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!
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.