### Another Prediction Request: S&P 500 For YE 2015

A request from the comment gallery:

OK, let's do it. I included the second sentence of the request because research shows that people still make overconfident predictions"I think you should have another contest to have posters give their 90% confidence interval on the closing high and closing low of the S&P 500 in 2015. I hate to give away the ending, but I'd bet that the S&P ends up outside far more than 10% of the predictions."

__even if__you warn them before they make the prediction that they need to be careful because most people make overconfident predictions!

My 90% confidence interval is 1200 - 2400 on the S&P 500.

## 8 comments:

90% confidence? And I have to come up with a range over all of 2015? Well...

For the downside, 1000 would still be a 50% gain from the bottom of the Great Recession. Under the right circumstances, we could go below it. What are the odds? Let's call it 5%.

As for the upside, I think +25% is almost always possible if investors decide they just can't get enough, so let's say 2550. What are the oddds it goes above? Let's call it 5%.

Put me down for 1000 to 2550. I'm apparently 90% certain that we'll stay inside that range.Because nothing says 90% certain like predicting the future using a gut feeling backed up with reams of historical data ("past performance is not necessarily indicitave of future returns") and a bit of elementary school math.

I'd make a great weatherman. Don't forget to take snowshoes, a heavy duty parka, a light jacket, a raincoat, an umbrella, shorts, a t-shirt, suntan lotion, sunglasses, and mosquito repellent. I'm 90% sure that you might need some of that stuff! Weather's coming! ;)

Yours is 350 points wider... yours is probably right.

I just think it means that I have less confidence than you when it comes to short-term predictions.

I spend most of my time looking at long-term trends. I'm not an active trader. I own long-term treasuries (TIPS) with intent to hold to maturity. That is not something a person with short-term confidence does. I don't try to time the business cycle. I just try to be the tortoise in the race, slowly trudging forward predictably. Since I am retired, boring is good.

I should also mention that I had the luxury of looking at your answer first. Perhaps your answer biased my answer to some degree. And unfortunately, together we will probably bias future answers.

I'm 90% confident that at least one person would predict, with 90% certainty, that the stock market won't fall much, if any.

That might shake things up a bit, if they choose to post such predictions anyway.

Put me down for 1,200 - 2,600.

Also, on your previous post regarding the 80% confidence, would getting 4 out of 5 really equate to being "calibrated correctly"?

If you're 80% confident on each one, wouldn't the odds of going 2 for 2 be 64%? So 5 for 5 would be ~30%? Or am I thinking about this wrong?

We can calculate a range from the options market; using January 2016 options yields a range of 1150-2450. That is an underestimate, though, since it doesn't allow for the possibility that the market rockets to 2800 and then get cut in half, or vice-versa. A continuous model would yield an estimate close to Stagflationary Mark's number.

Of course the whole prediction exercise is silly. There is a 90& chance that every single one of us will turn out to be nervous nellies, and the market will never come anywhere close to the 1000 and 2550 extremes next year. And that will feed into our rconfidence in the persistence of low-volatility regimes... Doh!

Biff,

If you are right to be 80% confident in everything you do, then you should be wrong 20% of the time.

If you make 5 predictions, on average, you should be wrong once.

That said, you could be 80% confident and still get all 5 predictions right. And what are the odds of that? You just did them. :)

You have a 33% chance of making 5 successful predictions if each one has an 80% chance. That's what your math is showing.

0.8^5 = 32.768%

Your odds of getting all 5 wrong uses similar math.

(1-0.8)^5 = 0.032%

Although it is still possible that you are right to be 80% confident, it would be horribly unlucky to get all 5 predictions wrong.

That would only happen about once out of 3,125 attempts.

Calculating the odds of getting anything other than all of them right or all of them wrong is more difficult. I haven't had to do these kinds of problems in many, many years and I'm "80% confident" that I'm too rusty to make the attempt here. I'd need to brush up on permutations and/or combinations first.

I could brute force the solution in excel fairly easily though. Maybe I will if I get properly motivated at some point.

Steve,

We can calculate a range from the options market; using January 2016 options yields a range of 1150-2450.Your are filling me with confidence! It's nice to have some evidence to back up our ballpark ranges! I think we're really zoning in on a good solution!

There is a 90& chance that every single one of us will turn out to be nervous nellies, and the market will never come anywhere close to the 1000 and 2550 extremes next year.And that will feed into our rconfidence in the persistence of low-volatility regimes... Doh!Indeed! Hahaha! :)

Thanks, Steve.

So my first guess was close to what the options market implies.

Nice! That suggests I'm well calibrated!

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