Bubblizer, a Request for Comments

Current Version:  1.2.4 (2006.04.25).  Release notes.
Download this version to be sure you have no errors.
Next Version Expected:  *none planned*
Password to unlock the spreadsheet:  cap20

9/25/2007: A number of folks have written to inform me that the spreadsheet does not operate properly in newer versions of Excel.  Rather than update the model right now I'm just making the password available to everyone (above).  I may get around to refactoring the model to operate properly sometime, but probably not very soon.

I offer the Bubblizer, an Excel spreadsheet model intended to help everyday folks rationally approach a home buying decision in today's uncertain bubble environment.  I am requesting comments, criticisms and improvements for this model.  Once this spreadsheet version of the Bubblizer is stable, I intend to create a web version (which does not require Excel, but is based upon the same model).

Please share the link to this article with your more financially and quantitatively minded colleagues and friends.

The Basis for this Model:

This model was inspired by the approach taken in the HSBC publication, A Froth-Finding Mission, Detecting US Housing Bubbles, and accompanying spreadsheet model.  HSBC forwarded a reasonable, consistent macroeconomic model for determining the existence and degree of US housing bubbles.  What I have done is distill their approach to analyze a specific, individual home buying decision.

This model attempts to take into account all relevant opportunity costs as well as expected inflation.  It then computes the price at which the home buyer would need to sell her home after her expected holding period (how long she'll live there) in order to break even in real terms.  The implied nominal return based on price appreciation and the implied annual return based upon the IRR are also computed.  Finally, some extra information is provided in order to help the concerned potential buyer figure out if she can afford the prospective home.

The Need for this Model:

This model is needed as a counterweight to the increasingly aggressive and often desperate advertising and advice being given to everyday home buyers by real-estate agents, mortgage brokers and various real-estate industry groups.  Worse, the popular media has failed to provide any critical analysis of the real costs faced by current potential home buyers in high-priced bubble markets.

This model attempts to take some basic inputs and give prospective home buyers a few simple numbers as outputs.  The home buyer should be able to look at these numbers and quickly be able to determine if she believes them reasonable.  This model makes no explicit value judgments.  Rather, it simply shows the user what price she will have to sell her home for in the future to justify the purchase on strictly financial terms.

The model also provides a number of optional inputs, allowing more sophisticated or exceptional users to express specific beliefs about the future (for example, future inflation) which differ from the HSBC findings.  Further, the user can capture the value of "intangibles" as a premium she would be willing to pay in excess of the strictly financial solution.  She can also plan for real appreciation (in excess of real break even), perhaps to plan for a home equity withdrawal or post-occupancy use of equity profits for consumption purposes (for example, college tuition for a child, retirement, etc.).

The inputs in the spreadsheet are fully annotated, and are intended to provide a clear explanation to the home buyer about how they work in the model.

The Current Limitations of this Model:

• Only fixed-rate, standard, US-style, mortgages are handled.
• The mortgage period must be between 10 and 30 years, inclusively.
• Holding periods beyond 30 years are not handled (because at this point the home would be fully owned, and this would require a two-step model).
• The buyer's income is assumed to increase at the inflation rate.  The model does not directly accommodate expected future income growth in excess of inflation.
• Rent is assumed to increase at the inflation rate.  Micro economic rent factors are not captured.

The Next Phase:

After this spreadsheet version of this model has stabilized and all acceptable comments incorporated, the next step will be to implement it as a web application.  The purpose of this will be to reach a wide audience with what should be a very useful tool.  Prospective home buyers can use this tool to educate themselves.  It should provide them some defense against falling prey to hyper-aggressive sales tactics being deployed against them in this uncertain, "frothy" housing market.

Contributions By:

Paul Ashby ([email protected])

Comments

[randolfe]

The spreadsheet requires a couple of XLA (Excel add-ins) to run, which should be installed in your version of Excel by default. One is to allow VBA to call Solver functions programmatically (Solver.XLA), and the other is the basic VBA add-in.

If you have any other problems opening the sheet post them here or email me (email on the right side bar under "Online Status").

The file has been virus checked with Norton 2005.

[randolfe]

If you wish to directly link to the Excel file use the URL:

http://randolfe.typepad.com/Resources/Bubblizer.xls

I ask that you not copy it to your site until it is stable, so that you can be sure you always are linking to the most recent version.

If you wish to trackback to this article, use the trackback URL as listed above.

[randolfe]

Also, if you want the password to unprotect the sheets, email me so I know who you are (and so I can reasonably expect to get an email back with your error fixes, additions and such included).

I would be especially grateful for interface design tips. I am not an interface designer, as is easily seen by my color choices.

[tjrsfca]

Randolfe,

This is a thoughtful model! You take into account alternate uses of funds as well as other variables not usually mentioned in the sales-speak of mortgages and the like.

As someone who currently owns a home, I was able to figure out how to jive the inputs with my existing bank note and after I pressed the button I found out how much the house would have to sell for in order for me to make a certain profit.

This is helpful stuff, but to my rather simple mind this does not help me understand my investment and real estate bublles. I am downloading the HSBC paper, but for time-crunched people I wonder if there is an easier way to be able to see how unrealistic or realistic a future scenario is compared with historical trends.

I will allow that I might have completely missed something. What say you?

[HARM]

Bravo, Randy.

Quite a nice little tool --and the default AGI & down payment are exactly one HaHa! Sweeet!

[randolfe]

Definition: The "HaHa" unit metric

This nomenclature comes from the Patrick.net blog, where a regular poster's handle is "HaHa", and he continually reminds us that $150K per year is a regular salary in the Bay Area (which is probably not true, but we still chose this amount as a base unit of measure for discussing the housing bubble).

Here is the precise definition:

For current purposes, 1HaHa = USD 150,000.

The precise definition of 1HaHa is 3x National median family income*, for which HaHa (after which the unit of measure is named) stands as a reasonable substitute. Therefore, we may peg the unit of 1HaHa to HaHa himself so long as:

1) HaHa remains in the state of California; preferably in the San Francisco Bay Area;
2) HaHa’s family median income remains within alpha=.05 of the predicted Bay Area median income level;
3) HaHa is still living.

At such time as HaHa becomes disqualified, the base formula may be still used to determine the HaHa unit of measure or a more suitable peg may be established which captures the spirit and intent of the measure.**

*Note that 1HaHa is a relative measure vis-a-vis National median family income compared to SFBA median family income. Therefore, the 3x multiplier will also be a dynamic variable in this system of measure.

**It is for the reasons of this inherit complexity that we prefer to us the HaHa measure as shortcut nomenclature when discussing real-estate issues on this blog. It’s also funny. “

[HARM]

I played around with the Bubblizer a little, and noticed a couple of small bugs:

1. You can’t get an IAR figure if you hold property longer than 15 years (shows as “#DIV/0″)
2. The columns on the right don’t self adjust to show numbers greater than column width (shows “#######”)
3. It’s possible to enter a holding period longer than the mortgage itself (which produces a bunch of “#NUM!” errors).
4. The data on left only allows you to go up to year 30 (no 40 or 50-yr mortgages).

[randolfe]

Thanks HARM.

I intended to not allow mortgages longer than 30 years. They are just a bad idea, but it would be easy enough to expand to 50 years if people think that would be useful.

Holding period should never be longer than loan-term, because to do that I'd have to implement a two-phase model because the game changes after you own the home outright. (If anyone has any alternative suggestions which would handle this better, please chime in).

The IAR is actually a bit of a problem. I think I need to change it from an IRR calculation to a more explicit annual return computation, since IRR's can get goofy in situations like this model creates. I've seen some cases where IAR is higher than total return or negative even when total return is positive. Any suggestions welcomed (I'm hoping Fewlesh comes by and drops some nice linear optimization on us).

[randolfe]

tjrsfca brings up an interesting design challenge: "How do I know if the answer the model gives me is 'reasonable' or not?"

I am unable to think about this clearly because I've read the HSBC publication and stepped through their model in some depth. So, for me, I have all this ownership-to-rent, ex-post and ex-ante risk, rent-yield kind of stuff floating around in my head. But, for the average home buyer, how do they know if, say 100% appreciation in 5 years, is a "reasonable" expectation?

I'd like to discuss how to create a model which, while not giving the prospective home buyer a direct answer, really helps guide them into making the best decision. Perhaps we need some kind of a historical-trend kind of comparison.

I could see something like: you need 100% nominal appreciation to justify this purchase if you'll live there 5 years. For your area, prices have appreciated an average of 80% as a moving 5-year average, but only 20% over 5-years if you exclude the past X years (if you believe there is a bubble). Or maybe something like that.

But the problem is this: we cannot directly link to or use the HSBC model, legally. So doing this will be very prohibitive. I can envision taking a few of the worst bubble areas -- maybe 4 or 5 -- and replicating their work in aggregate for these, but not for an open-ended analysis.

[Girgl]

Randy,

fantastic model, and purty, too!

Re: "How do I know if the answer the model gives me is 'reasonable' or not?"

One potential solution is to show (alongside the dollar figure) what percentage of your income you had to spend on PITI if you bought the house, and what percentage of their income the prospective buyer has to spend to buy the house from you. The simplifying assumption is that the buyer has the same income (inflation-adjusted) as you have, which kinda makes sense - they'll be moving into the same neighborhood.

The unknown variable is what the interest rate is going to be at that time - maybe there could be three figures for three different interest rates:
- half of what you got
- the same you had
- twice yours.

If the resulting percentages are much higher than what you had to commit to even at half the interest rate, it follows that it may not work out that way.

[randolfe]

Girgl,

Thanks, that is a very good suggestion. Actually, I could assume that mortgage rates are based upon the CPI inflation assumptions in the year of expected sale + the mortgage rate "delta". I could compute this figure based upon whatever rate the user puts in, then let them change it if they want to.

Another approach would be to do a real monte carlo simulation, but in order for that to work one needs an add-in that isn't standard in Excel, so I didn't implement anything like that.

[randolfe]

Changes for 2006.04.12 (Version 1.1.3)

* The Alt Investment calculation has been changed to properly account for inflation. The effect is that alternative investment now produces less return, by the amount of nominal expected inflation.

* The worksheet (right side grid) now automatically resizes the columns after you press "Solve".

* An additional factor has been included: Bubble Correction Risk Premium. The user can set likelihoods for 5 scenarios, ranging from 'continued boom RE market' to 'hard-landing RE crash', along with the price changes (in percent) for each scenario. A risk premium is computed and added to the specific risk premium in the final NPV calculation.

* The user's average affordability is shown to them in a convenient format.

* A "Next Buyer" analysis has been added, showing what the person who will need to buy the user's home when they go to sell will face in terms of loan payments and affordability. This should help users to determine the big "is this reasonable" question.

[NapoV]

Randy,
Question on Column S (Nom Rent Cost) in the Model worksheet. Why do you add back tax deduction in that column? Isnt that double counting the benefit of tax deduction when you compare Rent to Own ratio ?

[randolfe]

NapoV,

Thanks for catching the tax-shield double count. I was so caught up in the binary decision (rent or own), that I failed to see I wasn't considering renting on its on basis. Funny, as this falls right into realtor(tm) selling tactics "if you rent you're losing the tax benefit". No, if you rent, you rent; if you own you get the tax benefit.

I'll have a new version soon. I'm also adding separate a scenario analyzer tab, which takes the five scenarios and shows how you'll come out under each circumstance.

[Girgl]

Randy,

great additions to the model!

Once you do the math, you can see clearly how insane it all is, even if you assume very favorable conditions. My "next buyer's PITI to income" ratio always comes in at >150% :-)

I was wondering about the calculation of the next buyer's interest rate. If I understand the formula correctly, you're inflating the current rate using the assumed CPI. Is that right?

[randolfe]

Girgl,

Yes, I'm inflating the user's selected mortgage rate at the CPI rate, which is a bit of a rough estimate, but probably conservative because of the way mortgage markets lag the yield curve.

[randolfe]

Changes for 2006.04.12 (Version 1.2.1)

* Fixed a problem in the rent calculations that was double-counting the value of the tax-shield for ownership. Rent costs and alternative investments cash flows are now calculate on their own basis. This results in an even wider gap, and thus even higher necessary appreciation to justify a high-priced home purchase (when rent is low).

* Added a new tab providing a scenario analysis. The goal here is to reflect back to the home buyer what they think about the future likelihood of boom-or-bust. I draw a kind of a rough distribution curve, then plot the various NPVs for them, so they can see the outcomes in each case.

The hope is that someone puts in all the inputs, hits "solve", then goes to the analysis and sees that maybe they really don't believe it's all that likely after all.

[Paul@oakland]

Randolfe,
I downloaded v1.2.1 In trying to figure out the different contingencies, I sent almost everything to zero: no inflation, no appreciation, no friction, no taxes, no interest, etc. In this scenario all house payment money goes back in your pcket when you sell so it as if rent is free so I also set rent to zero. Thus nominal alternative investment cash flow is the house payments. But in this ideal world money paid 15 years earlier is worth the same as at sale. However, the spreadsheet calculated the nominal alternative present value to values other than that year's cashflow. This does not make sense to me. Is it a mistake in the spreadsheet or am I missing something fundamental? If it is the later, could you either explain it or direct me to a place where I can learn about how to understand the mechanics of the calculation? Thank you.

[randolfe]

Paul,

I haven't tested the model under MM or boundary conditions. It is possible that there is an error, or that the model simply can't handle the boundary. I'll do some testing later today and try to get to the bottom of it.

Thanks for the testing. If you find an explicit error, please feel free to post it here or email it to me.

[randolfe]

Paul,

I figured out the problem: The model is a binary decision tree. You must either rent or own (no other options). If your rent is free, then you will always do better to rent (live for free), even if you set the discount rate to 0% and the mortgage rate to 0%. This makes sense, because in one case you are paying P, of PITI, when you could be investing it for free (rather saving it at 0% return, but in a 0% inflation environment).

So, if I can buy at price P, selling it for P in year n, but I could instead rent equivalent housing for R=0, then I'd have to sell for P'=P+(p*n) or I am worse off buying. (p*n) = the opportunity cost of your buying, because R=0.

Introduce taxes, and I'm better off buying due to tax shield. Start adding back in other realistic costs, and the linear system will optimize differently.

Perhaps what you meant to do was set R to exactly P, where you see that you need 0% appreciation to justify the purchase.

Please let me know if that helps or if I have mislabeled something that is causing confusion.

[randolfe]

Changes for 2006.04.14 (Version 1.2.2)

Thanks to Paul Ashby (mailto:[email protected]) for finding a critical error in the present-value of the alternative nominal investment calculation.

In previous versions, the alternative investment was compounding incorrectly, resulting in an overstatement of the present-value of value of renting. This brings down the implied home sale price and implied total and annual returns.

Although this gives more reasonable numbers, it still shows that house prices are higher than supportable on a purely financial basis. This is especially true when you look at the implication for the "next buyer". With Paul's fix, now the next buy just needs to be crazy, not criminally insane.

Please don't hesitate to email me or post here if you find any other errors of have any other comments on this model.

[randolfe]

I've created a link in the prominent upper-left nav area featuring "Models and Tools". In that area I've placed The Bubblizer, as well as an adaption by Paul Ashby and a scenario calculator (built from scratch) by Christian Kaiser.

Those links will always contain the most recent versions of those tools. We will continue to use this thread to post new info about any revisions to the models.

Thanks to everyone for the massive input and interest in these models. We've had thousands of downloads already, and we're still getting between 20-50 downloads per day.

[randolfe]

Changes for 2006.04.25 (Version 1.2.4)

* Added monthly affordability info to summary.
* Added an affordability tab with useful data and graphics.

[zeke]

I was fooling around with the bubbalizer. Shouldn't the "Implied Home Sale Price in Selling Year" be a formula? Mine is a constant "1351849.06575488" regardless of what I put in for purchase price or target net PV.

Disclaimer: I opened it with open office so maybe that is my problem.

[randolfe]

zeke,

C8 should be a reference to the named cell "selling_price", which is C53

C53 will appear to be a constant, the number you posted above is the "default".

This number is generated by a programmatic call to Solver, which solves for C7 (NPV) = C12 (target NPV) by changing C53.

You can set up an algebraic formula to skip the solver call easily enough. I used Solver so people could easily change their parameters or goals, or impose arbitrary constraints into the system.

[zeke]

Thanks Randy,

After a little RTFM of the Open Office docs, I see that it doesn't run MS macros. I'll fool around with it and maybe learn a little something in the process.

[Sidney]

If it is helpful, you can view the spreadsheet online (no Excel needed, always uses current version) using the link:

http://zohosheet.com/view.do?url=http://randolfe.typepad.com/Resources/Bubblizer.xls

[randolfe]

Sidney,

Thanks. Neither zohosheet nor iRows yet support all the formulae, VBA code or Solver functions to make the Bubblizer work correctly online. I am keeping an eye open, though.

I am still working on a standard web-based app to provide the Bubblizer's functionality accessible by standard browser.

[randolfe]

Comments from Travis, a reader who downloaded the model

One thing I just noticed with the model.

I'm not sure that it's correct to have the mortgage rate for the next buyer rise with inflation.

Assume that inflation is 3% and there is an expectation that it will remain at that rate. If a mortgage is currently going for 6%, then the lender has priced it such that they make money even with the 3% loss in purchacing power that they get each year from the future loan payments.

Five years from now if nothing changed (inflation, inflation
expectations, default risk,...) then mortgage rates should still be at 6%.

Changes in inflation or expectations of future inflation changes should change mortgage rates, but constant inflation should not.

Emperically also if mortgage rates did increase with inflation then they'd be at some astronomical level possibly over 100% after many years of even moderate inflation.

[randolfe]

More comments from Travis

Two more quick comments.

1) I don't see anywhere that the oppertunity cost of the down payment is factored in. The forgone income from investing the down payment at the expected reinvest return rate should be considered a cost of buying.

2) I really like the idea of showing the outcome for different bubble correction assumptions. Doing a bunch of "what-if's" and looking at the outcomes seems better then just picking one value out of a hat.

However, I'm not sure that using the weighted average of the price appreciation assumptions as a correction risk premium is correct.

Can't quite put my finger on it and I don't have a better way to do it, but it seems wrong the way it currently is.

For example, the S&P 500 has histroically returned ~10% so this would be a reasonable assumption for future appreciation. But using the method in the spreadsheet this would imply that there is a -10% risk premium to investing in the S&P 500 which doesn't seem to make sense.

Also, the varrious assumptions seem to be assumptions about future home price growth rates. In my mind having a +20% or -20% long term growth rate is extremely improbable. Running the spreadsheet with a 15-20 year holding period with these numbers leads to extremely high or low home values.

If we are in a bubble, it seems more usefull to model a range of one time (or over a period of a few years) corrections followed by a return to long term growth rate.

Essentially, if you are modeling scenarios then there should probably be a narrow range of long term growth rates but a wide range of short term correction possibilites.

Modeling this would be easier said then done though.

You've done a great job on the spreadsheet though and I don't mean to nit-pick. Just sending in a bit of feedback.

[randolfe]

@Travis,

Thanks for all the great feedback. I'm going to repost your comments on the blog for public consumption, if you agree.

A couple of responses:

> Scenario Analyses: I had started down the path you described but quickly found myself attempting to recreate crude versions of what already exists in statistical packages, like Crystal Ball for Excel. The real way to model the scenario is to determine reasonable distributions for probabalistic events and then run the outcomes. I actually did something similar when we sold our house back in '05 with CB and found that the outcome produces a very abnormal distribution with numerous discontinuities. This kind of makes sense because there are so many tipping points built into the assumptions in the form of feedback loops. But, since very few people have CB, I cannot really use that kind of approach for a general model.

> Inflation & Mortgage Rates: You are correct that there is a defnite bias towards unexpected future inflation, which I very much hacked as CPI. This limits the model's use to the average 7-10 year holding period, and it tends to distort the later years. It is a good suggestion to make that a seperate variable that people can choose to set between 0 and X average Mort rate increase per year. That would still be simple but help to dampen future rate growth.

I had the idea originally to actually try to compute a value for mort rate growth from current market data using Interest Rate Forwards, which I think are one of the more well correlated indicators since MBS use rate forwards as hedges.

> Oppr Cost of the downpayment. I did not factor this in. You are correct that for every year one defers a purchase they should be assumed to be earning at least the risk-free rate on their downpayment. The problem that kept me from including it in the model was that I wanted to avoid having to model "savings patterns". That is, if you include the growth of downpayment then this would reflect back into the affordability so a projection over X holding years that relies upon an alternative use of downpayment will iteratively affect the affordability if the idea is that downpayment saved now is for downpayment later.

[Glen]

Hi Randy,

I have enjoyed your commentary on Patrick's blog. I just stopped by and checked out your bubblizer. This is a very thorough and thought provoking tool. I did have one question, though--

One of the opportunity costs of purchasing a home is that you lose the standard deduction (currently around $10,000 for a married couple). Should this be netted out from the mortgage interest tax benefit? Seems to me that the first $200K or so of mortgage debt really doesn't yield much of a tax benefit because of the loss of the standard deduction.

It gets complicated, of course, because once you are itemizing deductions, you can also deduct state income tax, charitable deductions, etc... so it may very well be that the net tax benefit really is pretty close to the amount of mortgage interest paid x owner's marginal rate. So I'm not sure whether it makes sense to factor this in. But for buyers in low or no income tax states, who do not have other itemizable deductions, it could make a material difference.

(There is also the hidden risk that Congress could change the tax rules at some point over the next 30 years. There have already been proposals to get rid of the state income tax deduction and/or convert the mortgage interest deduction to a credit. Either of these changes would be devastating to taxpayers in CA and other high income tax states.)

[randolfe]

Glen,

Thanks for the comments. I did purposefully ignore the specific tax consequences vis-a-vis the standard deduction versus itemizing. The primary reason is as you stated, complexity. It would really be impossible to do without some broad assumptions or detailed tax tables, etc.

I also justify this a bit more generally. I assumed that most people who'd be looking at the model live in a region afflicted by massive real-estate price bubbles, yet have incomes at least within "range" of thinking about buy-vs-rent. For the San Francisco Bay Area this means a family income of $150K minimum. Many people with that income or higher are already taking itemized deductions (or they should be). Therefore, whether these folks rent or buy the status of the std deduction is irrelevant.

I would welcome someone with more knowledge about income taxation to help clarify whether this is reasonable or the model needs to be adjusted.

[Nick Radov]

Thanks for providing this spreadsheet. I would like to suggest one small improvement: add a cell for entering monthly home-owners' association fees. That would make it more useful for condos.

[randolfe_]

Nick,

Thanks for the suggestion. I haven't worked on the model for a while now, but I intend to release a revision fairly soon. Mainly user-interface stuff to make it a bit more accessible, but yours is a good suggestion and I'll consider adding that field.

Thanks.

[hayden]

Just wanted to say thanks. Even though I don't understand half the terms in your spreadsheet, I know they exist now and can start some research on my own. Great learning tool and thanks again.

[Daud]

I am trying to use your tool to help me decide if and when to start construction of my house which is in blueprint now (missed the +50% appreciation in Phoenix). However, I can, even now, get the finsihed home cheaper than is its resale value (which will be reflected in the loan to value ratio by the bank). How shall I input the numbers ? The resale/value price as "purchase" price and the equity as a fictional additional downpayment with my real one ?

[Doug]

Sorry to drege up an old thread, but I couldn't pass this one up. I did a similar rent-versus-by analysis program a while back and what I found was that it was almost impossible to make renting look attractive with any reasonable holding period, even making fairly pessimistic assumptions about housing.

A major problem for any model is how to account for the opportunity cost of investing the downpayment, as well as to account for returns on any net different between monthly rental versus ownership costs, because, and this is critical, the investments must be of equivalent risk for the comparison to be fair. I found that I had to use the risk-free rate for any investments, otherwise one might as easily say that someone who owned a home outright would be wise to mortgage their home to invest in the non-risk-free investment. While a mortgage may not be risk-free from the lender's standpoint, paying off principal on a mortgage is close to risk-free from the borrower's.

Using the risk-free rate as a basis for comparison, then even assuming the price of a house did nothing but track inflation over the holding period, I found rent to lose so long as the holding period was long enough. Even at bubble prices, renting seemed to lose after about 20 years. The source of this difference is federal and California tax policy, specifically:

1. The owner gets to deduct mortgage interest
2. The saver must pay tax on interest earned
3. The owner gets tax-deferred compounding of his equity
4. The saver pays tax annually
5. The owner's property tax is fixed forever
6. The owner gets a one-time tax shield on the terminal value
7. The owner pays the lower capital gains tax rate on any further gains

Essentially, what happens is that the buyer is paying to freeze his/her housing costs forever, gets a tax break on interest payments, gets tax-deferred compounding on his/her investment, and gets a big tax break at the end. In contrast, the renter leaks money to taxes every year, and in fact is slowly losing purchasing power on his/her savings to inflation (net of taxes), while his/her housing cost is slowly rising. If you go out far enough, this inevitably succums to the owner's bias.

My conclusion is that some of the behaviour we have seen in house prices is similar in nature to the aggressive forward pricing of EPS growth during the tech stock bubble. A company with an above-average growth rate could be shown to justify almost any P/E ratio if you just ran the growth out far enough before you assumed the company became "mature" and reverted to the mean. You didn't even have to go out very far - 5 years of 20% growth could justify a very high P/E at the then-prevailing risk-free rate.

Cheers,

Doug

[randolfe_]

Doug

Those are all very good points. I'll do my best to respond with the reasoning in my model, and where I disagree with your conclusions.

* Firstly, keep in mind that my model attempts to take provide a quantitative core by which one can make qualitative decisions about buying or renting. As such, I make certain assumptions going in:

a) Your down payment must always be saved in a reasonably liquid, risk-free-equivalent vehicle. The reasoning is that you intend to buy a home and not be a permanent renter (if you wish to be a permanent renter then the entire model is comparing opportunity costs wrongly). Therefore your down payment is that, savings towards down payment. You can shield this from taxes to a degree in tax-exempt money funds, and that's not captured in the model (the model taxes your gains at marginal rate).

b) You will not stay in the home you buy forever. If you intend to pay down 100% equity then there is again a different set of opportunity cost assumptions.

So on to your points:

1. The benefit of the mortgage interest deduction is constraint-based, and is a threshold condition. It makes a big difference up until the point where the purchase price gets close to exceeding the allowable amount of qualifying mortgage interest deductions. Here in CA, as you know, often people borrow in excess of the $1.1mm deductible. Clearly there is no tax shield to the extra mortgage interest in that case. (There are also AMT scenarios I ignore in the model).

You must also offset mortgage interest rate deductions against deferrable or exempt taxes from alternative investments, which offsets a good portion of the deduction for all but the higher-bracket earners. Therefore, if you are in a low 20s% tax bracket then the mortgage deduction doesn't really help tilt the decision to owning by much. If you're at the maximum marginal rate and peeking into AMT territory, then it helps much more.

2. Savers can exempt and defer a portion of earnings offsetting some income tax deductions. Tax exempt AAA munis are a simple example.

3. True, but compounding only at a long-term historical rate of inflation + 1% + some constant premium in coastal desirable areas. It's a whole other argument and analysis to try to rationalize returns in real estate assets versus money assets over the long term. At best you can only justify real estate (non income producing, residential, owner occupied) outperforms risk-free investments by a couple of percent per annum.

4&5. The owner pays taxes annually also. Not income or gains on their asset, but taxes for holding the asset. Those taxes rise every year, they are not fixed, even under Prop 13. They simply are subject to rise at a fixed rate. This is a common misperception about Prop 13.

Under Proposition 13, the annual real estate tax on a parcel of residential property is limited to 1% of its assessed value. This "assessed value," however, may only be increased by a maximum of 2% per year, until and unless the property is resold. At the time of sale, the assessment may increase by an arbitrary amount, but future assessments are likewise restricted to the 2% annual maximum increase. If the property's market value increases rapidly (values of many detached dwellings in California have appreciated at annual rates averaging more than 10% over the course of several years) or if inflation exceeds 2% (common), the differential between the owner's taxes and the taxes a new owner would have to pay can become quite large.

The property may be reassessed under certain conditions other than a sale, such as when additions or new construction occur. The assessed value is also subject to reduction if the value of the house declines, for example, during a real estate slump.

6. The tax exemption on the terminal value is a politically controlled condition which is true today but has changed quite a bit over the past 25 years. When I bought my first home, only persons over the age of 59 1/2 could exempt capital gains (if I recall it was $250K per person, $500K per couple), and even then it was a once-per-lifetime exemption. Only recently have the rules become so loose as to allow repeated $500K tax free gains every 2 years. You cannot count on that condition remaining in tact. It might. It might not. You will not be grandfathered in if the rules change during your holding period.

7. The owner may pay a lower capital gains rate on future gains. This is again for the same reasons as (6). I agree, however, that the higher bubble price you pay for a house, the lower your taxable capital gains would be in the future because you are starting from a higher basis.

--

My conclusion is that the bulk of your arguments are based on tax positioning. I will admit that for some people tax planning might yield your results. I would be skeptical, however, that purchasing at bubble prices still makes sense. This leads to my final qualitative aspect of my model:

The Next Buyer. You have to sell your home to someone. And you can project an affordability scenario upon them that is roughly equivalent to your scenario, inflation adjusted, from your purchase point. Assuming your neighborhood doesn't gentrify, and your city is equivalently desirable in the year of your sale, then your next buyer must pay an amount equal or greater your Present-Value break even.

From that we can project that buyer's required income, savings, and/or percentage of AGI PITI load. This is where your purchase price informs you about the future. You must ask yourself, honestly, "will there be anyone making $X who is willing to put Y% of their income into this house to justify buying it for $Z,000,000 around to buy my house some years out?"

It is this final point where I rest The Bubblizer as a useful model to calculate rent-v-buy. For my area homes need to come down by about 20% give or take for that final question to be at all tenable.

[Doug]

1. I am indeed referring to houses with mortgages below 1.1 million. That's most of the housing stock, even now. My analysis was actually little affected by the mortgage interest deduction, it was equally valid for all-cash purchase (most high-end homes are purchased with a lot of cash or all cash, precisely because of the IRS limit). BTW I neglected to mention the not-insignificant "option value" that the holder of a US fixed-rate mortgage enjoys - rates/inflation go up, you are locked in, rates/inflation go down, you refi.

2. Munis pay a much lower rate of return - lower than the risk-free rate used in the analysis. It nets out the same, more or less.

3. This is exactly my point - owner-occupied real estate outperforms risk-free investments over the long haul because of tax policy.

4 & 5. Yes sorry, and I did know that. It would have been more accurate to say that the property tax adjustments will lag inflation so that over time the cost is greatly reduced.

6 & 7. This is all true, however you can also completely avoid the tax by simply rolling over into a more expensive property and defer the tax forever. In fact, it is interesting to do this analysis for an investment property, the 1031 rules allow the owner to defer paying tax on the gains indefinitely, while extracting cash through the financing of the next purchase.

Re. your conclusion, we'll have to agree to disagree. My program assumed a steady-state system, in other words, at the terminal point, the new buyer is basically in the same relative position as the current owner with respect to the purchase. This is true because I assumed nothing more than rate-of-inflation appreciation, so in real dollar terms, the next buyer is in exactly the same position, relatively speaking.

Basically, what I found was that the deck is heavily stacked in favor of ownership thanks to tax policy. The potential future value is quite large. Every transaction represents a split of this value between the seller and the buyer. What has happened over the years is that this split has shifted heavily in favor of incumbent owners.

The forward pricing of growth stocks represented a similar phenomenon; an existing shareholder in a stock that has projected growth of, say, 30% per year for 5 years, is going to be reluctant to part with his stock at the market-average P/E of, say, 20, to get the market-average 8% growth. The market reached the point where owners of these stocks demanded prices that, assuming growth reverted to mean, would appreciate in share price at a rate no better than the market average in order to rebalance the P/E of the growth stock with the average. Indeed, some stocks were "priced to perfection" with 10 years or more of their high growth rates priced into their then-current share prices. That in fact was a big part of the problem - you could justify almost any P/E if the above-average growth were projected far enough into the future. The market had, in effect, completely priced out the risk that this might not come to pass. Sound familiar?

I feel that the same thing has happened to real estate. There is, after all, no other inflation-protected, tax-deferred, and (normally) low-risk investment available to the average person than owning his/her own home outright or with a fixed rate mortgage. Everyone knows this, and, with a huge pool of cash chasing too few truly good investment opportunities, the rest, as they say, is history.

[randolfe_]

Doug

I don't think we disagree all that much. The primary difference in our models is that you seem to be assuming that the buyer of your home in year N will be in the same relative position you are in year N. I find a flaw in that logic as it relates to relative income levels.

Take a starter home, for example. If a starter home in the Bay Area was going for $350K in 1995 (roughly when and what I paid), and that constituted about 28% of an average AGI for a dual income household, in an average neighborhood of mainly starter homes, and for average aged first-time buyers: Then in 2002, seven years later equating to the average holding period, that house should ostensibly sell for at least something in the range of affordability for a roughly similar buyer demographic (assuming no gentrification). Instead, what has happened is those houses have spiraled out of control, that same house now costing nearly $1.2mm, which easily surpasses 55% of a similar buying household's AGI, even given very generous inflation assumptions.

These houses simply cannot continue to price for any kind of future assumptions of perfection in tax benefit because they are constrained by the ability of appropriate buyer demographics to demand the housing stock. By removing faulty lending practices, the demand curve for first time homes dramatically shifts back forcing the price downward--probably quite dramatically--and thereby strands owner occupiers with a higher basis.

There is a real disposable income affect as well. If "the next buyer" actually buys for significantly less than I did, ceteris parabus, they effectively enjoy equal or higher realized standard of living from disposable income than do I having bought a few years earlier at a higher basis, even considering tax shields.

I would hope that you could see that in your model home prices break down at a point whereby the payback period becomes longer than one's lifetime, regardless of financing options and tax deductions. Sadly, entry condos and SFHs in this area that price for approaching $1.5mm and command upwards of 65% of the buyers' incomes fall into this category.

Surely the built in put (or call depending on your perspective) in a US mortgage is real. It is hard to value, but it does have value. In CA the real valuable option, however, is the "walk-away" put that this state affords to homeowners who end up upside down and can "mail in their keys". In this case, if I can manage credit scores, I'm better off buying at any price, then defaulting and rebuying after prices fall. This is a moral hazard and unethical, in addition to creating 7 years of bad credit (which is not hard to overcome with credit sharing).

You are missing an option, however. By *not* buying at a higher basis, if one holds the disposition that near term prices will fall more likely than they will rise _in nominal terms_, then waiting creates an option on the avoided property tax basis. Since tax basis under Prop 13 can never rise, but also tax rates never fall, this option is tremendously valuable over the holding period, the longer the more valuable, with only the volatility of prices driving the valuation inputs. A slight bias to the negative creates considerable value in avoided property taxes.

Applying this to homes over $1.1mm in likely necessary mortgage funding, or alternatively homes more than $2.0mm purchased with at least 50% cash, and the value of every 1% in nominal price correction yields over 0.5% in optionable value on tax basis.

And property taxes are not deductible on CA returns, and soon they will probably not be on Federal returns either (though I ignored this in my model for simplicity, but it further emboldens the value of not buying in a downward price biased environment).

I guess my conclusion is that, so long as prices are falling or even simply not rising, it is very likely worthwhile financially to wait. The built in option is that one can buy after any price reduction, not only after all price reductions. So the buyer can select own break even against qualitative factors, and enjoy numerous factors offsetting the lost value of tax deductions.

My final comment relates back to incomes. Nowhere have I seen an iota of evidence suggesting or supporting incomes rising at even a fraction of house prices. I doubt inflation will fuel incomes closing the gap, either. Therefore sustaining current price levels relies solely upon the continuation of loose credit and faulty loan practices, unless you are ready to suggest a fundamental shift in the pattern of ownership in the US. That is, you are effectively saying there will be no more non-legacy home buyers unless they are granted subsidies through government programs to buy. Given the numbers involved this means that every "landed gentry" will need to own some 10 or more income producing investment homes in order to find a new macro equilibrium. I suggest that, were that to happen, the electoral power would begin to shift away from homeowners (as it has in much of Europe), and many of the perks of ownership would over time become burdens of ownership, again, as in Europe.

[Doug]

I was unable to get Bubblizer.xls to load. I've sent you my model, a C program, which I'm not sure is any use to you but it's all I've got.

Your example of $350k -> $1.2m rings true, I've seen that right around where I live. Then again, the starting salary for an engineer with a master's degree has doubled in the 18 years I've lived here, and salaries for people higher up the food chain are up even more, especially if you count all the stock-option income available to fund purchases.

I personally know of many renters who have large amounts of potential cash to bring into a purchase, and who have considered buying (and still are). It's my belief that a sort of gentrification is in fact occuring (and is occuring outright in places like East Palo Alto). Higher-paid people are displacing lower-paid people, there are going to be less and less lower-income who can afford to live in the bay area, but the ones who are already here and bought years ago aren't going away immediately, so when I see people pounding the table for median home price / median income as a metric, my eye roll. Prices are going to be set at the margin by the relatively small number of properties that turn over, just as oil prices on every barrel are set by the price that the most needy buyer is willing to pay for the last barrel produced. I have so many examples from personal experience of people buying in places like Hillsborough, from a senior citizen moving out of the area. Incrementally, the effect on the median income is small, but the effect on the median home price is large.

A side-effect of this process is the echo bubbles in surrounding areas like Stockton, as people with lower incomes left the SF BA with jaded price sensitivities and bid up properties beyond anything the economy could support. Yet back here in the BA, well, you and I are still here, are we not? I'm not rushing for the exit, nor are you apparently, despite the fact that I could buy a palatial home back in my home state (Virginia) for less than my current modest home is valued at. Until technology advances to the point where telepresence cause folks like us to not need physical face time to support our incomes, we're limited by the fact that transportation speeds plateaued in the 1950s, population is ever rising (9 billion by 2050), and (dare I say it) land within reasonable travel distance of major metro centers is limited.

Returning to the model, I'll think about what you've said, but it's not clear how I'd amend my model. 350k -> 1.2m in 7 years is way more than the inflation rate. My model doesn't make that assumption vis-a-vis the next buyer, it assumes only the inflation rate, or, optionally, at most a small real appreciation reflecting real income growth. So, assuming that most of the push up to 1.2m was based on real buying power, I can't see how the % of population that is priced out affects the model. The bubble will pop to the extent that it was fueled by the false buying power of bad lending - I guess I don't have any way to know how much of our immediate area was supported by that. I can only tell you what I see around me on Property Shark, which is pretty conventional financing. I obviously can't look at every home in the BA one by one to see where the sinkholes are. It's just a hunch, but I'm betting the more desirable neighborhoods won't have many, and so folks hoping to buy into a crash will be disappointed whtn it turns out that the places that are crashing aren't the ones they want to buy.

[Doug]

Sorry, I forgot to respond to this. You wrote:

"You are missing an option, however. By *not* buying at a higher basis, if one holds the disposition that near term prices will fall more likely than they will rise _in nominal terms_, then waiting creates an option on the avoided property tax basis."

Here I completely agree with you. I've often used this argument when talking about making a stock purchase - the basis matters, and it matters a lot. If you buy a stock for 20% less than another person did, then even if the stock doubles, triples, or whatever, you will *always* be 20% ahead. Where I would quibble is that we are talking about market timing here, and historically, at least for stocks, a mountain of evidence suggests that it cannot be done reliably even by professionals. I certainly have no ability to time any kind of market, and the average Joe probably has less ability than I do. So what do you tell him? "Listen to me, I'm an expert?" He's hearing that 24x7 with opinions ranging from yours to Carleton Sheets'. In the case of stocks, what I actually do to mitigate my handicap is dollar-cost average. Unfortunately, buying a house is more of an "all-in" proposition.