Mmmm, tasty tasty four dimensional graph

Apologies for the silence, I’ve been busy with moving and the fun that goes along with it. We used to be here, now we’re here. The old place was kinda dumpy facilities-wise, and we figured that with two incomes it was time to upgrade.

The new place stinks like smoke though, you wouldn’t believe the things we’ve done or had done to the place to try and get rid of the smell. There are few things I hate more than the smell of cigarette smoke, and the annoying thing is that there seem to be so many more smokers per capita in the K-W area than in Toronto. Stupid small town folk, if you’re bored you should be shagging, not smoking.

The dealing-with-other-people’s-messes thing is what I hate most about renting. So much so that I’ve started to seriously consider buying a house. Mind you, there’s a whole host of issues preventing something like that from happening anytime soon, but I’ve started to consider the logistics of such a purchase. Previously, I wrote about my habits when it comes to large purchases. I don’t like getting ripped off, and it’s doubly worse if the reason is because I didn’t do the requisite research beforehand. Yup, my impulse purchases are pretty much limited to the supermarket.

Housing has other factors that make it difficult to do research and make an informed purchase though.

  • Every unit is either unique, or from a limited run, so it’s hard to do direct comparisons.
  • House prices act like a thinly traded security – selling prices for similar units can have a high variance because there is so little supply. You don’t get the “law of large numbers” to smooth things out, so human factors dominate. i.e. In one case the sellers want out now so they’re willing to sell below fair value, in another case the buyers have their hearts set on the unit so they’ll pay above fair value.
  • Since the housing market is dominated by uninformed sellers and buyers, the laws of an efficient market do not apply. Specifically, before the central bank even announces interest rate changes, the expected change is built into stock prices. Not so with houses – information does not travel as fast or at all among the uninformed masses, so in theory there are more opportunities for arbitrage. Unfortunately, in practice it does not usually work like that, in fact the behaviour can even be opposite from what is rational.

For example, so far I’ve just been trying to answer one question: Is it better to buy when interest rates are low and houses are overvalued, or when interest rates are high and houses are undervalued? And the only answer is, “It depends.” It depends on how high/low the interest rates really are, and how high/low the house prices really are.

So it should be possible to graph interest rate, purchase price, and total cost in 3 dimensions. Then at any point in time when looking at housing, you can plug the current numbers in and see whether you’re at a maxima, minima, or somewhere inbetween.

Now that I think about it, there probably needs to be at least a fourth variable (time) in there as well. The longer you wait, the more you pay in rent, so the total cost goes up. Even for those people who don’t pay rent, you still need the fourth variable because yesterday’s “present value” is different from today’s present value. Meaning that because you delayed the purchase by a day, you earned interest on money in the bank, so the total cost goes down.

We were talking at work about how to represent graphs in higher dimensions without having to fix variables and graph the remaining ones in three dimensions. We came up with colour, taste, texture, sound, and smell as five more orthogonal bases. Imagine climbing into a chamber to “view” a graph – as you walk along the three dimensional portion, your other senses are stimulated. “It smells so good, but it tastes so bad! There’s something sharp jabbing at me, but this music is so soothing! … I think it’s time to buy the house.

That would rock, I’m gonna build an eight dimensional graphing machine.

One Comment

  1. Hubert says:

    It tastes like burning.