# Real Estate Mathematics

## Relation between Price Changes and Inventory Changes

At an intellectual level when inventory increases, price is expected to decrease and if inventory decreases, price is expected to increase. There are exceptions of course, for example if there is large scale immigration or emmigration, or changes in interest rates.

There is also seasonality involved in prices, so using the classic trick to reduce seasonality, we divide the current price by the price a year ago (same with inventory levels). This means that "1" becomes significant --- it's where there is no (or little) change and you would expect both price and inventory to become static/stable.

We will use King County (Seattle) to illustrate this.

As you see, we have the line being pretty stable, and following the expected pattern:

• If Inventory is below 1, price is above 1
• If Inventory is above 1, price is below 1

What I want to look next is the lag factor between the two.
Looking at the bottom red circle, we see that inventory started to fall in month 27 and price started to climb in month 31 -- approximately a 4 month lag. At month 47, there was a drop in inventory and in month 50 we see a major jump in price, a 3 month lag. At month 51 there was a jump in inventory (or at least a reporting of such) and in month 57 there was a major drop in price (a 5 month lag). In that same month, there was the start of a run up in inventory rate of change and in month 60, the drop in price rate started to decrease..

In short, rate of price change is lagging inventory by about four months. So what does that say about the next four months of prices in Seattle? They should be pretty flat (that is the same prices as seen a year ago) and may actually start to decline.