and the 4% Rule

The S&P 500 calculator is on the previous page, and its calculations include past fund survivability of withdrawals. My interest was about how appropriate is the 4% Rule for a 100% stock fund like the S&P 500? (as opposed to a balanced fund with bonds?) This page is the general introductory info describing the 4% Rule, the S&P 500, the general market, bonds, Bear markets, taxes, etc. This is some market stuff that you should know.

It's a large page, but a Menu to several subjects below is:

A few important first facts to know about bond investments

Computing gains compounded with time, and Annualized results

Three Annualized Compounded Gain calculators

How to make a Million dollars for retirement

It's financially best to Not even consider withdrawing the dividends

Bad times in the market with a recent graph of S&P 500

But instead of balanced funds, the point here is that I also wondered about 100% stocks (like the S&P 500 Index funds for example). Any X% percentage withdrawal rate might seem safe if the fund average earning gain was X% to support it, but years vary in gains, at an irregular rate. The bonds in balanced funds used to pay more to aid that, but times change, and with interest rates increasing now, bonds are also losing money now (see below). The 4% concept specifically means the withdrawal dollars are **adjusted each year** to not exceed withdrawing more than 4% of the then current fund. And market years do vary erratically, when a couple or three seriously bad years in a row can make a serious departure from the average. So the rule examines market history verifying survival of all starting dates enduring all known bad year periods. This sites S&P 500 calculator (link at top above) has the Test that does the same thing, with variable withdrawal rates. The future is unknown of course, but knowing the history should help know what possibilities could happen (the 2000 decade was particularly poor).

**Origin of the 4% Rule:** Interest rates of bonds were higher in older years, and the purpose of a balanced fund (*Balanced meaning equities mixed with some degree of bonds, often 40% composed of bonds called 60/40 stocks/bonds*) was market safety, because bonds are not affected by the market, and the bonds contributed to help tide it over in bad market times.

A good description of the 4% Rule was that it comes from a 1994 investigation of historical market data that tested for a reliable safe withdrawal amount, specifically for a balanced fund. Its conclusion was that a 4% withdrawal would survive 30 years of retirement withdrawals in past situations if invested anytime since 1928. However, it was done earlier than the worst times in the 2000s. Bonds are a different factor. The bonds did provide some income in those days for a degree of safety in bear markets. Here's a chart of the Federal Reserve Bank's interest rate history, and I'm thinking the 4% Rule look in 1994 could not foresee today's zero interest rate. A good recent article about the 4% withdrawal number 4 is at Morningstar.

IMO, a downside of the 4% Rule is that it does not consider the average gain of the fund, nor how much money it has accumulated before withdrawal begins. These seem serious factors in predicting how long the fund can survive the withdrawals.

All of the many S&P 500 Index funds try to exactly match the S&P 500 Index performance, but these funds do have different expense fees. There are actually 503 listed tickers in the S&P 500 (today), because three of the companies have two major classes of public common stock included (Google, Fox Corp, and I think Discovery). Google's company name is actually Alphabet, with two public stock classes A and C, with two tickers GOOGL and GOOG, which are added together in the table here. The S&P rules today prohibit including more than one class of public stock, but these three are grandfathered.

S&P 500 Weighting Top 10 as of 25 Nov 2022 | ||
---|---|---|

Apple | AAPL | 6.60% |

Microsoft | MSFT | 5.44% |

Alphabet (Google) | GOOG | 3.27% |

Class A & C | GOOGL | |

Amazon | AMZN | 2.44% |

Berkshire Class B | BRK.B | 1.69% |

United Health | UNH | 1.48% |

Tesla | TSLA | 1.44% |

Exxon Mobile | XOM | 1.39% |

Johnson&Johnson | JNJ | 1.37% |

Nvidia | NVDA | 1.20% |

The weighting method is that since Apples capitalization is several hundred times greater dollars than the smallest member company (Apple's worth is well more than $2 Trillion, which is about 7% of the total S&P 500 capitalization), so the weighting is per each invested dollar instead of per company. Some do fault it because so few companies dominate the total, but it seems very right and proper to me (it's the same as if you had directly invested the corresponding proportionate amount in each company). So the weighting numbers vary with the daily prices, computed each trading day (to compute the S&P 500 Index). All of the 500 "Weights" add to 100, so these numbers are the actual percentages of the total Index value.

See the current weighting of all of the S&P 500 companies. The numbers change slightly every day.

To be eligible for S&P 500 inclusion, each company's stock must be publicly held, and to be in the top 500, currently each is at least $14.6 Billion capitalization. However each company is selected by a committee with additional performance concerns. Companies can also be similarly removed from the S&P 500 (one must be removed for every company added). These S&P 500 are the Big Boys, the largest and most financially successful. Then all of the S&P 500 index funds simply plan to exactly track and match the performance of the S&P 500 index (less the fund's expense fee). The S&P 500 is near 80% of the total U.S. market capitalization.

Probably about any question you might have about the S&P 500 Index would be answered here: S&P U.S. Indices Methodology.

See the largest company stocks NOT in the S&P 500, but in some cases, these are just different classes of stock, those typically being non-public Class A. For example, this list shows Berkshire Hathaway private class A as the largest entry Not in the S&P 500, however Berkshire Hathaway public class B was added to S&P 500 in 2010.

Near 80% of the S&P 500 companies pay dividends in some degree. See a list of those ranked by dividend. Dividend dollars are per share, percentage is annual, and is typically paid 1/4 each quarter.

Similarly weighted, there is also the **Total Stock Market Index Fund** (Vanguard VTSAX) with stock of 4000+ companies (blend of selected large-cap, mid-cap, and small-cap U.S. companies). To me, it seems mostly a conceptual idea, because in practice, it is weighted by capitalization like the S&P 500, which boils down to be that much of the S&P 500 are still at the top of it, with the smaller ones still weighted much less strongly, with much smaller contributions. So in effect, it still has similar performance as the S&P 500 (usually around a percent or so less than the S&P 500 index in individual years).

There also are various S&P Equally Weighted funds, either for all of the S&P 500 or just of specific industries or concerns, but equally weighted, for example ticker RSP. It seems to have a slight advantage in the current bad times, but my notion is that the largest leaders are ahead in good times.

**Indexed funds vs. Actively Managed funds:** Index funds simply try to match performance of the fund to the actual daily index of the group of companies by using computers to maintain the index match by automatically buying the matching shares of each company (passive investing, computers instead of managers, low fee cost). Whereas actively managed funds instead have a human manager trying to pick the selected best paying investments (at larger fee cost). And managers might accomplish that now and then, but next year may be rather different, and it is commonly said that indexed S&P 500 earnings beat managers about 90% of the time (the lower fee is some part of it).

**So yes, there are other funds and stocks** that might sometimes earn more than the S&P 500 Index (the largest of those companies are also probably in the S&P 500, contributing their share, and the 500 is diversification). However their downside is these currently hot stocks are more volatile, their prices can swing widely, which is great when the market is good, but is the worst when the market crashes. And it does seem that the faster they grow, the faster they can fall. The current year 2022 is not a good year so far, with the biggest usual leaders way down (for an awakening, see current Total Returns of 60+ stocks). The market is usually good overall, but there certainly can be big surprises. If investing in individual stocks, you will need to watch closely, and know when and why to switch stocks (preferably before it changes, but that is very difficult, it happens before we know about it). The S&P 500 can be more comfortable long term without close watching (but it is negative too, so far this year).

**Diversification — Don't put all your eggs in one basket.** The S&P 500 mix of 500 companies is a diversification in the various industries (tech, energy, financial, consumer, health, industrial, materials, etc). **However all of the 500 are US large cap stocks** (which includes No small caps, mid caps, emerging markets, foreign markets, bonds, etc.). A S&P 500 Index fund earns more than **balanced funds** ("balanced" means majorly mixed with bonds for diversification), **but bonds can be very volatile too**, because bond value varies with interest rates, which goes up and down too (see Bond **Duration** in the Bond box below). But overall, the S&P 500 trend line is quite appealing. The nature of investing is that some risk is necessary to earn higher gains, a low risk investment doesn't earn much. The S&P 500 does have the normal daily market ups and downs, including the rare economy crashes, but the overall S&P 500 averaged gain has historically always been of about 10% a year, compounded long term. *Which is NOT a guarantee — years vary, a few years are negative, but there are many more good years than not. However a bad crash with a few bad years in a row will have a large effect*. The entire 2000 decade was down -9.4% with 2001 and 2008 crashes that were pretty bad. But the long term picture is very appealing, with only a few dips, which have always recovered of course.

**Nothing ventured, nothing gained.** Ben Franklin said that too, but the thought is centuries older. Some people do fear anything in the market is too much risk for them (yes, the market can crash in bad times, but then it always has recovered, after a while). At least it does if it was a good investment, and the S&P 500 are the largest and most successful Blue Chip companies in the US, which is a good strong bet.

**Compounding gains:** The greater number of years of **long-term** investments makes the compounding of gains be a huge exponential function (with years as the exponent power), which is an astounding big deal. A fixed 10% gain in each of 40 years becomes a final value of 1.10^{40} = 45x the initial value and 4400% overall gain. The market gains do vary each year (often large, but sometimes negative), see below for computing the overall gain. In addition to the price gains, another major factor is that reinvested S&P 500 dividends add very roughly about 2% to total returns each year, and then those additions see gains too, and those gains see more gains, compounding every following year. Even if a few random years are negative, compounded earnings are a Real Big Deal, so think of a long term investment always with reinvested dividends. Start young, and then it will be waiting at retirement. The S&P 500 calculator on previous page shows this with 50 years of past S&P 500 history. The math of compounding is shown below.

**The fund's average annual gain is Not the precise measure of short term withdrawal safety**. Because the average is just the **sum** of all years gain divided by the number of years, accurate "on average" over all of the total years. But the long term compounding result is about the **multiplication product** of the specific years of gains. I naively believe that average and annualized ought to be the same number, but this input data is rounded to only one or two decimal places, which is a little crude during many years of exponentiation, so it will differ a little. Either overall summary can hide a few adjacent down years during which withdrawals could deplete the fund. The S&P 500 will recover, but if all your money was depleted earlier, it ends there. The first early years are the higher risk, when small before it has earned much, since more money will of course always last longer in a crisis. So first building more money in the fund (before the retirement withdrawals) is the insurance to last longer when down, and to make recovery easier. Reason would suggest that first allowing maybe 20 or better 40 years for the fund to build and grow without any withdrawals would make all the difference of survivability, and would of course also provide much greater income during retirement. The market years do vary erratically, but continually withdrawing 10% also with average earnings near 10% might (on average) usually keep it drained down to always about the same level, more or less. It can't grow more then, but its value won't vary so greatly through a long retirement. Except there are variations outside of average, and limiting withdrawals to about half of the average fund earnings rate significantly improves odds against going the fund going bust (and would also leave something for future inheritance to your heirs).

Never withdrawing anything will not go to zero, also unlikely if withdrawal is a small percentage (but fixed withdrawals can become relatively huge when the fund is small, so recompute the percentage every year). Even an extremely bad rare crash probably leaves at least 50%, which is certainly no fun then, but it has in fact always recovered. Here is a chart of a few years of S&P 500 record highs. But when and if it is down low, then percentage withdrawals become fewer dollars of withdrawals when the fund is low. Instead, the biggest danger is fixed dollar value withdrawals, which if blind to current situations and not limited to a reasonable current percentage, of which an example is shown in the Test section on previous calculator page. Your planning for that should have occurred decades earlier. Withdrawals are the desired and necessary goal in retirement, but are very counterproductive during the growth phase. In every case, withdrawals should be reconsidered if the fund value gets low. We don't know the future but we can look at the effect of "typical" past periods, regarding our withdrawal feasibility.

**One issue of a 4% Rule is that it does not specify any specific fund contents, nor any specific fund value.** However a fund containing more money can obviously survive withdrawing in a crash longer than would the same fund with less money. Meaning, a large million dollar fund and a small $10K fund both withdrawing after a bad crash might both fall to 50%, but 50% of a $Million is much more survivable (and with greater gains in recovery) than 50% of $10K. **The survivability of investing for 20 or 30 years to build before starting withdrawals is a huge factor of retirement withdrawal success.**

The survivability of a reasonable **percentage withdrawal** not hitting zero seems relatively independent of value — only meaning a fixed withdrawal percentage rate (*if the withdrawal dollars are readjusted every year to hold that percentage rate*), it withdraws much less when fund is low, near zero withdrawal when near zero value, and worst case still always leaves a tiny value instead of zero. Maybe only a few cents left, but not exactly zero, so hitting zero can take a very long time. Which is the reason an adjustable $100 minimum limit was added to the S&P calculator to more clearly define the end of Survival due to depletion. Possibly this limit should be higher for a stronger recovery, and you can change it, because the fund does need some money left to be able to earn a faster recovery. But in the real world of fixed withdrawals in dollars, hitting zero is certainly about the fund value, since a higher value fund will always last longer through any crisis. The important thing is to maintain a fund value that can recover and survive. Withdrawals make remaining Fund Value be a very major survivability factor (and many years/decades of growth with no withdrawals until retirement is the obvious way to easily increase retirement fund value). If you had $1 Million in a fund, a bad crash might drop to 50%, but half a million would still last a very long time, and then the larger value will also recover with more dramatic gains than a tiny value could.

**Investing in bonds is a very different game than investing in stock.** I am not encouraging bonds now, just offering some facts you need to know first. **This is all true both of direct bond purchases, and of bond funds too.** Bonds may have paid higher dividends in 1994 (for the 4% Rule study), helping to support withdrawals, but interest rate has bottomed out near zero today, so IMO, now bonds seem an outdated investment idea. However, bonds do protect savings from market volatility, and in a market crash, a 50/50 balanced fund may drop half as much as a 100% stock fund, and the bonds still could provide some earnings. But markets always do recover, and bonds don't earn what the 100% stock fund can, and don't earn today what bonds have historically earned, and don't even match inflation today. **Most of all, you must realize that bonds are also quite volatile too, maybe safe from the market, however bond value is very seriously affected by current interest rate changes, which are increasing this year, lowering resell value of existing bonds.** Also, inflation is a serious concern, at a 40 year high at 7.7% in Oct 2022.

Government bonds are different yet, sold at auction to bidders. U.S. Treasury bonds of 1 to 10 year maturity are called Notes, and those of 20 or 30 years are called Bonds (why I don't know, but "bonds" here refer to both). The Treasury bonds are safely backed by the government, and have face values and a fixed interest based on face value, and are redeemed at maturity at full face value. However initially, buyers buy by bidding at treasure auctions on new treasury notes and bonds, so the actual final yields vary with the selling prices (basically what buyers will pay). The variable auction prices are why interest rates of new government notes vary every day. The bid price drops if buyers won't pay more, and then the yield goes higher (the yield to maturity), and of course vice versa too. **But until redeemed at maturity (at full face value then, for the expected income), the bond resell value varies every day, due to current interest rates.** The bond pays a fixed initial dividend in dollars, but resell value varies, making investment gain percent vary too, if sold early. The current **SEC Yield** reported is the previous 30 day interest result annualized to be a hypothetical 12 month rate, which is a standard way to compare the current earning rate of varying gains.

**Definition of very important bond "Duration":** Bond resell value varies with current interest rates. The term Duration computes that **for Each 1% change in current interest rates, the resell value of existing bonds is expected to change in the opposite direction by "Duration" percent**. If Duration is 5 years, and interest rates increase 1%, the bonds decrease value by 5%. Interest rates dropped the couple of prior years, so existing bond resell values increased then, and bond funds showed better results. But vice versa, today existing bonds lose resell value when interest rates increase (and now last one year return is negative, and interest rates are near zero now with only one direction they can move). The U.S. Federal Bank has announced plans for more interest rate increases in 2022 to fight inflation.

Morningstar shows the bond **Duration** (in balanced funds at Portfolio tab, Bond sub-tab, if any). The meaning of a **Duration** of say 3 means the expected bond value will decrease 3% with each 1% interest rate increase, and vice versa, existing bond values also increase when interest rates fall. But either way, **when and if held and redeemed at maturity they do still pay face value**. Short term bonds will have lower duration with lower risk from interest rates, but they pay even less. Speaking of all bonds, including commercial, municipal or treasury (but excepting federal Savings Bonds, which are not sold at auction, and can be cashed in, but cannot be resold to a third party). Bonds have a face value and pay a fixed interest rate, of dollars based on their face value. However, when bought new at treasury action, or any bonds resold later in the market may pay a different price than face value, but they still redeem face value at maturity. Bond resell value varies with current interest rates and with Duration, and then the actual purchase price computes the new effective interest rate (when redeemed at face value). If interest rates increase, existing bonds earning lower effective interest can only sell at a lower price to attract any interest in them (and also vice versa, price goes higher when interest rates decrease). This fact is Extremely Important, especially with interest rates currently increasing from a rock bottom low. The bond value decreases and also inflation exceeds the bond interest.

Bond resale value becomes volatile when interest rates change. I say "resale" because if held, bonds are still eventually redeemed at full face value. So short term bonds, and bonds nearing maturity date, will have low durations. Long term bonds will have higher duration (more volatile). Morningstar.com shows the Duration of bond funds (on the Portfolio tab, computed each quarter, I think).

However, as individual bonds approach their maturity date, their duration drops towards zero, because **directly purchased bonds do still repay full face value when redeemed at maturity or recall**. And existing bonds do continue to pay their same fixed face value dividends, but their resell value varies with current interest rate (existing bond resell value drops with higher current interest rate). **But if you buy bonds directly yourself, and hold until recalled or redeemed at maturity, the face value return then will be as expected.** But if sold early, they will have current market value.

**But if in a bond fund, or if planning resell, there's much more to know about the volatility. Resell value of existing bonds varies inversely with current interest rates**. And bond funds must buy and sell bonds continually as investors buy and sell shares, and bond values are computed daily, not necessarily held until redeemed, and you get whatever the fund is paying that day (due to interest rates). That could be a plus if interest rates fall, or costly if interest rates rise. Right now, interest rates are near zero but the Fed is planning to fight inflation with multiple interest rate increases during 2022.

*When inflation increases interest rates of new bonds, it lowers old bond resell values. That's because no one would pay full price for old 1% bonds if they can buy new 2% bonds at same face value price. So then buying two existing 1% bonds at half price is required to match earnings of one new 2% bond.* So existing old bond resale value can drop to half each time interest rate doubles (because then it takes two old bonds to pay what one new bond pays). And also vice versa, lower interest rates will increase the value of existing bonds that still pay more. (But see Duration too).

Some bonds are "callable" (most municipal bonds and some corporate bonds), with a callable date when the issuer can redeem the bond early (at full face value but which terminates dividend income), perhaps planning to issue new bonds paying lower interest rate (if rates are falling).

Note that **Junk bonds exist too (politely called high-yield bonds)**, from companies with lower credit rating, paying more dividend to attract buyers, but with higher possible risk of default failure (meaning 100% loss of your investment). For bond funds, Morningstar.com Portfolio tab shows bond ratings too. AAA is most secure rating, including government bonds. Bonds rated down to A are considered investment grade. Generally bonds rated B or less are considered speculative and non-investment grade (speculative meaning offering greater dividends if paid, but with greater risk they could fail and default and stop, and not redeem at all). See bond credit rating.

The significant fact to know is that Interest rates dropped in 2019 and 2020 (to near zero), increasing existing bond resell values, so bond funds showed good results then. Results may look real good, but **it is important to realize why you see that value increase in the history**, because the interest rate situation has changed. Since then, existing bonds lost resell value when interest rates on new bonds increased, and then bond return went negative. With interest rates near zero, there is only one direction they can move. The U.S. Fed has announced several interest rate increases are expected in 2022 due to inflation.

Bond price changes when reselling are taxed as capital gains if held one year or more. However *bond dividends* are taxed like interest, at regular income tax rates (except municipal bond dividends are tax free of federal tax, and sometimes free of state tax in same state, at least in some states).

Repeating the important stuff: **Bonds do still pay full face value when redeemed at maturity** (or when recalled earlier). And until then, they continue paying face value interest rate. **So if you buy bonds directly yourself, Not in a fund, but in your name as owner, and hold them until redeemed at maturity, the return will be as expected. That's the good news.**

However **bond funds currently own existing bonds, which will have dropping value as the U.S. Federal Bank interest rate increases (which the Fed is currently doing in a big way, due to record high inflation). The bond funds must buy and sell bonds continually, as investors buy and sell shares**. And bond resell value varies daily with current interest rates. Bond funds recompute bond values with every days interest rate change. However, bond value does not vary much when close to maturity, so a complication is that bond value sensitivity to interest rates depends on how close it is to maturity, in the special calculation called Duration.

The big point here is to not be confused by market return statistics showing bond and balanced funds had good performance history in recent past years. They in fact did, but that is history, when interest rates fell more than 2% over 2019 and 2020, causing the existing bonds to increase in resell value. **But it's very wise to also check their current YTD (Year To Date) results too. The current SEC 30 day yield is shown annualized to represent one total year, which is the accurate current annualized rate value today, but it of course changes all during the rest of the year.** The Federal Reserve Bank interest rate was near zero at the start of 2022, so the only way it could go is up. And the high inflation continues to increase it now, and increased interest rates means resell values of existing bonds are going down. However, bonds held until redemption at maturity do retain full face value then, except bond funds might not be able to hold them to maturity when their shareholders are ordering withdrawals because the value is going down. Since interest rates are near zero now, the danger for existing bonds is that rising rates (and lower values) are the only change possible now. We are expecting inflation to cause increasing interest rates. Bond dividend income is taxed with regular income tax rates, but the price changes are capital gains or losses if held a year or more.

**If considering stock dividends for income**, see Stock Dividends are valuable, but withdrawing them is just a withdrawal, and Not new income. There are about 65 stocks referred to as Aristocrat Stocks, which to be included, companies must be in the S&P 500 (largest US companies), and must have increased their dividend every year for 25 years, a point of pride indicating a stable business. See that Aristocrat Stocks list. The annual increases can be small, and a good half of them still pay less than 2.5% dividends, and a few of those pay less than 1%. A favorite of Warren Buffet at Berkshire Hathaway is Coca Cola (KO) paying 3% plus decent earnings. Whereas most of the best growth stocks pay no dividends, and also can have prices varying widely.

Inflation has historically averaged about 3%, and after being 1.2% in 2020, now inflation in 2022 is currently at 7.7%, which is a 40 year high, so the times have become very different. But the S&P 500 Total Returns (includes dividends) has averaged 11.77% gain for the last 50 years (including the 13 negative years).

Since very low earnings today from bonds is less appealing, my interest was about something like the 4% Rule, but for 100% stocks, such as the very popular S&P 500 index funds. A good stock fund earns a lot when the market is good, but market value can drop significantly when market times are bad. But which is more just a delay, since long term, even a 50% drop is not the end of the world, since the bad market crashes have always fully recovered if you can hang in there and wait it out. **This is definitely NOT speaking of bad investments recovering**, but is instead speaking of good investments in bad times. However there is always risk that withdrawals at suffering prices can deplete a small fund. More money in the fund can survive fixed amount withdrawals longer. But if no withdrawals, it should recover and last indefinitely.

So if interest rate (of bonds in balanced funds) is near zero today, what about a "4% rule" for 100% in a S&P 500 Index fund? The S&P 500 calculator and Survival Test on the first page is about that.

My emphatic opinion is that all withdrawals ought to be planned to occur after retirement, not before. Repeated withdrawals drastically limit long term performance. The big issue is that retirement generally means having no job or salary, requiring living off of savings for maybe 30 years, perhaps even with major health care expenses, which will require some planning. The time to realize this is when young with still many years of great opportunity.

Compounding is the largest gain effect of **long term market investments**. One year has earnings, which (if positive) then that greater working total increases the greater total amount producing earnings the next year, and continuing so on growing every year. But market gain is variably different every year, so here's a math example with six years of example Total Return statistics. For it to be Total Return, don't forget to add any reinvested dividends and readjust cost basis.

The same percentage numbers are computed regardless of any initial value, $10 or $10,000,000. But calculations with rounded significant digit precision might be slightly affected. These are just made-up example gain numbers, accurate math but NOT representative of any actual real result.

Example of the Manual Calculation Method of Annualized Return | ||||||
---|---|---|---|---|---|---|

Year | Initial Value | Gain | Annual Gain | Final Result | Compound Gain | Annualized Return |

15.0% | ||||||

23.5% | ||||||

10.4% | ||||||

-5.2% | ||||||

12.1% | ||||||

20.0% |

**Method A:**

Percentage gain =

New value - Old value

Old value

× 100Old value

From this computed table, this overall example six year gain (initial to final amount) is

**((19995.35 - 10000) / 10000) × 100 = 99.9535% gain.**

If you already know the final and initial values, then use this gain formula, or see the 1st Gain calculator below. Stock price does Not include dividends, but dollar amount does include your reinvested dividends. Any withdrawals are received value which should be added back into the final total, but withdrawals will drastically reduce gains.

**Method B:**

This first year gain of 15% (in the table above) means the first year result was 1.15 × (the initial 1x amount). That becomes the initial amount for the second year. These same six individual yearly gains (as 1 + percent/100) will also compute total compounding result as

**(1.15 × 1.235 × 1.104 × 0.948 × 1.121 × 1.20 - 1) × 100 = 99.9535% gain.**

Or see the 2nd Compounding of Yearly Total Return Percent calculator below. Morningstar.com shows ten years of these annual **Total Return** numbers (including reinvested dividends, which for stocks are at the *Price vs Fair Value* tab, and for funds are at the *Performance* tab).

The order of the years makes no final difference. Compounding is simply repeated multiplication of gains. These methods do use the annual gain numbers with only 3 or 4 significant digits, but it does fairly well. The initial dollar value does not affect the gain percentage. And then, the final Total Result **value** is (1 + gain/100) × initial invested value. **For an initial $10000, then 1 + 99.9535% is 1.999535 × $10000 = $19995.35 result value.**

**Important Details: The ±1 in these equations represents the initial 1x investment value.** That 1 becomes 100% when multiplied by 100 for percentage, and the gain is computed from the Initial and Final values. If the gain is 10%, the final value will be 1.10x. The (final value / initial value) fraction is the gain ratio, like 2x doubles the value. If the gain was 1.12x (12%), then (1 + the gain 0.12) is the 1.12 result of the gain (as done in the six yearly terms at B above, and with current dollar value of 1.12 × initial value, whatever 1x was). Subtracting the initial 1 from final multiple leaves just the gain portion. *The gain computes the same numbers regardless of whatever the value of initial dollars.* The 99.9535% gain in this example is 1.999535x value, which is essentially 2x total value. So the final value would be 200%, but subtracting 1x initial value, the gain was 2×100% - (2-1)×100 = 100% (1x less than value, for any gain). The 1st Gain calculator below tries to differentiate gain and value.

Each year's gain is an individual multiplier of the initial value. Each factor is **(1 + gain/100**, with 15% gain becoming a 1.15x multiplier of value. **Negative gains** use the same method, for example **-5.2% is 1 + (-5.2/100)** resulting in 0.948x value that year. The -1 is subtracting the 1x initial value, to see just the gain portion. Or the 1 is added to gain (the 1 is actually 1 x 100, which is 100% of the original initial value), to see the final total value result. The amount of "gain" does not include the initial value, but the total value result does.

Note that a **price** result does not include dividends or compounding, but a formal **Total Return** does, including reinvested dividends. However, if there were no withdrawals, the final **value** resulting from the investment is a clear total answer including everything that happened. So $50,000 value result from $25,000 invested is a 50000/25000 = 2x gain, pure and simple. And it is a (2x - 1x)×100 = 100% gain. If a market result that took 10 years, it is (2^{1/10} - 1) x 100 = 7.1773% Annualized Return. Meaning, (1 + 0.071773)^{10} = 2x value would be the same result if it had come from a fixed rate interest source. Annualized Return seems a useful way to compare varying market results. Annualized gain is the same result, but of a fixed gain rate.

**To compute the annualized gain rate** for the example in the above table with the above gain formula is:

**Total gain**is ($19995.35 - $10000) / $10000 = 0.999535 x 100 =**99.9535% gain in 6 years**. The final total value in dollars would be (1 + 0.999535) × initial investment. The 1 is the initial 1x investment included in the final total value.Or using Method B, (1.15 × 1.235 × 1.104 × 0.948 × 1.121 × 1.20 - 1) × 100 = 99.9535% gain in the six years.

Note that Percentage Gain formula above (and calculator below) can enter units of either this method (like a 1.15 multiplier) or can use actual values like dollars (for example, if the initial value was $1, the 1.15x gain is $1.15 value). Percentage comparisons compute correctly regardless of the actual value, just meaning, $8 vs $1 or $800 vs $100 is exactly the same percentage as $8,000,000 vs $1,000,000. These are 8x or (8-1)×100 = 700% gain. The -1 subtracts out the 1x initial investment to show only the gain. The gain percentage is not affected by the initial investment value. Percent only reflects the degree of difference between Start and Final value.

**Annualized gain**of an overall gain of 99.9535% is**((1 + 0.999535)**^{(1/6 years)}- 1) × 100 = 12.24185% Annualized gainAnnualized meaning AS IF this result were from the same fixed gain every year that would produce the same result. The first +1 adds the initial amount to compute gain, and the final -1 subtracts it to show just the gain, instead of the final total money amount. Again, if the final gain period is negative, like -8.2% over 6 years, still use

**1 + (-8.2/100)**which is (0.918^{1/6}- 1) × 100 = -1.4158% annualized.The annualized gain is not what actually happened each specific year, however the point is AS IF an investment did somehow pay fixed 12.24185% interest every year, the resulting total in six years would be that same result. It is a good way to think of investments that vary each year. It could still matter if comparing with a published fixed rate compounded every day or month, but using each year is what Annualized Result means. Stocks are basically compounded on the date of every dividend and with every market day's price, but annualization computes accurately using whatever final dollars are actually present at the end of the year. That is also how annual Total Return stock numbers are computed. So whenever Morningstar says the 10 year Total Return of a stock was say 12.5%, that means annualized, as if every year. That didn't literally happen every year, but the final result was the same. You may want to compare the fixed rate gain as the resulting dollars annualized too (should be the same, unless fees or other costs). The purpose of Annualization is for comparing the return of a varying rate as if it was a fixed interest rate of results, perhaps useful to better visualize a number for the varying market gain.

The Withdrawal Depletion Test on the S&P 500 calculator page shows the S&P 500 Annualized Return is usually around 10 to 12% (a few times are a bit more or less) if starting in any of the last 50 years. Or 26% for the previous three years (read at the 2019-2021 start line), before 2022 drops it to 16% (2019-2022). But that is only 4 years, and it always has recovered. Always recovering is the only way we got to today. Any withdrawal does drastically reduce the total returns. You do get the withdrawals, but then the future earnings are seriously reduced, which does not compute well.

- Reversing the computing direction to verify that the Annualized number is accurate (with same example numbers):

((1 + 0.999535)^{(1/6 years)}- 1) × 100 = 12.24185**% Annualized gain**

((1 + 0.1224185)^{6 years}- 1) × 100 = 99.9535**% Overall gain**

Or ((1 + 0.1224185)^{6 years}) × 100 = 1.999535**x value**, from 1x value (value computed without the - 1 subtraction).**The large number of digits are shown in the calcultors in case someone wants to reverse calculate for verification.**Values like $1,000,000.01 are 9 significant digits. If reverse calculations don't quite reach the same exact number, you need more decimal digits for better precision. It is possible for a calculator or computer to use FULL precision of all the numbers, especially for exponent calculations. Meaning, don't round off the data until time to show it. Computing 7 digit values (like $19995.35) needs that many significant digits all along for full precision. You would round off final results to show them, but while in the computer, compute with the full available precision, without any rounding. Rounding during calculation (of dollars or percent) affects result precision, however even a rough approximation might still be adequate as a ballpark comparison.

**Significant digits:** The extreme number of decimal places for the interest were actually intentional here. It could have been rounded, but it doesn't hurt anything this way that allows it to be possible to calculate backwards from the result back to the original data. To validate the first calculation for example.

Any computed result will not have any more precision than the precision in any number we used to compute it. Some numbers are Exact Numbers, and fully precise, like 3 apples or 10 people or 2 times investment or 5 years. However if it really was one day more than 5 years, that should be be 5.00274 years. And sometimes, especially with exponents and large numbers, even one more digit will help.

To see that in real life, copy the first calculators initial default values to the third calculator, as $1 at 41.25% for 40 years. The 1,000,000.00 is 9 digits, but the 41.25 is only 4 digits. The omitted significant digits show a result more than $1000 less that the $1,000,000.00 value expected. That's only about 0.1% off, perhaps close enough for many things, but everyone would call it an extremely poor result if their bank did that. Each additional digit that you add to the 41.25 gets closer to the number you expect. When you get 9 digits in, it is within 2 cents. When you get ten digits in, it shows the original value exactly. That is what significant digits are about. Your results will not have more precision than in each number you used to compute it. However, the numbers like the $1 or the 40 years in this example are very special in that they can be considered Exact numbers, stated by definition accurate as is for any purpose. Making them be 1.000000 or 40.000000 does not make them any more accurate or more precise.

**Annualized rate** is AS IF this were this same hypothetical fixed gain every year that does produce the same value result.

Annualized Return does NOT include dividends UNLESS the data includes the reinvested dividends. Stock price alone does not include dividends but Total Return data does.

**1st calculator, Gain:** Hopefully it is both self-explanatory and the most useful. Technically, any units work (like price or distance or weight or time). Or Dollars or Euros, but gain calculations need Not be money.

**2nd calculator, Total Return Percentage:** To be descriptive here, the six initial defaults are the same six years of example numbers in the "manual calculation" table above. To be the complete return, each real data percentage should be the years **Total Return**, which includes reinvested dividends. Morningstar.com shows ten years of these annual Total Return numbers (which for stocks are at their *Price vs Fair Value* tab, and for funds are at their *Performance* tab). But meaning, here enter the yearly percentage, like as 15 instead of 1.15x. Then this method makes getting the compounded gain numbers be easy.

**3rd calculator, Future Value:** This one is perhaps less useful, but if no withdrawals or additions, it might estimate expectations of final value, however a future variable market gain rate is not predictable.

Or it can be used to reverse compute to verify an Annualized calculation is correct, and in that use, the apparently exorbitant number of digits shown is because large values like $1,000,000.00 have 9 digits, which needs at least that many significant digits in the interest rate to accurately match the precision desired (years is an exponent of interest). For example, in the initial default shown, using instead 12.2% (3 significant digits) computes $999,342.31, also accurate to three digits. However approximations don't know full precision and should be adequate with fewer digits. For example, the initial default value could instead be the 12.2% and still compute final value within 0.07% ($658 difference in a million). So approximations should be an adequately useful estimate, but full precision does require the necessary number of significant digits. Again, the precision of future market result estimates is unknown anyway, but exactly matching a reverse verification of Annualized rate needs about all the digits you can manage (compute it first, before any rounding).

**All 3 calculators above:** The Annualized gain is defined as the gain for an entire year. If the final year is as yet a partial incomplete year, there is a tricky issue to understand. This also applies to the last one of multiple years if it includes the current year to date, but for example, if you had data only for half of one year which at that mid year was 10% gain, computing it as a full one year would show 10% annualized (for entire year), which is currently correct for year to date, but is not accurate as annualized because we don't know yet the final result for the remaining year. And calling it a total year computes the missing remainder as zero gain (as if this is to be the years final gain), but that approximation can seems reasonable for a fixed growth rate, but of course, a volatile rate may not happen that way. That may not happen either. Saying, don't give too much attention an annualized partial year number.

Calculators 1 and 3 will allow entering a partial year, like 6.4 years. If you do enter the final partial year as like 50% of the year, the gain values will still correctly show the SAME value and gain percent numbers (which is what actually happened so far either way), but since you called it half a year, the annualized rate will assume the gain rate continues for the rest of the year, so from the halfway point, to then show double, to 20% annualized gain for that year. Which would be the correct annualized rate for a fixed interest rate, but the stock market always varies and the future is unknown. Calculator 2 used to offer to compute the actual partial fraction of the final year, but that part is now removed, as it seems more wrong than right, at least to call it annualized.

Calculate the Fixed Interest Rate

and actual Rule Number that will

compound value to x value

and actual Rule Number that will

compound value to x value

An Enter key in these fields will

recompute this table

Extend range to years

Off-topic a little, but checking that these numbers are reasonable, a simple rule of thumb check is the Rule of 72 that says an investment value **about doubles** if *the years × fixed percentage gain = 72*. So 6 years × 12% = 72 would double to be 2x value (1.12

The Rule of 72 is just an approximation dating back to at least the first known mention in year 1494 (in the time of Columbus), when the calculation was difficult. The Rule of 72 is most accurate for 8 to 10 years, and technically 6 years should be Rule 73.477 for 12.246% doubling in 6 years. The 12.24% annualized is an impressive rate of gain when compounded, awesome over many long term years.

This calculator was to look at doubling with the Rule of 72, but you can enter different multipliers here (other than 2, like 2.5 or 3 or 10). Or the "Rule" can also be determined by the first Gain calculator just above (by specifying two values that will double, like 2 and 1, or that will triple, like 3 and 1). Then multiply corresponding interest rate and years to get its "Rule" number.

But in exploring the Rule of 72 (see this table), it became clear it is only a simple rough approximation. Speaking only of doubling, the worst accuracy with 72 is if less than 6 years. The best case for Rule 72 doubling is for 9 or 10 years. But a Rule of 70 works better for doubling long term 20 to 50 years. That much time to double would not seem a great investment, but you could specify it to 10x or 20x growth.

So I suggest the first Gain calculator above will be more useful and versatile and certainly more precise than the Rule of 72. In that calculator, New = 2, Old = 1 over 6 years is 2.0x Value, 100% gain at 12.246% annualized gain. The actual money value is not a factor then, this math is only about the ratio of 2/1 = 2 which represents doubling.

Based on past S&P 500 performance history, earning a million dollars has been relatively easy, if given the sufficient span of years to let it grow. See the 3rd Future Value calculator above.

Maybe it does take either a lot of years or a lot of investment, but the years are doable if starting early enough. One million is roughly 40 years from $10K, or 30 years from $35K, or 25 years from $60K, or 20 years from $100K. **The long range of years is a magic opportunity.** The S&P 500 calculator on previous calculator page can also show that only $10,000 invested in 1980 for 40 years (which sounds like an extremely long time, but it is like age 25 to 65) and left untouched until today would have been worth about $1 Million now. That assumes 12.2% annualized gain (which has been a valid average), with dividends reinvested and **compounded for 40 years, despite including the few very bad market years** (the 2000s decade did not help, but it still got there). And much of it remains to continue growing 20 or 30 years after retirement too. Results of starting in any year, and/or with any other starting value, is shown in the Survival Test Mode chart on the previous S&P 500 calculator page. The $10,000 doesn't earn so much initially in the beginning, but after it's grown to more digits in the last several years, the growth seems amazing. And that growth keeps earning more too, which is the concept of compounding.
.

Compounding is easy, all you have to do is start early and then just wait long term. And think what adding even more investment to that now and then could have done. **Starting or adding when the market is down (certainly including today, 2022) is a really good time (to buy low for maximum growth opportunity). A drop in the market is Not the end of the world, and recovery provides opportunity for much additional gain.** The young probably think other things are more important now, but I promise that your priorities will change near retirement time, after it is too late (trying to get your attention if you need it). That growth will become quite important at retirement time, and the best tool is an early start. It also continues earning and compounding after retirement, during 20 or 30 years of retirement withdrawals. If looking for magic, this comes pretty close, and seems a mighty big deal.

$10,000 might have seemed impossible for me at age 25, but starting with $1200, and adding $1200 a year ($100/month) to it for 40 years all along (without fail, adding $51.6K overall) also creates $1 Million. Think of it as supporting yourself in your old age.

Or one approach is you can create a self-directed IRA that invests in a S&P 500 fund. A S&P 500 Roth or IRA that adds the $6000 maximum every year could reach $1 Million in just 25 years (example 5 on previous calculator page). A 401K plan has a much higher maximum contribution, and a possible company addition. And of course, if possible, a Roth instead of IRA or 401K would eliminate the taxes on the million, which would be a real big deal then.

Age 65 will come for all of us, when salary stops and we will need replacement income, which will become extremely important then. It is too late then, but planning makes that possible if you start early. Then thereafter, 4% withdrawals from $1,000,000 is $40,000 a year to add to Social Security. The fund would continue making its gains then, but if $1 Million, then withdrawing $40K a year would last 25 years even if zero additional gain. However taxes will be due on it, making any large lump sum withdrawal seem unwise. But spread out into smaller withdrawals over more years, taxes on high income will be the best problem you could have.

**The easy and best solution** is simply to start a good investment early, without fail, as early as possible, today. The 4% Rule was concerned with market bad times surviving 30 years of retirement withdrawals, after building substantial value with years of investment without withdrawals. From my own experience, my notion is that it takes many young people many years to realize that the many years of opportunity available to them would have been their very best and easiest and greatest tool BY FAR, but then there is no going back for a redo. Wasting that most valuable opportunity would be a tragic shame.

Again, these results are computed from the past years in history, **and future results are not known. The standard obligatory investing advice is that past success does not guarantee future performance**. There have been bad times (including today, 2022), but it always has recovered. Past success of long term investing in the S&P 500 seems clear enough (the 500 largest and most successful companies in the USA).

Compounding is certainly a real big deal in investments, making many **long term** years be the most profitable part. Only a year or two is not so dramatic, but compounding is exponential with time, becoming huge over many years. Long term can be exceptionably good. The S&P 500 (gain and reinvested dividends) has averaged an annual return around 12% for the last 50 years. The future is not known, but it sure seems a good bet if you consider "long term"). It is true that the S&P 500 is down now. Two facts though, this or worse has happened several times over the years before, and it always recovers and continues. The S&P 500 was down 25% at $3585.62 on Oct 3 2022, but 40 years ago it started with only about $122, which is an increase of about 30x so far, not even counting the dividends.

Plug in your own numbers, but if your age is 40 years or less, then you still have at least 25 years before retirement at 65 (when you will certainly be needing a source of income). Today is the latest time to be considering that. And the investment can continue earning during 30 years of retirement withdrawals too. The years will be your largest growth multiplier, so wake up, and get with it, now (the term *Buy Low* means, the market is currently very low to making buying right now be the very best and most profitable time, very wise). I've just shown how $10K now can grow to $1 million in 40 years, so don't foolishly waste the years. (25 years will need about $60K.) The market always recovers, but lost years cannot be recovered.

**A large number of years as an exponent can grow to become a really huge investment factor**. Long term compounding is the largest effect of investment. **And the reinvested dividends especially adds to that too.** All of the earning keeps earning more again, every year. The S&P 500 prices moves up and down daily, but for much longer than 50 years, the S&P 500 has averaged an annualized price gain of 10%, and a dividend of 2%, so then:

1.10^{40} = 45x value (withdrawing dividends has a high cost)

1.12^{40} = 93x value (reinvesting a 2% dividend doubles the 40 year result)

**Withdrawing dividends is extremely costly long term — and the same is also true of any withdrawal.** The best plan is to automatically reinvest all withdrawals, at least until retirement time when it may be needed. Hoping that will be realized, here is a chart of this repeated from the previous S&P 500 calculator page (this S&P 500 data date is start of year 2022):

S&P 500 | No withdrawals | Withdrawing all dividends, WD | ||||||
---|---|---|---|---|---|---|---|---|

$25K Start | Yrs | Fund Value No WD | Dividends reinvested | Fund Value after WD | Dividends Withdrawn | End Value incl WD | Cost | Loss of Income |

1970 | 53 | $5,142,603 | $924,715 | $1,190,385 | $279,994 | $1,470,379 | $3,952,218 | 71.41% |

1980 | 43 | $2,926,998 | $518,818 | $1,019,322 | $230,459 | $1,249,781 | $1,907,676 | 57.30% |

1990 | 33 | $599,014 | $101,390 | $312,591 | $64,954 | $377,545 | $286,423 | 36.97% |

2000 | 23 | $114,570 | $17,199 | $75,482 | $13,271 | $88,753 | $39,088 | 22.53% |

2010 | 13 | $126,496 | $14,694 | $99,861 | $12,811 | $112,672 | $26,635 | 10.93% |

2020 | 2 | $35,989 | $1,307 | $34,605 | $1,293 | $35,898 | $1,384 | 0.25% |

**Reinvesting dividends is a very major part of long term earnings.** Withdrawing dividends reduces the remainder that could have been earning in all those years (it is the same as any withdrawal).
The cost of Withdrawals is the money "that could have been" minus the money actually remaining available.

Long term, dividends have the exact same result as any fund addition or withdrawal. Regular withdrawals remove shares. Reinvesting dividends adds shares, and withdrawing them does not. See next page, Stock Dividends are valuable, but withdrawing them is Not income.

If some example were simple fixed interest at 12% every year, each year is 12% gain, and the 30 year value would be 1.12^{30} = 29.96 x initial value, or 2896% gain, which is ((1 + 28.96)^{1/30} - 1) × 100 = 12% annualized gain (same 12% this time of course, because this was already a fixed interest rate). The value of the annualized rate is to allow more insight into the variable years of market results.

In history, most by far of the S&P 500 years are positive gain, but market years vary, and the future is always unknown. However the preceding 50 years of the S&P 500 have actually averaged about 12% simple average return (speaking of individual years Total Return, but which includes reinvested dividends). Your retirement might be a long time away, but the wise are already planning for it today, because **a longer time is by far the best investing tool** (assuming a good investment worth keeping). You run out of options if you wait. The loss of wasting that most valuable opportunity would be a real shame. Lost time is not recoverable.

The market goes up and down a little every day. It can make you crazy to watch it every day. But don't sweat the small stuff, it will be different tomorrow. Do understand that it is very normal to go up and down every day. Another page shows four years of this daily S&P 500 activity highlighting the peaks and valleys.

There are some bad times, and some people are scared off and will cash in and get out of the bad market, but that simply locks in their losses and makes it permanent, not recovered. Others grit their teeth and bear it, and hang on and wait for the correction, and then continue on recovering and happily earning more money. I recommend this latter course. It happens now and then, and waiting it out is no fun, but it pays off. The alternative is accepting the loss. But the world continues on, it does not end.

A Brief History of U.S. Bear Markets provides a very clear and informative view and details of our bear market history, that you ought to see. That one does not show the good times, but for that, also see its second green graph just below it (click it to enlarge it slightly). Certainly you should realize that crashes do happen now and then, but also, that they do recover. A Bear Market is defined by at least a 20% decline, which can seem mighty uncomfortable at the time. The worst ones have hit -50%. Many investors panic and sell and end their fund then, which just makes their loss permanent and very real. But instead hang in there, and it will eventually recover into happy times again with continued gains. Most years are good, and the long term gains are hard to ignore. Politics and taxes do need watching, and bad times do happen every once in a while, but then recovery also happens too.

The market is usually good, with many more good years than not, and long term wins. But starting the calculator data at 1970 was deliberately chosen here to include actual real data for some seriously bad times. The crashes of 1974 and 1982 and 2001 and 2008 were exceptionally bad economic and market times. In contrast, the 2020 pandemic crash, -34% was tough on the economy and market, but its cause was not economic or political, and the market recovered quickly to current all time record highs. There were other smaller dips, but the 1970s were poor (one crash) and the 2000s were worse (two crashes), all near 50%. The recovery from 2008 took the longest in modern history (until 2012), and the entire 2000s decade was down 9.4% (a "lost decade"). So 2000 was the worst year to start the fund in the last 50 years of history. The price of the actual S&P 500 was under $1000 in 1997, again in 2002, and again in 2008, but even so, reached $4700 in 2021. That is just the price (less dividends), but the compounded gains have been exponential in the many years of gains. Investing for long term is the way to bet.

This is a Google chart.

The 2001 and 2008 dips made the entire 2000-2009 decade lose 9.4%. It recovered in 2013. The 2020 pandemic dip was deep (-34%) but relatively short duration. The S&P 500 was down 25% at $3585.62 recently (Oct 3 2022). The current inflation (2022 is the highest in 40+ years) is a factor, but it will recover. See a current status of Total Returns of 60+ stocks.

**Corrections:** Market drops of more then 10% are called Corrections. These are fairly routine, and happen more often then you might think, but they typically don't last long before the correction recovers. Again, we learn to take it in stride, and in fact, the low times are often welcomed as great times to buy more at the lower price. That is the meaning of "Buy low, sell high".

**Bear Markets:** Drops of more than 20% are called Bear Markets, occurring less often but much more severe. These might reach 50% down in truly bad economic times, but they have always finally recovered (could take a year or two then, or even more). The worst action would be to cash in by selling during the low times, **which simply locks in your loss permanently with no opportunity for recovery**. Buying more then is the better choice, the recovery will be profitable, but timing the exact bottom of the market is impossible (the bottom likely will not be in the first few weeks though).

One accounting of this says "Most declines are quickly erased but the deeper the stock market decline, the longer the recovery." They make this report about history (I am unsure how precise the numbers could be in the future):

- 5% or greater pullbacks occur about every 7 months
- 10% or greater pullbacks occur about every 2 years
- 20% or greater pullbacks occur about every 7 years

And the few worst past ones have reached 50% down. But it happens, and then it recovers, always has. The 2020 pandemic dropped the market 34% in March, quite bad but short. It recovered quickly 100% by August, and the year ended up at a new record high with 18% annual gain despite the lost months. In the following March the S&P had achieved a 76% gain (a year after the low). Recovery of bad economic situations can take a couple of years though, until the economy is corrected. 1974, 2001 and 2008 crashes were spectacularly bad, and each took a few years to recover. But they do recover.

Currently, most companies are down and negative for the year, but the leading growth stocks (Apple, Microsoft, Amazon, Google, Nvidia. Tesla, etc) are down big time, -25 to -45%. It's just market fears due to all the current problems. There is nothing wrong with the companies, their earnings are doing great. The Russian invasion of Ukraine is of course a big worry, but the painful self-inflicted inflation is another of the current big concerns about the US economy. The government's massive spending of Trillions is a large factor, and their own self-imposed policies last year limits our own U.S. oil production, which has had very strong effect increasing inflation. The U.S. oil production was self-sufficient before, but now we must import oil again, and pay the price. Oil affects the price of about everything (transportation, plastics, etc), and the doubled oil price has increased U.S. inflation, up from 1.2% in 2020 to 7.7% in Oct 2022 (2022 is by far the worst inflation in 41 years). But the cavalry will come and the market has always recovered.

**Recessions:** The definition of a recession is about the decline of national GDP growth and the rise of unemployment. Recessions are NOT about the stock market. Some imagine a recession is just when there is two consecutive declining GDP quarters, and we do have that now, but a recession is also additionally about unemployment statistics, which are still rather low now, so there has been no recession called. Technically, the National Bureau of Economic Research (NBER) decides if and when it is actually a recession. The unemployment rate is still quite low right now, so it is not yet a recession. It's bad though anyway.

Predictions about the market future are only guesses, and at any given time, many "expert" guesses heard will always be rosy and bright, and many others are always gloom and doom. It doesn't take long to understand that no one actually knows the future. I am certainly no expert, and I don't know either, but it is easy to see that the long term S&P 500 graph (meaning a few decades) sure always looks great, but with some dips. The market goes up and down every day of course, with many more good years than bad years (but yes, expect a few bad years as a matter of course). Withdrawing everything when it is down in bad years is the worst plan, which simply guarantees the loss is real and permanent, with no recovery possible. It is scary, and it takes some patience, but it will recover if no withdrawals. Market crashes do happen every few years, and they are survivable. The S&P 500 does recover.

**But there is no one safe magic percentage withdrawal such as 4%.** Because how long a fund can survive retirement withdrawals in bad times actually depends on how much money it makes available. **This 4% number does assume it is recalculated every year** (same 4% percentage, which calculates different withdrawal dollars each year, depending on the different current investment total).

- Before retirement, just hang in there. Make no withdrawals, preserve the funds value. Assuming it is a good investment, adding additional investment is good, and doing it while prices are low is the right time to see even greater gains during recovery.
- At retirement, salary stops and withdrawals likely begin. There might still be Social Security then, but your fund can add to it. How large is the market drop? How much had the fund previously grown? How much of the fund value was previously withdrawn?
- Specifically, how much value is left in the fund to support recovery and withdrawals during retirement? Was the fund newly started or had it grown large?

4% withdrawal from $1 million is $40K a year and will last 25 years even if no further growth, but 4% of $10K is $400 a year ($33 a month) which doesn't seem much help. - How long the recovery will take is unknowable. Perhaps a year, or maybe two, or maybe less, or perhaps even more. The end of September 2022 is 9 months from the last record high of the S&P 500 Index (and the S&P 500 low on 30 Sept 2022 reached -25%). But the 2020 Covid pandemic crash (-34%) was only six months between record highs. The 2001 and 2008 crashes were each about 50% and made the entire 2000 decade negative. But it always has recovered.

Building a larger fund by retirement time is the best help, and it should be seriously planned. The more years you have to do it will make it much easier. Pulling the money out of the market after it falls low simply ensures the loss is both real and permanent (with no chance of recovery then). But it always has recovered.

We don't know those things about the future, but we can see such instances in the past, to suspect what we might expect sometime in the future. We can see that it has always recovered. If the fund value drops 50%, then from there, it must recover 100% to reach the same original value again. Our own withdrawals also during the low times are dangerous to the survival of our fund. Even innocent looking fixed amount withdrawals can become drastic in bad times (see the $200/month fixed withdrawal in the 50 year S&P 500 calculator which fails soon, but a 10% withdrawal finishes 50 years, without growth, but no failure). The advantage of a percentage withdrawal is that (if the withdrawal rate is then adjusted every year to the same percentage of the funds then current value), the withdrawal becomes very low when the fund value is low. Except actual withdrawals are usually set up as fixed dollar amounts every month. But a percentage withdrawal definitely implies the withdrawal is recomputed every year from current fund value, which becomes less withdrawal when the fund value is lower.

Withdrawals of course depend on money still remaining available in the fund. If no withdrawals, the fund will survive and continue growing, but withdrawals will drop the fund value fast, especially when low in bad times. The S&P calculator program cannot predict future gains, but its purpose is to see the result of some typical actual bad times from recent history, and also to see the results of withdrawals, to help know the best future plan.

**Again, this is definitely NOT speaking of bad investments recovering**, but is instead speaking of good investments in bad times.

25 years ago, the original 4% Rule data looked at the market back to include the Great Crash of 1929, but times and laws and market rules have since changed so much, and IMO the last 50 years seem typical enough of today's world. The calculator Test on the previous page is ONLY about actual S&P 500 Index history. It has no historical data for any other funds except S&P 500 Index funds (which are a very popular class). All of those will show the same S&P result, except they do vary in the fee they charge (the fund fee is withdrawn every year, and a fund with a low fee is a big plus).

**How much withdrawal can survive bad crashes is a vague question though.** Situations vary. A market crash just when you need the withdrawals is the fear. Another danger is an early crash before the fund has grown to be able to survive it. Do realize if a fund loses 50%, the low price then has to regain 100% to recover.

The market goes up and down every day, but fund survival depends on how much value is in the fund, and specifically, how much value is also being withdrawn from the fund.

- A really bad crash can drop value to 50%, and has occurred a few times, but its date is not predictable. So then, how much other money is also being withdrawn? If no withdrawals, a crash will recover in time. Sitting tight long term might be uncomfortable, but it is has always recovered to continue growing, whereas significant withdrawals during the crash could endanger emptying the fund.
Withdrawing from a fund of low value won't last long in worst situations, but a larger fund value certainly helps. If for example, a $2 Million fund crashes to 50%, it still has $1 Million, which is $40K a year for 25 years, even without any recovery or future gains. That case seems a lesser problem, and recovery will come. Just saying, starting early to accumulate a larger fund is a great plan.

- A 4% Rule sort of assumes the fund should survive if its average return is at least 4%. The S&P 500 has always earned about 10%, however in practice, the fund might often gain more, but then suffer a 50% drop. So it is uneven, and unknown, so there can be some difficult spots. Withdrawing only about half of the funds annual gain seems safer. The S&P 500 does gain more than a balanced fund can, but it also crashes deeper.
Realize that 4% of not much money is even less money, but 4% of a lot of money is much more satisfying. The S&P 500 has always averaged about 10% all along, meaning withdrawing 10% should stay at more or less the same fund value (with risky variations), but withdrawing the average gain cannot grow much, so will 10% not pay much either. The S&P calculator shows (if starting with $25K) the S&P 500 would have survived 10% withdrawals every year of the last 50 years, but 10% of say $25000 is only about $200 month, and is even less withdrawal when fund value is low.

- The most reasonable plan is to first let the fund grow to a larger value, for say 20 or 30 years before starting any withdrawals. That would then allow withdrawals greater than 4% during retirement. This is shown in Example 4 on that previous calculator page (10% withdrawals survives more then 30 years then, and still grows to 10x ending value). This seems very worthwhile.
And for example, 10% withdrawal even from the first year did survive if starting with $25K in any of the past 50 years, but it could not grow or pay much if 10% withdrawals. The point is, more fund money does last longer, but withdrawals approaching the fund gain rate cannot grow. But the main goal in retirement is that it just needs to last 30 or 40 years.

The commonly seen market advice about risk is **"Past success does not guarantee future performance."** Meaning, we don't know the future, and unexpected bad times do happen. But IMO, that is speaking of short term events (up to a few years). I get my encouragement by looking at a graph of the S&P 500 history. Market gains certainly offset inflation, however *do unclick the Inflation-Adjusted box there* to show the actual S&P data. The world might someday end, but the graph long term trend does look very promising. 😊 The notches in the rising curve are the bad times, and there's been many of them, but they get forgotten as the curve goes up. It does show that the 1970s and the 2000s decades were serious bad times (a mouse-over there shows the dates). The bad times will seem drastically bad at the time, but they always recover (might take a year or two, but retirement is a long term goal, right?)

**The actual risk** is that if the fund is saving for a specific time, like for retirement or a child's college expense, a 100% recovery might not be fully available at the time needed. But college is a four year duration, not all needed at once on the first day, so it has more time. And retirement is possibly a 30 year duration, and growth continues all during that time. We don't know about the future, but the program can show the effects of some past bad time drops.

Fund values seriously suffer from any withdrawal, both by reducing the remaining balance, which also limits the future gains. IRA RMD (Required Minimum Distribution) is required after age 72, but otherwise withdrawals are a choice, but if the withdrawn money had remained invested, that money would have earned more money itself, repeated every year, compounded. **It is certainly wise to cut back on withdrawals in really bad times, to avoid depleting the fund. And it is always best to reinvest the dividends**, and you can see the tremendous difference that makes here (of compounded growth in time). Bad times are the worst possible time to sell out and close the fund since that absolutely locks in and guarantees maximum loss, with no recovery possible. The market will drop in value now and then, maybe to around 50% in the very worst times, which will seem catastrophic and unbearable at the time. But if you can hang in there, it will recover and will then be forgotten (eventually, which could be fast, or could take one or more years). It no withdrawals, the S&P 500 has always recovered to hit new highs, and will resume and continue earning more. Currently, the last ten years have had good results, but the market behavior before 2010 might be considered expected now and then, however it always recovers.

Investment tax is a pretty serious consideration. When cashing in (selling or withdrawing), taxes on gains are expected. U.S. IRS tax law extracts a penalty unless income tax is prepaid before the April 15th due date, with at least 90% of tax due, or 100% of last years tax amount. IRS RMD withdrawals can specify a withholding amount, or Estimated Tax returns can be paid quarterly.

There are different classes of market investments. This info this tries to cover the basics about tax expectations (but tax laws can change)

**Regular stocks and funds (Not IRA)**

Bought with after-tax money.**Dividends are always taxed the same year paid (regardless if withdrawn or reinvested)**. It's a congressional law. Otherwise stocks and funds don't owe tax on gains until sold. Then tax is owed on the gain portion withdrawn (less the cost portion). If first held one year or more, it is mostly**Capital Gains tax**— which is normally a 15% rate, except capital gains tax rate is 0% (tax-free) if the 1040 taxable income is not more than $40,400 (single) or $80,800 (joint). Above that, more income becomes 15% tax rate (on the capital gains part), and becomes 20% tax at around $445K to $500K income. This is likely less than ordinary income tax rates in those brackets. Since tax on dividends is paid each year, any reinvested share purchase does increase the fund cost basis which reduces taxes when selling future growth, so the tax balances out eventually. Bonds are an exception, price changes are capital gains, but dividends are always taxed as regular income.**IRA stocks and funds (Not Roth), in regard to RMD (Required Minimum Distribution of IRA at age 72)**

IRA is bought with pre-tax money (which is a deduction from that years taxable income). IRA contributions (total of all IRA accounts) are limited to $6000 per year ($7000 if age 50 or older), must come from earned income, and also cannot exceed your income. There is a 6% penalty each year until any excess contribution is removed. Reinvested IRA dividends are not taxed yet. Any IRA withdrawal is 100% taxed as income at ordinary income tax rates (IRA is not as capital gains). IRA money withdrawn before age 59 1/2 pays a 10% penalty.**At age 72, you must start withdrawing the IRA RMD each year**, which RMD increases with age. There are 50% penalties on the RMD money not withdrawn, but your IRA brokerage firm should make it difficult to ignore.IRA RMD details are in the IRS chart showing the annual IRA RMD calculation according to age.

**Each of your IRA custodians**(providers) compute their part of your RMD on 2 January based on the value of your IRA that they hold for you. For the IRA total, then if using the chart:

RMD dollar amount is end-of-year total IRA fund dollars / Distribution Period (for your age)

or, RMD withdrawal percentage is 100 / Distribution Period (20 years is about 5%).Some say this IRS RMD chart is not a bad plan for a safe amount from non-IRA withdrawals too, but the RMD requirement and rate does apply to age 72 and beyond. The rate may be a bit conservative, but the purpose of the RMD law is Not about fund survival, but that the tax gets paid.

If multiple IRA accounts, each IRA fund holding firm only knows of their part, and computes RMD only for your IRA funds they hold (so you would have multiple RMD from each holder).The RMD is computed at the beginning of each year from the total IRA values in each IRA provider then. At any one provider, the RMD applies to the total IRA amount there, but the RMD can be withdrawn from any IRA fund or funds, just so long as the total is done. The RMD plan is that the tax must be paid, but if this mandatory withdrawal is more than you need, the withdrawal can always be reinvested somewhere else. Since you are paying tax on the withdrawal, then it would go into a regular investment instead of another IRA.

However,

**any IRA you might inherit must be kept very separate, with different rules**. It cannot accept contributions, and its withdrawals are still 100% taxed but the new law has very different rules. Now, unless inherited from a spouse, then**IRA inherited after 2019**have no annual RMD as such, however 100% of it must be withdrawn within 10 years, regardless of age. Be aware that one lump-sum total IRA withdrawal likely increases income into a higher income tax rate than if it were distributed more evenly over the full 10 years, while it can also still be earning.IRA withdrawals are always taxed at ordinary income tax rates.

**Capital Gains tax does not apply to IRA.**All IRA withdrawals will pay regular income tax on 100% of the withdrawal, so pay attention to the tax rates on the tax brackets. Aside from the IRA MRD, perhaps other investments may have capital gains withdrawals possible with a lower tax rate.**Controlling your own IRA investment**.A self-directed IRA fund can invest in ways that you choose, for example in individual stocks. The IRA is taxed only at withdrawal, and ROTH is tax-free. Therefore trading events (buying and selling, changing the investment) are NOT taxable events for an IRA or a ROTH. That part could be an advantage. When you retire, or any time you change employer, if desired, you can withdraw your previous company 401K and (within the first 60 days), reinvest it into a self-directed IRA of your own choice, which then

**allows your direct control of its investment choices**(and likely is smaller fees too). Then example, it could be invested in any stocks or funds you wish (or others, like real estate or gold, etc). Which is neat, because then**buying and selling are not taxable events in an IRA**. (Tax is only due on IRA withdrawals, but as regular income tax, NOT capital gain). For one example of self-directed, my own IRA is held by Vanguard.com as IRA custodian. Then upon my orders, those IRA stock and fund trades are handled like any other stock or fund, except trades in an IRA are not yet taxed. You will get a tax 1099 for any withdrawal, including RMD withdrawals. Again, IRA withdrawals are NOT taxed as capital gains, so regular income tax will be owed then, so specifying some RMD withholding is suggested. Depending on your investment success, retirement tax rate may be higher than when working. An IRA to Roth conversion as early as possible may be an advantage, in that less tax is owed when fund is still smaller, with more future tax-free gains too.**ROTH IRA stocks and funds**All Roth contributions can only come from earned income (from wages or self-employed income, but Not from other or investment income). You can withdraw*the contributions*to a Roth account tax free and penalty free at any time and any age. Then after 5 years and age 59 1/2, you can make any withdrawals from Roth accounts tax free and penalty free. Roth IRA accounts have NO RMD, but Roth contributions have the same $6000 maximum annual limit for all combined IRA/ROTH accounts ($7000 limit if age 50 or older). Roth has an eligibility income limit, maximum incomes are*about*$129K single or $204K joint. Roth is bought with after-tax dollars (no initial tax break). However the really big deal is that Roth withdrawals after age 59 1/2 pay no income tax or penalty at all. You can continue Roth contributions at any age. "A backdoor Roth" can be created by converting an IRA to Roth without limit (except it must be completed within 60 days), which means paying income tax on the IRA converted amount, but then future Roth gains and withdrawals are tax free, with no RMD and no further tax. However consider any effect on Social Security benefits that a large IRA conversion income can cause. One advantage of either an IRA or Roth, especially if it is a self directed account, is you can change its stocks and funds to others at will without it being a taxable event.**Employer 401K plans**are very similar to IRA, except allowing higher contribution limits. You can have both 401K and IRA, but both have limits on annual contributions. Like IRA, 401K contribution income is not taxed and withdrawals are taxed 100%. Maximum 401K contribution limits are much higher than IRA, but 401K contributions have to come from earned income. And employers can choose to provide some degree of matched 401K savings, which if so, is free money into your account (but 100% of all withdrawals are taxed). There are investment choices, but the typical default 401K fund may be more conservatively invested than the S&P 500. Like IRA, 401K withdrawals suffer penalty before age 59 1/2, and RMD withdrawals are required after age 72.**Social Security**

Don't forget that most of your retirement USA Social Security income may also be taxed, depending on income. S.S. tax currently begins at an adjusted gross income of $25000 (single) or $32000 (joint), when 50% of Social Security income can be taxed. Total income higher than $34000 (single) or $44000 (joint) will be taxed up to 85% of Social Security income, at regular income tax rates. In addition to the taxes, even greater income can also reduce the total Social Security amount paid.

Also see these pages:

Previous page with the S&P calculator.

Next page, Stock Dividends are valuable, but withdrawing them is Not income.