital gains and usually have to sell a loser to balance it out. Both of these sales come with transaction costs that make the loss deeper and the gain smaller. By holding investments with unrealized gains for a long time, you forestall capital gains on your portfolio. The longer you avoid capital gains and transaction costs, the more you benefit from compounding.

The Bottom Line.
Value investing is a strange mix of common sense and contrarian thinking. While most investors can agree that a detailed examination of a company is important, the idea of sitting out a bull market goes against the grain. It's undeniable that funds held constantly in the market have outperformed cash held outside the market that is waiting for a downturn to end. This is a fact, but a deceiving one. The data is derived from following the performance of market measures like the S&P 500 Index over a number of years. This is where passive investing and value investing get confused.

In both types of investing, the investor avoids unnecessary trading and has a long-term holding period. The difference is that passive investing relies on average returns from an index fund or other diversified instrument. A value investor seeks out above-average companies and invests in them. Therefore, the probable range of return for value investing is much higher.

In other words, if you want the average performance of the market, you're better off buying an index fund right now and piling money into it over time. If you want to outperform the market, however, you need a concentrated portfolio of outstanding companies. When you find them, the superior compounding will make up for the time you spent waiting in a cash position. Value investing demands a lot of discipline on the part of the investor, but in return offers a large potential payoff.

July 25, 2020

How to Start Investing

How to Start Investing.

It is never too soon to start investing. Investing is the smartest way to secure your financial future and to begin letting your money make more money for you. Investing is not just for people who have plenty of spare cash. On the contrary, anyone can (and should) invest. You can get started with just a little bit of money and a lot of know-how. By formulating a plan and familiarizing yourself with the tools available, you can quickly learn how to start investing.

Part 1 Getting Acquainted with Different Investment Vehicles.
1. Make sure you have a safety net. Holding some money in reserve is a good idea because (a) if you lose your investment you'll have something to fall back on, and (b) it will allow you to be a bolder investor, since you won't be worried about risking every penny you own.
Save between three and six months' worth of expenses. Call it your emergency fund, set aside for large, unexpected expenses (job loss, medical expenses, auto accident, etc.). This money should be in cash or some other form that's very conservative and immediately available.
Once you have an emergency fund established, you can start to save for your long-term goals, like buying a home, retirement, and college tuition.
If your employer offers a retirement plan, this is a great vehicle for saving, because it can save on your tax bill, and your employer may contribute money to match some of your own contributions, which amounts to "free" money for you.
If you don't have a retirement plan through your workplace, most employees are allowed to accumulate tax-deferred savings in a traditional IRA or a Roth IRA. If you are self-employed, you have options like a SEP-IRA or a "SIMPLE" IRA. Once you've determined the type of account(s) to set up, you can then choose specific investments to hold within them.
Get current on all your insurance policies. This includes auto, health, homeowner's/renter's, disability, and life insurance. With luck you'll never need insurance, but it's nice to have in the event of disaster.
2. Learn a little bit about stocks. This is what most people think of when they consider "investing." Put simply, a stock is a share in the ownership of a business, a publicly-held company. The stock itself is a claim on what the company owns — its assets and earnings.  When you buy stock in a company, you are making yourself part-owner. If the company does well, the value of the stock will probably go up, and the company may pay you a "dividend," a reward for your investment. If the company does poorly, however, the stock will probably lose value.
The value of stock comes from public perception of its worth. That means the stock price is driven by what people think it's worth, and the price at which a stock is purchased or sold is whatever the market will bear, even if the underlying value (as measured by certain fundamentals) might suggest otherwise.
A stock price goes up when more people want to buy that stock than sell it.  Stock prices go down when more people want to sell than buy. In order to sell stock, you have to find someone willing to buy at the listed price. In order to buy stock, you have to find someone selling their stock at a price you like.
The job of a stockbroker is to pair up buyers and sellers.
"Stocks" can mean a lot of different things. For example, penny stocks are stocks that trade at relatively low prices, sometimes just pennies.
Various stocks are bundled into what's called an index, like the Dow Jones Industrials, which is a list of 30 high-performing stocks. An index is a useful indicator of the performance of the whole market.
3. Familiarize yourself with bonds. Bonds are issuances of debt, similar to an IOU. When you buy a bond, you're essentially lending someone money.  The borrower ("issuer") agrees to pay back the money (the "principal") when the life ("term") of the loan has expired. The issuer also agrees to pay interest on the principal at a stated rate. The interest is the whole point of the investment. The term of the bond can range from months to years, at the end of which period the borrower pays back the principal in full.
Here's an example: You buy a five-year municipal bond for $10,000 with an interest rate of 2.35%. Thus, you lend the municipality $10,000. Each year the municipality pays you interest on your bond in the amount of of 2.35% of $10,000, or $235. After five years the municipality pays back your $10,000. So you've made back your principal plus a profit of $1175 in interest (5 x $235).
Generally the longer the term of the bond, the higher the interest rate. If you're lending your money for a year, you probably won't get a high interest rate, because one year is a relatively short period of risk. If you're going to lend your money and not expect it back for ten years, however, you will be compensated for the higher risk you're taking, and the interest rate will be higher. This illustrates an axiom in investing: The higher the risk, the higher the return.
4. Understand the commodities market. When you invest in something like a stock or a bond, you invest in the business represented by that security. The piece of paper you get is worthless, but what it promises is valuable. A commodity, on the other hand, is something of inherent value, something capable of satisfying a need or desire. Commodities include pork bellies (bacon), coffee beans, oil, natural gas, and potash, among many other items. The commodity itself is valuable, because people want and use it.
People often trade commodities by buying and selling "futures." A future is simply an agreement to buy or sell a commodity at a certain price sometime in the future.
Futures were originally used as a "hedging" technique by farmers. Here's a simple example of how it works: Farmer Joe grows avocados. The price of avocados, however, is typically volatile, meaning that it goes up and down a lot. At the beginning of the season, the wholesale price of avocados is $4 per bushel. If Farmer Joe has a bumper crop of avocados but the price of avocados drops to $2 per bushel in April at harvest, Farmer Joe may lose a lot of money.
Joe, in advance of harvest as insurance against such a loss, sells a futures contract to someone. The contract stipulates that the buyer of the contract agrees to buy all of Joe's avocados at $4 per bushel in April.
Now Joe has protection against a price drop. If the price of avocados goes up, he'll be fine because he can sell his avocados at the market price. If the price of avocados drops to $2, he can sell his avocados at $4 to the buyer of the contract and make more than other farmers who don't have a similar contract.
The buyer of a futures contract always hopes that the price of a commodity will go up beyond the futures price he paid. That way he can lock in a lower-than-market price. The seller hopes that the price of a commodity will go down. He can buy the commodity at low (market) prices and then sell it to the buyer at a higher-than-market price.
5. Know a bit about investing in property. Investing in real estate can be a risky but lucrative proposition. There are lots of ways you can invest in property. You can buy a house and become a landlord. You pocket the difference between what you pay on the mortgage and what the tenant pays you in rent. You can also flip homes. That means you buy a home in need of renovations, fix it up, and sell it as quickly as possible. Real estate can be a profitable vehicle for some, but it is not without substantial risk involving property maintenance and market value.
Other ways of gaining exposure to real estate include collateralized mortgage obligations (CMOs) and collateralized debt obligations (CDOs), which are mortgages that have been bundled into securitized instruments. These, however, are tools for sophisticated investors: their transparency and quality can vary greatly, as revealed during the 2008 downturn.
Some people think that home values are guaranteed to go up. History has shown otherwise: real estate values in most areas show very modest rates of return after accounting for costs such as maintenance, taxes and insurance. As with many investments, real estate values do invariably rise if given enough time. If your time horizon is short, however, property ownership is not a guaranteed money-maker.
Property acquisition and disposal can be a lengthy and unpredictable process and should be viewed as a long-term, higher-risk proposition. It is not the type of investment that is appropriate if your time horizon is short and is certainly not a guaranteed investment.
6. Learn about mutual funds and exchange-traded funds (ETFs). Mutual funds and ETFs are similar investment vehicles in that each is a collection of many stocks and/or bonds (hundreds or thousands in some cases). Holding an individual security is a concentrated way of investing – the potential for gain or loss is tied to a single company – whereas holding a fund is a way to spread the risk across many companies, sectors or regions. Doing so can dampen the upside potential but also serves to protect against the downside risk.
Commodities exposure is usually achieved by holding futures contracts or a fund of futures contracts. Real estate can be held directly (by owning a home or investment property) or in a real estate investment trust (REIT) or REIT fund, which holds interests in a number of residential or commercial properties.

Part 2 Mastering Investment Basics.
1. Buy undervalued assets ("buy low, sell high"). If you're talking about stocks and other assets, you want to buy when the price is low and sell when the price is high. If you buy 100 shares of stock on January 1st for $5 per share, and you sell those same shares on December 31st for $7.25, you just made $225. That may seem a paltry sum, but when you're talking about buying and selling hundreds or even thousands of shares, it can really add up.
How do you tell if a stock is undervalued? You need to look at a company closely — its earnings growth, profit margins, its P/E ratio, and its dividend yield — instead of looking at just one aspect and making a decision based on a single ratio or a momentary drop in the stock's price.
The price-to-earnings ratio is a common way of determining if a stock is undervalued. It simply divides a company's share price by its earnings. For example, if Company X is trading at $5 per share, with earnings of $1 per share, its price-to-earnings ratio is 5. That is to say, the company is trading at five times its earnings. The lower this figure, the more undervalued the company may be. Typical P/E ratios range between 15 and 20, although ratios outside that range are not uncommon. Use P/E ratios as only one of many indications of a stock's worth.
Always compare a company to its peers. For example, assume you want to buy Company X. You can look at Company X's projected earnings growth, profit margins, and price-to-earnings ratio. You would then compare these figures to those of Company X's closest competitors. If Company X has better profit margins, better projected earnings, and a lower price-to-earnings ratio, it may be a better buy.
Ask yourself some basic Question : s: What will the market be for this stock in the future? Will it look bleaker or better? What competitors does this company have, and what are their prospects? How will this company be able to earn money in the future? These should help you come to a better understanding of whether a company's stock is under- or over-valued.
2. Invest in companies that you understand. Perhaps you have some basic knowledge regarding some business or industry. Why not put that to use? Invest in companies or industries that you know, because you're more likely to understand revenue models and prospects for future success. Of course, never put all your eggs in one basket: investing in only one -- or a very few -- companies can be quite risky. However, wringing value out of a single industry (whose workings you understand) will increase your chances of being successful.
For example, you may hear plenty of positive news on a new technology stock. It is important to stay away until you understand the industry and how it works. The principle of investing in companies you understand was popularized by renowned investor Warren Buffett, who made billions of dollars sticking only with business models he understood and avoiding ones he did not.
3. Avoid buying on hope and selling on fear. It's very easy and too tempting to follow the crowd when investing. We often get caught up in what other people are doing and take it for granted that they know what they're talking about. Then we buy stocks just because other people buy them or sell them when other people do. Doing this is easy. Unfortunately, it's a good way to lose money. Invest in companies that you know and believe in — and tune out the hype — and you'll be fine.
When you buy a stock that everyone else has bought, you're buying something that's probably worth less than its price (which has probably risen in response to the recent demand). When the market corrects itself (drops), you could end up buying high and then selling low, just the opposite of what you want to do. Hoping that a stock will go up just because everyone else thinks it will is foolish.
When you sell a stock that everyone else is selling, you're selling something that may be worth more than its price (which likely has dropped because of all the selling). When the market corrects itself (rises), you've sold low and will have to buy high if you decide you want the stock back.
Fear of losses can prove to be a poor reason to dump a stock.
If you sell based on fear, you may protect yourself from further declines, but you may also miss out on a rebound. Just as you did not anticipate the decline, you will not be able to predict the rebound. Stocks have historically risen over long time frames, which is why holding on to them and not over-reacting to short-term swings is important.
4. Know the effect of interest rates on bonds. Bond prices and interest rates have an inverse relationship. When interest rates go up, bond prices go down. When interest rates go down, bond prices go up. Here's why:
Interest rates on bonds normally reflect the prevailing market interest rate. Say you buy a bond with an interest rate of 3%. If interest rates on other investments then go up to 4% and you're stuck with a bond paying 3%, not many people would be willing to buy your bond from you when they can buy another bond that pays them 4% interest. For this reason, you would have to lower the price of your bond in order to sell it. The opposite situation applies when bond market rates are falling.
5. Diversify. Diversifying your portfolio is one of the most important things that you can do, because it diminishes your risk. Think of it this way: If you were to invest $5 in each of 20 different companies, all of the companies would have to go out of business before you would lose all your money. If you invested the same $100 in just one company, only that company would have to fail for all your money to disappear. Thus, diversified investments "hedge" against each other and keep you from losing lots of money because of the poor performance of a few companies.
Diversify your portfolio not only with a good mix of stocks and bonds, but go further by buying shares in companies of different sizes in different industries and in different countries. Often when one class of investment performs poorly, another class performs nicely. It is very rare to see all asset classes declining at the same time.
Many believe a balanced or "moderate" portfolio is one made up of 60% stocks and 40% bonds. Thus, a more aggressive portfolio might have 80% stocks and 20% bonds, and a more conservative portfolio might have 70% bonds and 30% stocks. Some advisors will tell you that your portfolio's percentage of bonds should roughly match your age.
6. Invest for the long run.  Choosing good-quality investments can take time and effort. Not everyone can do the research and keep up with the dynamics of all the companies being considered. Many people instead employ a "buy and hold" approach of weathering the storms rather than attempting to predict and avoid market downturns. This approach works for most in the long term but requires patience and discipline. There are some, however, who choose to try their hand at being a day-trader, which involves holding stocks for a very short time (hours, even minutes). Doing so, however, does not often lead to success over the long term for the following reasons:
Brokerage fees add up. Every time you buy or sell a stock, a middleman known as a broker takes a cut for connecting you with another trader. These fees can really add up if you're making a lot of trades every day, cutting into your profit and magnifying your losses.
Many try to predict what the market will do and some will get lucky on occasion by making some good calls (and will claim it wasn't luck), but research shows that this tactic does not typically succeed over the long term.
The stock market rises over the long term. From 1871 to 2014, the S&P 500's compound annual growth rate was 9.77%, a rate of return many investors would find attractive. The challenge is to stay invested long-term while weathering the ups and downs in order to achieve this average: the standard deviation for this period was 19.60%, which means some years saw returns as high as 29.37% while other years experienced losses as large as 9.83%.  Set your sights on the long term, not the short. If you're worried about all the dips along the way, find a graphical representation of the stock market over the years and hang it somewhere you can see whenever the market is undergoing its inevitable–and temporary–declines.
7. Consider whether or not to short sell. This can be a "hedging" strategy, but it can also amplify your risk, so it's really suitable only for experienced investors. The basic concept is as follows: Instead of betting that the price of a security is going to increase, "shorting" is a bet that the price will drop. When you short a stock (or bond or currency), your broker actually lends you shares without your having to pay for them. Then you hope the stock's price goes down. If it does, you "cover," meaning you buy the actual shares at the current (lower) price and give them to the broker. The difference between the amount credited to you in the beginning and the amount you pay at the end is your profit.
Short selling can be dangerous, however, because it's not easy to predict a drop in price. If you use shorting for the purpose of speculation, be prepared to get burned sometimes. If the stock's price were to go up instead of down, you would be forced to buy the stock at a higher price than what was credited to you initially. If, on the other hand, you use shorting as a way to hedge your losses, it can actually be a good form of insurance.
This is an advanced investment strategy, and you should generally avoid it unless you are an experienced investor with extensive knowledge of markets. Remember that while a stock can only drop to zero, it can rise indefinitely, meaning that you could lose enormous sums of money through short-selling.

Part 3 Starting Out.
1. Choose where to open your account. There are different options available: you can go to a brokerage firm (sometimes also called a wirehouse or custodian) such as Fidelity, Charles Schwab or TD Ameritrade. You can open an account on the website of one of these institutions, or visit a local branch and choose to direct the investments on your own or pay to work with a staff advisor. You can also go directly to a fund company such as Vanguard, Fidelity, or T. Rowe Price and let them be your broker. They will offer you their own funds, of course, but many fund companies (such as the three just named) offer platforms on which you can buy the funds of other companies, too. See below for additional options in finding an advisor.
Always be mindful of fees and minimum-investment rules before opening an account. Brokers all charge fees per trade (ranging from $4.95 to $10 generally), and many require a minimum initial investment (ranging from $500 to much higher).
Online brokers with no minimum initial-investment requirement include Capital One Investing, TD Ameritrade, First Trade, TradeKing, and OptionsHouse.
If you want more help with your investing, there is a variety of ways to find financial advice: if you want someone who helps you in a non-sales environment, you can find an advisor in your area at one of the following sites: letsmakeaplan.org, www.napfa.org, and garrettplanningnetwork.com. You can also go to your local bank or financial institution. Many of these charge higher fees, however, and may require a large opening investment.
Some advisors (like Certified Financial Planners™) have the ability to give advice in a number of areas such as investments, taxes and retirement planning, while others can only act on a client's instructions but not give advice, It's also important to know that not all people who work at financial institutions are bound to the "fiduciary" duty of putting a client's interests first. Before starting to work with someone, ask about their training and expertise to make sure they are the right fit for you.
2. Invest in a Roth IRA as soon in your working career as possible. If you're earning taxable income and you're at least 18, you can establish a Roth IRA. This is a retirement account to which you can contribute up to an IRS-determined maximum each year (the latest limit is the lesser of $5,500 or the amount earned plus an additional $1,000 "catch up" contribution for those age 50 or older). This money gets invested and begins to grow. A Roth IRA can be a very effective way to save for retirement.
You don't get a tax deduction on the amount you contribute to a Roth, as you would if you contributed to a traditional IRA. However, any growth on top of the contribution is tax-free and can be withdrawn without penalty after you turn age 59½ (or earlier if you meet one of the exceptions to the age 59½ rule).
Investing as soon as possible in a Roth IRA is important. The earlier you begin investing, the more time your investment has to grow. If you invest just $20,000 in a Roth IRA before you're 30 years old and then stop adding any more money to it, by the time you're 72 you'll have a $1,280,000 investment (assuming a 10% rate of return). This example is merely illustrative. Don't stop investing at 30. Keep adding to your account. You will have a very comfortable retirement if you do.
How can a Roth IRA grow like this? By compound interest. The return on your investment, as well as reinvested interest, dividends and capital gains, are added to your original investment such that any given rate of return will produce a larger profit through accelerated growth. If you are earning an average compound annual rate of return of 7.2%, your money will double in ten years. (This is known as "the rule of 72.")
You can open a Roth IRA through most online brokers as well as through most banks. If you are using a self-directed online broker, you will simply select a Roth IRA as the type of account while you are registering.
3. Invest in your company's 401(k). A 401(k) is a retirement-savings vehicle into which an employee can direct portions of his or her paychecks and receive a tax deduction in the year of the contributions. Many employers will match a portion of these contributions, so the employee should contribute at least enough to trigger the employer match.
4. Consider investing mainly in stocks but also in bonds to diversify your portfolio. From 1925 to 2011, stocks outperformed bonds in every rolling 25-year period. While this may sound appealing from a return standpoint, it entails volatility, which can be worrisome. Add less-volatile bonds to your portfolio for the sake of stability and diversification. The older you get, the more appropriate it becomes to own bonds (a more conservative investment). Re-read the above discussion of diversification.
5. Start off investing a little money in mutual funds. An index fund is a mutual fund that invests in a specific list of companies of a particular size or economic sector. Such a fund performs similarly to its index, such as the S&P 500 index or the Barclays Aggregate Bond index.
Mutual funds come in different shapes and sizes. Some are actively managed, meaning there is a team of analysts and other experts employed by the fund company to research and understand a particular geographical region or economic sector. Because of this professional management, such funds generally cost more than index funds, which simply mimic an index and don't need much management. They can be bond-heavy, stock-heavy, or invest in stocks and bonds equally. They can buy and sell their securities actively, or they can be more passively managed (as in the case of index funds).
Mutual funds come with fees. There may be charges (or "loads") when you buy or sell shares of the fund. The fund's "expense ratio" is expressed as a percentage of total assets and pays for overhead and management expenses. Some funds charge a lower-percentage fee for larger investments. Expense ratios generally range from as low as 0.15% (or 15 basis points, abbreviated "BPS") for index funds to as high as 2% (200 BPS) for actively managed funds. There may also be a "12b-1" fee charged to offset a fund's marketing expenses.
The U.S. Securities and Exchange Commission states that no evidence exists that higher-fee mutual funds produce better returns than do lower-fee funds. In other words, deal with lower-fee funds.
Mutual funds can be purchased through nearly any brokerage service. Even better is to purchase directly from a mutual fund company. This avoids brokerage fees. Call or write the fund company or visit their website. Opening a fund account is simple and easy. See Invest in Mutual Funds.
6. Consider exchange-traded funds in addition to or instead of mutual funds. Exchange-traded funds (ETFs) are very similar to mutual funds in that they pool people's money and buy many investments. There are a few key differences.
ETFs can be traded on an exchange throughout the business day just like stocks, whereas mutual funds are bought and sold only at the end of each trading day.
ETFs are typically index funds and do not generate as much in the way of taxable capital gains to pass on to investors as compared with actively managed funds. ETFs and mutual funds are becoming less distinct from each other, and investors need not own both types of investment. If you like the idea of buying and selling fund shares during (rather than at the end of) the trading day, ETFs are a good choice for you.

Part 4 Making the Most of Your Money.
1. Consider using the services of a financial planner or advisor. Many planners and advisors require that their clients have an investment portfolio of at least a minimum value, sometimes $100,000 or more. This means it could be hard to find an advisor willing to work with you if your portfolio isn't well established. In that case, look for an advisor interested in helping smaller investors.
How do financial planners help? Planners are professionals whose job is to invest your money for you, ensure that your money is safe, and guide you in your financial decisions. They draw from a wealth of experience at allocating resources. Most importantly, they have a financial stake in your success: the more money you make under their tutelage, the more money they make.
2. Buck the herd instinct. The herd instinct, alluded to earlier, is the idea that just because a lot of other people are doing something, you should, too.  Many successful investors have made moves that the majority thought were unwise at the time.
That doesn't mean, however, that you should never seek investment advice from other people. Just be wise about choosing the people you listen to. Friends or family members with a successful background in investing can offer worthwhile advice, as can professional advisors who charge a flat fee (rather than a commission) for their help.
Invest in smart opportunities when other people are scared. In 2008 as the housing crisis hit, the stock market shed thousands of points in a matter of months. A smart investor who bought stocks as the market bottomed out enjoyed a strong return when stocks rebounded.
This reminds us to buy low and sell high. It takes courage to buy investments when they are becoming cheaper (in a falling market) and sell those investments when they are looking better and better (a rising market). It seems counter-intuitive, but it's how the world's most successful investors made their money.
3. Know the players in the game.  Which institutional investors think that your stock is going to drop in price and have therefore shorted it? What mutual fund managers have your stock in their fund, and what is their track record? While it helps to be independent as an investor, it's also helpful to know what respected professionals are doing.
There are websites which compile recent opinions on a stock from analysts and expert investors. For example, if you are considering a purchase of Tesla shares, you can search Tesla on Stockchase. It will give you all the recent expert opinions on the stock.
4. Re-examine your investment goals and strategies every so often. Your life and conditions in the market change all the time, so your investment strategy should change with them. Never be so committed to a stock or bond that you can't see it for what it's worth.
While money and prestige may be important, never lose track of the truly important, non-material things in life: your family, friends, health, and happiness.
For example, if you are very young and saving for retirement, it may be appropriate to have most of your portfolio invested in stocks or stock funds. This is because you would have a longer time horizon in which to recover from any big market crashes or declines, and you would be able to benefit from the long-term trend of markets moving higher.
If you are just about to retire, however, having much less of your portfolio in stocks, and a large portion in bonds and/or cash equivalents is wise. This is because you will need the money in the short-term, and as a result you do not want to risk losing the money in a stock market crash right before you need it.

Community Q&A
Question : I have low money, how I can get rich?
Answer : Expect it to take many years to get rich. Follow any or all of the steps outlined above.
Question : How do I find a broker to invest in the stock market?
Answer : There are several discount brokers online who charge a small fee for buying stock for you. There are also stockbrokers in most cities you can deal with in person. They charge a bit more, but they can offer you more personal service and help you choose stocks if you'd like.
Question : What if I have a stock in mind, but don't want a broker/brokerage firm? How do I actually purchase stock from that particular company, immediately?
Answer : Look online for the company's investor-relations department phone number. Call and ask if they offer direct stock purchases. If so, they will give you instructions for purchasing their stock. They may take a credit card, or you can write them a check.
Question : How do I start investing? Do I need an agent? Can Canadians invest in US Stocks?
Answer : Canadians -- and anyone else -- may invest in U.S. stocks. The typical way it's done is through a stockbroker. A good way to start investing is to consult with an experienced, fee-based financial advisor. A fee-based advisor does not make money by convincing you to make a particular investment.
Question : What is the difference between "ex-dividend date" and "record date"?
Answer : A "record date" is the date a dividend distribution is declared, the date at the close of which one must be the shareholder in order to receive the declared dividend. An "ex-dividend date" is typically two business days before the record date. When shares of a stock are sold near the record date of a dividend declaration, the ex-dividend date is the last day on which the seller is clearly entitled to the dividend payment.
Question : Is a financial planner really necesary?
Answer : Not if you can supply your own financial acumen and practical level-headedness. If you are not clueless about finances, or if you're personally acquainted with someone with considerable financial experience to share with you, there's no need to pay for advice. Having said that, however, the more money you want to place at risk, the more a fee-only advisor is worth hiring.
Question : How do I initiate an investment process after I open the account?
Answer : Your broker can explain the process to you. It's just a matter of telling the broker which investment(s) you want to buy. A full-service broker will help you make that decision if you'd like.
Question : I want to buy Exxon stocks right now online. What's the best way?
Answer : See Part 3 of Buy Stocks.
Question : If my company is closing, can I withdraw the 401k without any penalty?
Answer : Your 401k is probably "portable," meaning you can take it with you without penalty if you switch jobs. In your case, you shouldn't have any trouble removing the funds (assuming you plan to deposit them in another similar plan).
Question : Is it OK to connect my stock market account with my savings account?
Answer : Yes, that's a safe place to keep your money while you're not using it to buy stock.

Tips.
One of the most painless and efficient ways to invest is to dedicate a portion of each paycheck to regular contributions to an investment account. Doing so can provide some great advantages:
Dollar-cost averaging: by saving a steady amount every payday, you purchase more shares of an investment when the share price is lower and fewer shares when the price is higher. That keeps the average share price you pay relatively low.
A disciplined savings plan: having a portion withheld from your paycheck is a way of putting money away before you have a chance to spend it and can translate into a consistent habit of saving.
The "miracle" of compound interest: earning interest on previously earned interest is what Albert Einstein called "the eighth wonder of the world." Compounding is guaranteed to make your retirement years easier if you let it work its magic by leaving your money invested and untouched for as long as possible. Many years of compounding can bring astonishingly good results.

Warnings.

If you intend to hire a financial advisor, make sure s/he is a "fiduciary." That's a person who is legally bound to propose investments for you that will benefit you. An advisor who is not a fiduciary may propose investments that will mainly benefit the advisor (not you).
When looking for an advisor, choose one who charges you a flat fee for advice, not one who is paid a commission by the vendor of an investment product. A fee-based advisor will retain you as a happy client only if his/her advice works out well for you. A commission-based advisor's success is based on selling you a product, regardless of how well that product performs for you.

June 04, 2020

How to Use the Rule of 72

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