kitchen table math, the sequel: Aloha from guillotine-deadline land

## Monday, September 7, 2015

This weekend's events:

I just got the answer to this problem right:
Ten out of every 1,000 women have breast cancer. Of these 10 women with breast cancer, 9 test positive. Of the 990 women without cancer, about 89 nevertheless test positive. A woman tests positive and wants to know whether she has breast cancer for sure, or at least what the chances are. What is the best answer?
I realize most ktm readers can do this in their sleep, but I had to reason it through ... and I did!

That really makes me happy.

Which brings me to yesterday's challenge: I wrote a proof!

On purpose!

I had been talking to friends about index funds, the stock market, and the ever-terrifying Federal Reserve...and pretty soon I found myself utterly confused.

My question was whether Ed and I needed to get the 401(k) out of an index fund and into cash while the stock market is losing its mind.

Both of my friends seemed to think that something called "dollar cost averaging," which I had never heard of, meant that you don't actually lose more money when the stock market declines because your dollar cost average now goes down as you buy more shares with each new deposit into the 401(k).

One said she sees stock market declines as opportunities to buy more stock at a discount. She doesn't seem to worry about stock market "corrections" at all.

Neither of my friends was making an argument about timing the market. Both seemed to be saying that when the market falls, your dollar cost average falls, too, so you come out OK regardless of whether the market has hit bottom or not.

I was so flummoxed that I pulled up an Excel sheet and did three hypotheticals comparing two investors starting with the same amount of money distributed between the market and savings. In each one the investor who stayed in the index fund as it sank, or who put more money into the fund from savings as it sank, ended up worse off.

Then I wrote a proof!

That was a moment.

Regardless of whether my proof is correct or incorrect, I had just had a real-life experience of the incredible power of mathematical proof. I was thinking about all those people asking when students will ever use algebra in 'real life' -- I just used mathematical proof in real life.

Several years ago, I read a book which explained that a loss is a loss is a loss: money you've lost in the stock market today doesn't come back tomorrow. That made sense to me, but now I find that, apparently, few people believe it.

And it is a hard idea to hold on to, because intuitively it feels like money "comes back" when the stock market rises again.

Intuitively, it feels like you lose the money only when you sell after the loss, not when you hold.

Now I can look at my proof and know that money lost is money lost. You can sell, you can hold. Either way, that money is gone.

What to do about it--if anything--is another question, of course.

TerriW said...

I would argue the money is never there to begin with to be lost. You only lose money if you sell. Otherwise you have exactly what you had the day before: X number of shares.

How much money did we lose? Nothing, because we didn't sell. That question doesn't apply until we cash out, whenever that may be.

FedUpMom said...

As an investor, here's how I think about my stock holdings. Imagine a graph of the price of your stock. Now imagine that you take an opaque piece of paper and lay it over the graph. Now take a hole punch and punch a little hole over the graph, only at the spots where you bought or sold the stock. What you can now see is the only information that matters for your account. If you bought the stock for less than you sold it for, you made money. Congrats! Everything else is just noise, from your point of view.

Your friend who sees a low stock market as a buying opportunity probably makes money on her investments.

Somebody published a book some years ago that looked into the stock market's historical performance. They put together "the world's worst portfolio" -- that is, they imagined buying a whole bunch of stocks at the worst possible time, 1929 right before the crash. Then they figured out how long you would have to hold those stocks to be able to sell at a profit. The moral was that even the worst portfolio wasn't as bad as you might think, and that if you could hold out you could still turn a profit. If you held the stocks long enough you could make a very handsome profit.

Jim Beall said...

I have been a fee only financial advisor for over 20 years. A few things to consider. These are generalities
1. Investors are horrible at timing the market. Investors returns are generally about half of the return of a mutual fund because they get in and out. Whereas if they had just stayed in they would have done roughly as well as the mutual fund (taxation does play a role in returns.)
2. Index funds are the way to go for most investors. That being said an S&P 500 index fund can vary widely in performance based upon its underlying fee.
3. Don't let politics influence your investing.
4. Always consider your time horizon for the money. If you retire at 65 in good health the odds of you living another 25+ years is high. Your portfolio therefor should reflect this time horizon and stocks have not lost money over any 20 year period based upon the last 100+ years. Individual stocks yes Stock Markets no.
5. Debt is a tool to be used wisely.
6. Always consider your tolerance for risk when investing.
Remember Warren Buffett lost 6+ billion dollars in 6 weeks. It was a paper loss based on the fluctations of the stock price. He didn't actually lose anything since he didn't sell for he knew his time horizon was decades not days or weeks or months. This is the big advantage you have over Wall Street your time horizon is not measured in hours or days but years and decades.

Hope this helps.

Catherine Johnson said...

I'm pretty sure it's not the case that you only take a loss when you sell. In fact, I'm positive.

Mark to market says that you take the loss that day, whether you sell or not, and that's what traders are taught, too.

Here's what my various friends are telling me (and I've discovered this is a near-universal belief).

During the bear market of the Great Recession, stocks lost 57% of their value.

Anyone who stayed in index funds all that time lost that 57% (or 35% or thereabouts if they were in 60/40).

Then the Federal Reserve did three rounds of quantitative easing, and the stock market gained 200%.

My friends all think this means the 57% loss wasn't a loss because the money "came back."

But that's not mathematically correct. First you lost money, then you gained money on the lower amount.

If you had gotten out of the stock market, you would have preserved your "position" (I think it's called) & the QE gains would have come on top of it.

Catherine Johnson said...

FedUp - That's the other idea I'm encountering --- you shouldn't get out of your index fund when the market is down because as you add more money to it, the average price of each share increases so you're making a bigger profit.

But that doesn't factor in the money you lost by staying in.

We stayed in our Vanguard index for the entire 18 months the market was falling. We had no idea what we were doing, and it never crossed our minds we could do anything other than feel bad about what was taking place. (In fact, our retirement plan does have a money market, which we're in now, until things calm down.)

I checked Vanguard today & found that in 2007-2009 the small retirement account I have lost money every single month for 17 months, except one, and that one bump was tiny.

Meanwhile, Ed was putting as much money as we could possibly swing into his retirement index fund, matched by NYU, and every single month for 18 months 35% of that was instantly destroyed, the minute it was put in.

Everyone I know seems to have done the same thing: we poured money into an 18-month long bear market.

Meanwhile the 'smart money' got out. I vividly recall Ed's money-manager friend saying the **only** thing he was doing was helping his clients preserve their money. He had nothing in stocks, and he wasn't searching for investments to make a profit. He was trying to preserve capital, and people were paying him to preserve capital.

Catherine Johnson said...

<< Your friend who sees a low stock market as a buying opportunity probably makes money on her investments. >>

She bought at the point that the stock market was going to lose another 37% in value.

The market was low in comparison to what it had been before Lehman.

It was going to go a lot lower.

I'm sure she made a profit once QE happened.

But first she sustained major losses, so that profit was on a much lower investment.

ChemProf said...

Catherine,

The problem is that people pull their money out once it is clear they are losing money - say when they've lost 30% of what will then be 60%. Then they put their money back in when it is clear the market is going up, which means they miss much of the following rise. With real people, most of the time, you are better staying in not because you haven't lost money but because you will wind up missing the rise and have less money over all.

Let's use your numbers - say we have \$100 in the market and it loses 60% of its value so it is worth \$40. Then it rises 200% so this person ends up with \$120. Yes, they really only gained 20% total. But now, let's say they pull it out at 50% (waiting that long before they pull out) and only get 100% of the gain, because they wait too long to go back in. Now they have \$100. If you time it right, you can do better, but people in real life don't.

FedUpMom said...

Catherine: let's try a thought experiment. Suppose I said to you, "give me \$100 and in 6 months I'll return \$120 to you." Would you care what I did with the money during the 6 months?

To make it more like the stock market, I would have to say "... and if you wait for the right moment, your \$100 will probably be worth \$120." Do you care what's going on while you wait for your \$120?

On average and in the long run, stocks are the best investment. If "average" and "long run" are too painful for you, you might prefer to put your money elsewhere. However, interest rates right now make the stock market look good.

Also, some stocks give dividends, which you can take in the form of more stocks ("reinvest"). In the depths of a bear market, I comfort myself by thinking of the shares I'm getting cheap because of dividend reinvestment.

Jen said...

Okay, I didn't do a proof,I did a write out a list and figure out a hypothetical and my investor won, over my time frame, though it would depend on when you decided to sell based on the dropping price.

I assumed starting with \$1000 and investing \$100 month for two years. I set my starting stock price at \$10 and had it stay there for one month, then drop to \$8, \$7, and then 5 months at \$5 (so it lost half its value over three months and then stayed there for 5 months. Then I climbed it back up, \$6, \$7, \$8, \$8, \$8, \$9, \$9, \$9, \$9, before it got back up to its original price per share of \$10 which I let go up to \$11 and stay there for the 4 months left of the two years in example and left it at \$10 in the other.

But, with the initial \$1000 and the \$2400 (\$3400) added in, I have either 415 shares @ \$11 or 419 shares @ \$10 (\$4565 or \$4191).

In a money market account (currently ~1%) I'd have \$3443 if I hadn't gotten back in the market.

If I had gotten back in at the 19th month when it went back to \$10/share, I'd have \$2830 to invest, getting 283 shares. Under the same two options listed above for those additional 5 months, I'd end up with \$3330 if it stayed at \$10/share and \$3608 for 328 shares if it went up to \$11.

So, what am I missing here? Obviously this was really quick and dirty, but the dollar cost averaging did work -- I had a lot more shares when the price came back up. And I didn't have to pay to buy and sell. Taxes? Beyond my pay grade of \$0 on a Saturday night!

Catherine Johnson said...

Sorry -- haven't read everything yet (I will) --- but following up, I've discovered the language I was missing.

I'm not talking about "market timing."

People with 401(k)s are told: "Don't do something, just stand there." That's John Bogle.

During a bear market, we are supposed to stay put -- and, even worse, continue to pour money into 401(k)s -- while everyone else is bailing.

We're supposed to do this because the market will "go back up" and our money will "come back."

Money doesn't come back. The market will probably go back up because this is America and at some point the Federal Reserve will make sure the market does go back up.

But the money we lost waiting for the Federal Reserve to step in is lost for good.

Ed and I both finally looked at the month-by-month in the bear market of 2007-2008.

For 17 months in a row, my little IRA lost money every single month but one. (I wasn't putting any more in, so it was easy to see.)

If I had been paying attention --- if I had had any understanding that I didn't **have** to lose money month after month just because that's what people like me do --- I would have moved my money to a money market a couple of months in and left it there until probably a couple of months after the bear market ended. (I don't remember what was going on when the bear market finally ended -- if I'd known anything about the Fed, I may have put my money back in closer to when the bear market actually did end)

I would have sustained two months of loss and missed three months of gains.

I would have been far, far ahead.

Ed looked at his 401(k) and found that for several months every penny he & NYU added to his 401(k) was burned up in the market instantly.

Then, somewhere along the line, principal started being burned up, too.

He and NYU would put more money into his 401(k) each month, and at the end of the month that money would be gone & so would some of the money that had been there before the month began.

Nobody in 401(k)s should have continued dumping money into the stock market for 18 months in a row (I think the bear market was actually 18 months).

Investment people actually have little sayings for this:

"Invest the trend"

and

I can't time the market, but I can certainly understand what a bear market is.

Catherine Johnson said...

I've also seen, recently, a short article looking at best & worst days in the market. (I'll find & post.)

As it turns out, the best & worst days clump together during periods of volatility, like what we're in now.

And they aren't equal.

If you exit the market during volatility you miss the best days & the worst days & you come out ahead.

Catherine Johnson said...

In accounting terms, and in real-life terms, you lose money the day you lose it.

If you think about the crash ----- why was there a crash?

Why did anyone think the banks were insolvent or bankrupt?

They all had tons of stocks, bonds, derivatives, credit default swaps --- you name it.

Why couldn't they just say "We're just waiting for the market to go back up? Then we'll be rich again?"

The reason they couldn't say that is that "a loss is a loss is a loss."

Whatever money you lose today is gone.