Why Yesterday’s 11% Gain Isn’t What You Think It Is

by Kevin on October 14, 2008

Yesterday all of the major US indicies jumped up around 11% or so. Wall Street and Main Street cheered in unison. The end is here! And everyone lived happily ever after. As nice as that sounds, I want you to know it doesn’t necessarily mean what you think it means.

A quick look at the 3 month return of the S&P 500 index:

Now don’t get me wrong, I am thrilled everything went up yesterday. I’ve got money in the market, too!

But I want to be the voice of reason.

What this is:

  • a nice little bump off of the bottom of a multi-week fall

What this isn’t:

  • a guarantee that the market slump is over — the stock market could go up, down, or stay flat for any length of time
  • a reason to change your investment plan

Some quick math:

I also want to point out that a 11% gain yesterday is not equivalent to a reduction of losses by 11%. That is, an 11% gain is not equal to an 11% reversal.

For example, let’s say you have $100. You lose 11% of your $100 dollars, or $11. You now have $89.

If you gain 11% on your $89, you now have $98.79 — not $100. To return to your original $100 you need a gain of 12.35%.

It’s a small difference, but is a pretty serious difference. If your investment has lost 50%, you need a 100% return to get back to where you were (rather than 50%).

Any way you cut it, I’m glad to see a jump in the markets. Hopefully it will continue and the worst is behind us. My only regret is I didn’t have more money in yesterday before the jump.

What about you guys and gals? Did any of you try to time the market? Who pulled their money out on Friday and is now kicking themselves for missing out on the gains of yesterday?


JB October 14, 2008 at 7:23 am

The ‘quick math’ section was very insightful. I’m sure that’s something most people don’t realize.

philip October 14, 2008 at 9:23 am

I have had to show lots of people that same math, and yes even when I do the math in front/with them they still argue with me, argghhhh!

That is why I watch point value changes in the market instead of percentage changes, it is a little more truthful.

Like they saying goes “There are lies, damn lies and statistics” they will use whatever makes it the biggest topic for the news. Hopefully more people will see your post and keep me from having to explain it to them again.

philip October 14, 2008 at 9:53 am

I checked what my actual growth was on my Vanguard plan, with my distribution I only had a gain of 9.01% no the 11% on the DOW. Mostly because the REIT fund did not show the same growth as most of the market.

Laura K October 14, 2008 at 10:32 am

Thanks for explaining the math. I’m kicking myself for not investing the cash I had sitting in my Roth on Friday, but who’s to say we’re not going to go back down some? I did put a little in yesterday, but I’m not sure what to do with the rest. I’m thinking maybe just some chunks at a time over the next few months.

Russell October 15, 2008 at 8:23 am

Great that you pointed out the mathematics of percentage, particularly making the point 50% loss is only offset by 100% gain afterwards. This is evident when you look at longer-term results, companies that have 200% gain. Obviously you cannot have 200% loss so the mathematics of percentage ought to stand out in those cases.

I’ve been intrigued with CNBC particularly the High-Def channel where they’ve got room for all sorts of statistics on the right portion of the screen. So many little red down-arrows for almost every company, even in long-term results, and they show the percentages there. (I did see one yesterday had something like 45150% gain over 5 years, must have started out at 25 cents.)

Personally the timing has been right for me, I left my job at the end of June which means left the 401(k) contribution plan at that time. With costs of starting up my home office (computer, office furniture, internet access) then quarterly income tax payment, I couldn’t afford to make any other kind of tax-deferred investments.

My schedule was to make Roth IRA contributions in October, November, and December of this year, and made the first one last week. Long-term that account should look pretty good when market valuations get back to normal range. Regardless of that happening, the account looks better than if I had continued making 401(k) contributions through employment in July, August, and September.

To answer the question why Roth IRA, because the rules are fuzzy about traditional IRA when you are participating in an employer-sponsored 401(k). I could not find any clear answer to part-of-the-year participation in a 401(k), all the tax publications seem to presume you never change jobs during a year. Roth IRA is independent of any other plan participation. And opening a Roth IRA account is a lot easier than setting up a SEP-IRA or SIMPLE plan.

ChristianPF October 15, 2008 at 11:52 am

I agree, this is one of those math lessons that people often miss or don’t think of off the bat. Looking at a failing stock I own (the company I used to work for BTW) dropped from about $55 to $5 – bummer, I know 😉 While it dropped almost 90% in value it will have to go back up almost 400% to get back to where it was when I got it…

YoungMoneyTalks October 15, 2008 at 11:59 am

As someone who might be described as “math impaired” I also appreciate the quick mathematical explanation. If I had more money to put in the market, I would have loved to have gotten in a few days ago. Alas.

BD October 16, 2008 at 11:18 pm

Like everyone else, I have to comment about the math. It perplexes me why reporters, who unlike the layperson are paid to be more analytical and insightful, throw numbers and percentages about without analyzing or elaborating on them in the way you have here. I suspect when it comes to numbers most reporters are about as clueless as the general public.

Russell October 17, 2008 at 7:30 am

Numbers are still mystical to many people, look at the fascination with Lottery by the general public. And I’d agree that journalists, except those with the financially-oriented outlets, don’t have a good grasp of math.

I’ve never understood how the DJIA has survived as the prime indicator in modern times, it represents only 30 stocks in a universe of thousands, plus it has a wacky weighting formula from adjustments over the years. (Not to mention that the stocks in it change when one falls out of favor.) When it was devised it was a shortcut in the day of manual calculation, but now we can instantly compute statistics of all variety for the stock markets as a whole.

Back on topic, Kevin asked if we are making any investment changes based on the changes in market value. I opened my first Roth IRA last week. Yesterday I opened my second. The online calculators say this was a good idea, and in my mind it seems like it too. Has anybody else given thought to making a Roth IRA Conversion now?

I took some of my Rollover IRA and converted it to a Roth IRA. It occurred to me that the IRA is currently worth a lot less than I expect it will be in the future. For that matter it might even be worth less than it was when I made the contributions. So of the choices of when to pay income tax — when I earned the money years ago, in a conversion today, or when the account is worth more in the future — it made sense that now is the time, when the funds are at their lowest value, thus the lowest amount of tax will be due.

I know it ignores a lot of things, like changes in tax rates past present and future, and what the money I’ll pay the tax with could have earned if invested, but the online calculators seemed to back it up that this was a good choice.

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