## need help with basic investing math

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schmitz
Posts: 166
Joined: Thu Sep 01, 2011 5:21 pm

### need help with basic investing math

please bare in mind that these numbers are rounded just for the sake of discussion. I also admit I am not a pro at investing so any help is appreciated (please dont laugh at me too much ).

say you start with 50k invested and add 10k per year for 5 years. and each of those 5 years makes 10% return.
however, the 6th year the market crashes and loses 50%.

year 1: 50k + 10% = 55k + 10k invested = 65k
year 2: 65k + 10% = 71.5k + 10k invested = 81.5k
year 3: 81.5k + 10% = 89.7k + 10k invested = 99.7k
year 4: 99.7k + 10% = 109.7k + 10k invested = 119.7k
year 5: 119.7k + 10% = 131.7k + 10k invested = 141.7k

then the crash...

year 6: 141.7 - 50% = 70.6k

so after 6 years you have put in 100k and you are down to 70.6k. so about 30%.
five 10% increases + one 50% drop = 30% drop. yikes.

now like i said these are made up numbers but it makes me wonder, how (in the long run) does investing even work when drops hurt a lot more than rises in the market help. i think my math is right but my logic is wrong. for me personally, i started investing about 3-4 years ago so ive really only seen the good of the market (it was pure luck when i decided to get into investing). then i read rumors that the inevitable crash is coming...if i lose 50% of my portfolio itll easily wipe out everything ive earned the entire time...plus more. im not planning on selling anything now or if it crashes (got awhile until retirement) however, it does concern me. and i know the market, in the long run, does go up.

my guesses as to where im wrong:
1) the market goes up usually more than 10% on its up years
2) the market goes up more than 5 out of every 6 years (83% of the time)
3) when the market crashes it wont be 50%
or some combo of the above?

dickenjb
Posts: 2941
Joined: Tue Jan 05, 2010 1:11 pm

### Re: need help with basic investing math

How about your scenario is perfectly plausible but then it starts going up again?

Trevor
Posts: 235
Joined: Tue Jul 08, 2014 3:16 pm

### Re: need help with basic investing math

then i read rumors that the inevitable crash is coming...
I've been hearing that rumor for the past year and a half, including some people who withdrew from the market in 2013 to avoid the so-called inevitable crash. It's often called "noise" and it's something you need to ignore if you want to be a rational investor. I would actually agree that a crash is "inevitable" but NOBODY knows when the next one will actually happen.
if i lose 50% of my portfolio itll easily wipe out everything ive earned the entire time...plus more. im not planning on selling anything now or if it crashes (got awhile until retirement) however, it does concern me. and i know the market, in the long run, does go up.
As long as you don't sell low, you aren't actually "losing" anything. Market crashes are actually considered a good time to invest because you are buying equities for low price while other investors are panic selling. Just stay the course and you will do great
WWJD - What Would Jack Do?

galeno
Posts: 1413
Joined: Fri Dec 21, 2007 12:06 pm

### Re: need help with basic investing math

1. Determine how much in % of your portfolio you can afford to lose. If you can tolerate a 50% loss you can go 100% stocks. 30%? Go 60% stocks and 40% fixed income (intermediate term bonds and cash).

2. Rebalance back to your asset allocation every year. This technique has you buying low and selling high. Exactly what you should do.
AA = 40/55/5. Expected CAGR = 3.8%. GSD (5y) = 6.2%. USD inflation (10 y) = 1.8%. AWR = 4.0%. TER = 0.4%. Port Yield = 2.82%. Term = 33 yr. FI Duration = 6.0 yr. Portfolio survival probability = 95%.

hornet96
Posts: 429
Joined: Sun Nov 25, 2012 6:45 pm

### Re: need help with basic investing math

You need to calculate the geometric return (not the arithmetic average return). So the math for your example is:

(1.10)(1.10)(1.10)(1.10)(1.10)(0.5) -1 = -19.47% total return over 6 years. Not pretty, but....

You also need to consider the effect of the \$10K new contribution in year 6, in your example. I get \$80,788 when I plug the numbers into my financial calculator.

But yes, overall the stock market is expected to increase in value, over the long haul. At the most fundamental level, the valuation (price) of stocks is tied to the underlying earnings of the companies, which are expected to grow with the economy (and inflation). There are other factors that cause gyrations over shorter periods of time, of course.

Stocks are generally considered to be the best long term hedge against the damage to purchasing power caused by inflation. Note the emphasis on long term.

schmitz
Posts: 166
Joined: Thu Sep 01, 2011 5:21 pm

### Re: need help with basic investing math

ok I knew it still worked out in the long run...thanks to everyone for the input/advice. ill keep doing what I AM doing and invest for the future whether the market is up or down.

dickenjb : thanks, but have you really never misspelled a word on a message board?

JoMoney
Posts: 6269
Joined: Tue Jul 23, 2013 5:31 am

### Re: need help with basic investing math

I think your made up scenario describes the period leading up to the 2008 crash pretty well.
You seem to be leaving out the possibility of recovery though, which has been the case over much of history. Also, you seem to be using sort of a normal distribution on the positive side, and a fat tail on the down side. This is not the typical case, their are fat tails on the upside of stock investing as well. A 10% annual return year after year is not typical. Here's what rolling one year returns for the S&P500 looked like (Notice there've been a lot more +30% years than -30% down years:
"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks." - Benjamin Graham

schmitz
Posts: 166
Joined: Thu Sep 01, 2011 5:21 pm

### Re: need help with basic investing math

JoMoney wrote:I think your made up scenario describes the period leading up to the 2008 crash pretty well.
You seem to be leaving out the possibility of recovery though, which has been the case over much of history. Also, you seem to be using sort of a normal distribution on the positive side, and a fat tail on the down side. This is not the typical case, their are fat tails on the upside of stock investing as well. A 10% annual return year after year is not typical. Here's what rolling one year returns for the S&P500 looked like (Notice there've been a lot more +30% years than -30% down years:
thanks - that graph definitely helps me see the market in a different light.

Phineas J. Whoopee
Posts: 7684
Joined: Sun Dec 18, 2011 6:18 pm

### Re: need help with basic investing math

schmitz wrote:...
say you start with 50k invested and add 10k per year for 5 years. and each of those 5 years makes 10% return.
however, the 6th year the market crashes and loses 50%.
...
Eyeballing them, your numbers look plausible. I've not recalculated to confirm, because that's not the point I want to make.

It is always the case that there probably will be at least one significant stock market decline within the next five years. Fifty percent hasn't been all that common historically, but it happened twice in a ten year period within living memory.

The difficulty I see with your series is it ends as soon as there's the, expected, significant decline. If you feel you would panic and sell all your equities in the face of it, then you need to think carefully about your asset allocation, based on your (all credit to Larry Swedroe for this concept) need, willingness, and ability to take risk. Larry suggests you assess each separately, then use the lowest to inform your asset allocation choice.

If you split your assets between equities and fixed income, or to be more general, more-risky and less-risky, in such a way that the stock decline, remember it's all but certain to happen fairly often but unpredictably, won't phase you, and you can keep going on your plan, then you should be all right. I don't know you personally, but frequently when posters ask about the extreme risk of a stock market decline, or a bond market decline, and those questions tend to be interleaved, it usually turns out they haven't really worked out the right asset allocation for themselves.

My main point, I'll reiterate, is the stock market fluctuates wildly, and significant, 50% or otherwise drops are always possible. It does that. It's expected behavior. Any rational investing plan takes the fact into account.

PJW
Last edited by Phineas J. Whoopee on Fri Sep 05, 2014 8:18 pm, edited 2 times in total.

happyisland
Posts: 420
Joined: Thu Oct 03, 2013 1:36 pm

### Re: need help with basic investing math

dickenjb wrote:

555
Posts: 4955
Joined: Thu Dec 24, 2009 7:21 am

### Re: need help with basic investing math

hornet96 wrote:You need to calculate the geometric return (not the arithmetic average return). So the math for your example is:

(1.10)(1.10)(1.10)(1.10)(1.10)(0.5) -1 = -19.47% total return over 6 years. Not pretty, but....
Moreover, the OP got an even bigger drop than that because some of the contributions had less than 5 years of those 10% gains.

hornet96
Posts: 429
Joined: Sun Nov 25, 2012 6:45 pm

### Re: need help with basic investing math

555 wrote:
hornet96 wrote:You need to calculate the geometric return (not the arithmetic average return). So the math for your example is:

(1.10)(1.10)(1.10)(1.10)(1.10)(0.5) -1 = -19.47% total return over 6 years. Not pretty, but....
Moreover, the OP got an even bigger drop than that because some of the contributions had less than 5 years of those 10% gains.
Good point. My example doesn't take the timing of the cash flows into account. One would need to do an IRR calculation to get a more exact result.

I mainly wanted to point out to the OP how to calculate the geometric mean (compound returns), using a simple illustration.

The Wizard
Posts: 12433
Joined: Tue Mar 23, 2010 1:45 pm

### Re: need help with basic investing math

schmitz wrote: ...now like i said these are made up numbers but it makes me wonder, how (in the long run) does investing even work when drops hurt a lot more than rises in the market help. i think my math is right but my logic is wrong...
Market moves care nothing about percents; it's only in retrospect that we come up with with this analysis.
You can say truthfully that if the market declines 50%, then it has to increase by 100% to come back to where it was.
But that's just a waste of a good breath of air.
If it was easier for the market to decline over time, then the S&P 500 would be continually shrinking from one decade to the next.
But it's not...
Attempted new signature...

dh
Posts: 292
Joined: Sun Mar 13, 2011 8:01 pm

### Re: need help with basic investing math

schmitz wrote:...

now like i said these are made up numbers but it makes me wonder, how (in the long run) does investing even work when drops hurt a lot more than rises in the market help. i think my math is right but my logic is wrong. for me personally, i started investing about 3-4 years ago so ive really only seen the good of the market (it was pure luck when i decided to get into investing). then i read rumors that the inevitable crash is coming...if i lose 50% of my portfolio itll easily wipe out everything ive earned the entire time...plus more. im not planning on selling anything now or if it crashes (got awhile until retirement) however, it does concern me. and i know the market, in the long run, does go up.
Some other posters have given you some great information and I am not going to add to the math aspects of your post. I simply want to encourage you to increase your holding period (you hinted at that strategy in the section of your post I quoted above). Don't focus on big losses or big gains in any given year.

I find it helpful to look at "The Callan Periodic Table of Investment Returns" (check it out if you are unfamiliar); it helps me focus on the long-term and how different asset classes move. I took a look at the table before sending this reply and found that in 2008 the S&P 500 index dropped 37% (not 50%, but still a huge drop!). However, the table shows that the following year (2009) the S&P 500 index had a larger than average increase of 26.47% (that doesn't get you back to even, but it is a substantially larger return than the 10% per year you used in your example).

Obviously, there are no guarantees of "bounce back" years. I hold the position that I am going to worry about what the market does in 1 year, 5 years, or the next 10 years (at my age 15 years for me is becoming an "issue"). I say to myself that this is my long term money and I am not going to touch it until 20xx (come up with your own year depending on your age). You didn't mention your age, but if you are younger than 40 you should welcome 50% decline. If a huge drop happens, "pour the coals" to your investing for the very long run. I am many years past 40, so I hope a 50% decline doesn't happen! Good luck to you!

dbr
Posts: 27207
Joined: Sun Mar 04, 2007 9:50 am

### Re: need help with basic investing math

Why not just look at a chart like this one and see what actually happens (yes, I know dividends are not in there):

http://finance.yahoo.com/q/bc?s=^GSPC&t ... z=l&q=l&c= expand to max

Some mathematical quibbles aside, your example shows something that can and does happen in the stock market. That is why we call stocks risky.

I would say at least one flaw in your logic is that you hand picked one particular example rather than looking at the whole. You could call this a virtual example of what we call "cherry picking" when it is done with real data. Taken differently it has the flaw of looking at too short a time span or the flaw at looking at an arbitrary period without attending to what happened (or might happen) before and after that time period.

However, if you are shocked, it means you do not understand risk in investing in risky investments.

inbox788
Posts: 5691
Joined: Thu Mar 15, 2012 5:24 pm

### Re: need help with basic investing math

Yes, a little of everything. Your situation is probably worse than the great recession an even the great depression. Not that worst case scenarios couldn't happen again, but it hasn't happened that often that badly, and we don't expect it to. Just think, if you have cash and cash in the market, how much better you are compared to the average person suffering through such extreme downturns.

Here's some data (sp500 column 2 & 5):

The lost decade 2000's: If you invested \$142,508.98 in SP500 in 2000, you'd have only \$142,344.87 in 2009.
Great Depression recover: Similar dips in 1928, \$143.81 invested recovered to \$145.38 in 1936 only to dip again and not get back to \$139.59 in 1943, so 15 years of stagnation.

Also, hidden in these dip years is that many investor who were able to regularly invest through these downturns wound up doing much better. The effect of DCA if you will. Buying anytime in the in-between years would have been at a lower cost and would lead to gains at the end of the decade. So not truly a lost decade for the typical investor.

Meanwhile, we've had some terrific gains in boom times to more than offset these worst years, and we seem to be in one of them now, with investing \$142,344.87 in 2009 worth nearly double today, \$255,553.31 in 2013.

So using this data set and my quick analysis:

1) Simple average over 86 years is 11.5%, so on average, yes more than 10%. In 48 out of 86 years it was up 10% or more.
2) In 62 out of 86 years (72%) the market was up. Less than your 83% example.
3) The market hasn't crashed 50% in a year yet. These are the 10 worst years in the data set:

1931 -43.84%
2008 -36.55%
1937 -35.34%
1974 -25.90%
1930 -25.12%
2002 -21.97%
1973 -14.31%
1941 -12.77%
2001 -11.85%
1940 -10.67%

Wow, hadn't realized that 3 out of the 10 worst years have been in the 2000's. No 80's, no 90's, and cross our fingers, so far no 10's.

And just noticed the math they did at the bottom:

Arithmetic Average
1928-2013 11.50%
1964-2013 11.29%
2004-2013 9.10%

Geometric Average
1928-2013 9.55%
1964-2013 9.89%
2004-2013 7.34%

Lafder
Posts: 3843
Joined: Sat Aug 03, 2013 7:56 pm
Location: East of the Rio Grande

### Re: need help with basic investing math

schmitz,
Sounds like a great mathematical argument for not holding 100% stocks and having a % bonds you can sleep well at night with.

You should also play with some scenarios with a % bonds to see what a difference it makes to buffer the downturns in the market, which become rebalancing, investing opportunities if you are continuing to buy.

You sound like you are scared of a drop. In 2008 our portfolio went below what we had put in over the years. It was a sickening feeling. We could have "blown" the money on new cars or a house remodel and been in the same spot we were in at the moment. We did not pull out the lowered holdings we did have left. We waited and kept adding and it went above where it started eventually. But those months of seeing the vanished \$\$ in the account balances was painful.

I tell myself I am prepared for a drop. But I know I won't like the way it feels when it happens.

Best wishes,
lafder

sometimesinvestor
Posts: 1208
Joined: Wed May 13, 2009 6:54 am

### Re: need help with basic investing math

No one else has said it so I may be wrong but it looks like your numbers are only correct if you invest each year on Dec 31. Otherwise you would make some money on the 10k you invest each year.
r

jimb_fromATL
Posts: 2278
Joined: Sun Nov 10, 2013 12:00 pm
Location: Atlanta area & Piedmont Triad NC and Interstate 85 in between.

### Re: need help with basic investing math

schmitz wrote: ... it makes me wonder, how (in the long run) does investing even work when drops hurt a lot more than rises in the market help. i think my math is right but my logic is wrong. for me personally, i started investing about 3-4 years ago so ive really only seen the good of the market (it was pure luck when i decided to get into investing). then i read rumors that the inevitable crash is coming...if i lose 50% of my portfolio itll easily wipe out everything ive earned the entire time...plus more. im not planning on selling anything now or if it crashes (got awhile until retirement) however, it does concern me. and i know the market, in the long run, does go up.

my guesses as to where im wrong:
1) the market goes up usually more than 10% on its up years
2) the market goes up more than 5 out of every 6 years (83% of the time)
3) when the market crashes it wont be 50%
or some combo of the above?
It can be a wild ride if you look at only 6 years at the bottom of a crash. And you are right to look at the long term. If the entire history of the stock market is any indicator, it’s not so bad if you have at least 10 to 20 or 30 years until you need the money for retirement.
• Since the crash of '29 the worst 30 year rolling average for the S&P 500 was 8.46% ending in 1958.

Since the great depression the average of 30 year rolling averages has been 11.13%; the CAGR 11.38%; and the median has been 10.86%.

As of the end of 2013 the S&P 500 has had an average APY of 9.22% for the last 20 yrs, 10.3% for the last 25 yrs, and 11.1% for the last 30 yrs.
You don’t actually suffer the loss unless you have to take your money out while the market is down, anyway. If you don't have the tolerance for the wild ups and downs, or if you don't have at least 10 to 20 years until retirement, it's a good idea to balance your investments with more bonds and other stable value funds that don’t lose as much during a market crash in order to minimize your loss -- especially as you near retirement and won’t have time to recover from a crash before you need to withdraw the money.
• As an example, the market crash of 2008 was the worst we’ve seen since 1929. But Vanguard’s Wellington, (symbol VWELX) --which has in the range of 60-65% stocks and 40% to 35% bonds depending on their best guesse-- dropped only a bit over 20% by the bottom of the crash. But it recovered in less than two years and has averaged very well over longer periods of time even including the crash.

The S&P 500 and their index fund VFINX , which is all stocks, dropped much worse -- in the range of 40% during the crash. That would have been a problem if you had to withdraw the money at the bottom. But it recovered within a couple of years and has grown even more than the balanced funds.

(Over several years I've lost track of the number of times I’ve seen even very complex portfolio recommendations on various money forums , websites, and newsletters that when checked more closely turned out not to do have done as well as just buying VWELX and leaving it alone.)
The following graph shows rolling averages for the S&P 500 for 6, 20, and 30 year periods. Notice that there have been very few 6 year periods that were negative, and that since the recovery from the crash of '29 and WW-II there haven't been many 20 year periods that even averaged less than 8% for very long. There have been no 30 year periods averaging less than 8% since around 1950 ... including the crashes of 2001/2002 and 2008.

This was constructed from yearly data from money chimp … which is well worth a visit to learn more about historical performance and the math for quantifying it. It goes into some details about how to calculate the CAGR (Compound Annual Growth Rate) to compare things like your example to actual historical performance for the stock market and funds. More about that coming in a later post.

Also bear in mind that these numbers and most historical performance data for long periods are for a lump sum at the beginning. Since most folks do dollar-cost-averaging by investing in their retirement funds such as 401(k)s at perhaps monthly intervals, and perhaps yearly for IRAs, the ups and downs are not likely to be even as as volatile as the graph shows.

jimb

PS: One of the most convenient ways I know of to get the shiller yearly historical performance data for the S&P 500 into a spreadsheet is to select the entire menu for the money chimp calculator, copy it, and paste it into the spreadsheet.

.