Reversion to mean

[sdduuuude]

Reversion to the mean is typically used in retrospect to describe an event that has already happened. Using it for a forward-looking calculation is almost always destined for failure, especially in this case.

When data has a simple history of nice clean data around a fairly clear trend line (i.e. if the mean is the same no matter how far back in time you go), using reversion to the mean for a forward-looking estimate makes some sense.

However, if the mean of the last 5 years is different from the mean of the last 10 years is different from the mean of the last 50 years, the results of your reversion to the mean calculation are going to be basically random numbers.

Picking too short a timeframe means you don’t have a large enough number of samples. It also can ignore long term market effects.

Furthermore, the mean can revert to the data as well if your timeframe is too short. If I am looking at annual data and I choose a timeframe of 5 years, my next two datapoints are going to have a significant effect on the mean, even if the next two data points are the same as my 5th data point. If you wait long enough, eventually the mean will get very close to the data, even if the data does not change at all.

Picking too long a time frame ensures you have enough samples, but can underestimate the effect of any unusual short-term, current market conditions.

Secondly, picking the right variable is critical – is it prices? price growth? price growth relative to interest rates? prices relative to income? Interest rates themselves? Some combination of price, income and interest? Not all these variables can simultaneously revert to their means because they play off each other.

In the case of housing in the US, the tax anomaly in 1997 could have a drastic effect on the mean, so you have to be careful looking at data before then. But, that really isn’t enough time to get an understanding of what the mean is under these conditions. So, this is just an awful market in which to use this technique.

Finally, when data is random, we don’t know when the reversion will happen.

So, yes at some random time, something will revert to the mean of the last x years. Alot of good that does us.

Reversion to the mean is an analysis performed when they analyst doesn’t really know very many analytical techniques.

[4plexowner]

Excellent points, sdduuuude (did I get enough ‘u’s in there?).

How about if we just say, “The bubble has popped and it’s a long way to the bottom.”?

As an investor, all of this talk about reversion to the mean and what will the inflation-adjusted-mean-price be is just mental-masturbation.

When it makes sense to buy real estate in San Diego again I will be buying.

[powayseller]

Reversion to the mean is an accepted asset bubble principal, among those who understand bubbles. There are always those who say this time is different or we’ve reached a new permanently higher plateau. Every bubble in history has reverted to the mean. Anyone who has any doubts, like sduuude, ought to read up on the topic. There are excellent books on bubbles.

In my charts, I went to December 1999 to make my trendline, because I wanted to see the effect of the bubble, which started in 2000. So for 2 full years after the new tax laws were enacted, home prices did not change. But what had a big effect? Low interest rates, looser underwriting guidelines. But as soon as interest rates were lowered, poof, up went prices.

To me, the mean is the period from 1968 to Dec 1999. Over 3 decades of data, all in a straight line more or less.

[sdduuuude]

It may be an accepted principal when explaining the bubble that just burst, but not for estimating the bottom of the current one, except by those who understand bubbles but are clueless about statistics.

In your statement, you assume the bubble started in 2000, with no basis for the assumption, then go back 1 year, assuming that 1 year before your assumption is the right place to start. Then you come up with a number and it is close to your unsupported assumption, which makes you happy and leads you to believe your assumption is correct.

See, you have to wait for the bubble to stop bursting before you really know where it started. Then you say “it reverted to yada yada.” That’s reversion to the mean.

Your analysis so “freshman-in-college” I can’t believe it. Well, actually I can. I’ve come to expect it.

[powayseller]

sduuude, your post is seething with contempt. Why do you hate me so much? You will see if you subscribe to my service, that the mean is a straight line going back to the 1960s. So we start with 4 decades of data, ending in Jan 2000. If you have a different idea for what is a mean, by all means post it. I would love to read diverse opinions.

[Anonymous]

[img_assist|nid=1970|title=
Price and Rent Index, 1976=100|desc=|link=node|align=left|width=466|height=267]

[img_assist|nid=1971|title=
Price to Rent, 1976-2005|desc=|link=node|align=left|width=466|height=267]

Straight line through 1999? I found a range from 16 to 22, a span of ~40%.

OFHEO data only goes back to 1976. What data set on San Diego home prices goes back to 1968?

No wonder you libs/progressives are called ‘the elite.’ We right wingers just can’t do math like you do.

Hey, maybe this is that new math stuff that you guys like to use in your government schools!

[sdcellar]

powayseller, I seriously doubt the duuude hates you, but is likely just dishing it back based on your suggestion that he “read up”. Especially when he appears to be a fairly intelligent guy when it comes to statistics and the like AND he’s just shared his “diverse opinion” on bubbles and mean reversion.

[4plexowner]

And how many more times do we have to see powayseller pimp her new website?

For less than $10/mo we can read more of her opinionated ‘analysis’?

For less than $10/mo we can read her re-posting of articles that are available on other web sites for free?

Hahahaha!

[Anonymous]

Potential rejoinder: “But maybe it’s straight line relationship if we compare home price to income (instead of home price to rent)?”

Nah.

[img_assist|nid=1977|title=
Home Price and Income in San Diego, 1976-2004|desc=|link=node|align=left|width=466|height=267]

Pick one or the other — income or rent — to compare to home price, because the relationship to price appears nearly identical (i.e., the plots of price-to-income and price-to-rent are mighty similar).

[img_assist|nid=1978|title=
Price to Income and Price to Rent, 1974-2004|desc=|link=node|align=left|width=466|height=267]

But, hey, maybe I can’t tell the difference between the two, or don’t see a straight line, because I’m a simple-minded, right-wing, (ex) military Christian Neanderthal. I’m sure that there’s some ‘nuance’ that I’m missing here. You leftist/progressive/liberal elites, please enlighten me!

[unlawflcombatnt]

[img_assist|nid=1981|title=Price versus Income|desc=|link=node|align=left|width=100|height=57]

The above graph shows an increase in per capital income of about 20-25% from 2000 to 2004. It shows a home price increase of about 125%. I’d say home prices are completely out of line with per capita income. That looks completely unsustainable to me. Is that the point you were trying to make? That prices are way out of wack and are guaranteed to come down? If that’s your point, I completely agree.

Economic Populist Forum

[powayseller]

yes, unlawfulcombatant, that is what I meant. Specifically I had in my mind something like jg’s chart of the OFHEO index, which is an index that tracks the percent change in housing prices (resales and refinances of single family homes financed by Fannie Mae, so under the conforming loan limit, fixed rate mortgages). We can visualize pretty much a straight line for 3 decades, and then in 2000 we see a divergence. I’m not sure why some are arguing about this, as it is pretty clear that we have a trendline going back 30 years.

If someone would like to make a case for a permanently higher plateau, the burden of proof is on them. Why should the median be higher now; what fundamental factors support higher prices? In my opinion, the current housing prices are unsustainable, because people need artifically low teaser rates just to afford a home, and are spending up to 50% of income on housing. A true higher plateau would require wage increases or tax benefits, to allow people to afford the higher prices. The 1997 tax law change did not make any difference in 1997, 1998, or 1999. We also see a huge spike in 2003, when exotic loans became popular. So the rise in prices is linked to the 1% federal funds rate, not to a tax law enacted many years before. I am checking with my CPA about the impact of the tax law on the housing market. It is a very good point that was raised.

[sdrealtor]

Some rudimentary regression analysis here: I just put a ruler on the screen and extended the 3 decade long straight line to see where the mean should have been for 2007. It looks to be roughly 2003 prices. I have long maintained that is where we need to get back to in order for prices to make sense again. Prices intuitively made sense to me back then as people with good jobs could afford to buy nice homes in nice neighborhoods with top rated schools. The real estate world went bonkers near the end of 2003 and got downright insane in early 2004. I stand by my prediction that the market for good homes in good areas will return to the levels in early/mid 2003. Anything beyond that would be a bonus for buyers.

[powayseller]

Perhaps off topic, but fitting reply to the two posters above who tried to berate me.

Dr. Roubini defended me today on his blog. “Aviram,good you enjoy my blog; most appreciated. But no reason to make fun of names of commentators. Shahrzad is a thoughtful lady who is a frequent and lively and insightful commentator on this blog. … ”

I am posting this here only to balance the increasingly negative comments directed at me over the last few weeks.

[Anonymous]

“but fitting reply to the two posters above who tried to berate me”
powayseller, you need some serious therapy.
this post forced me to create a login ID. they posted with graphs using a RATIONAL methodology. i may not agree, but they did not appeal to my EMOTIONS and are not diverting each topic into an issue about THEMSELVES. you’ve been asking them to “read up” on bubbles and even calling others who disagree, liars and charlatans.
remember shorting wamu? buying foreign currency? investing entire retirement funds into rydex inverse ? predicting a september stock crash ? a run on the dollar this fall?

[powayseller]

sdrealtor, in jg’s first graph, OFHEO index, my simple ruler test puts the mean at the years 1976 – 2000. I align my ruler between the first data point and 2000, and only the data points of the bubble years are off the ruler line. I’m curious how you lined up your ruler. BTW, it’s nice to have you back.

mls, Please try a little civility in your future posts. My recession prediction for fall 2006 was early. Roubini and Merrill Lynch’s David Rosenberg are predicting a recession in Q1 or Q2 2007. It is like watching paint dry; the economy moves so slow. The dollar’s strength is questioned even by Greenspan and the IMF; a couple years ago, Warren Buffett and George Soros lost billions of dollars betting against the dollar. It is only a matter of when, not if, the dollar falls. I still believe WaMu stock will decline substantially, but we just don’t know when, so it’s hard to short it. Are you a realtor / homeowner? Do you predict a recession too, or a depression as some others on this forum, or continued growth?

[Author]

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