Second derivatives are mathematical values where, often, we come out looking like geniuses or numbskulls. Housing, where upfront investment in land, infrastructure, time, and talent amounts to very big bets with risky timelines, is where second derivatives often decide winners and losers.
Here is a Fannie Mae outlook about young adults and homeownership trends, that home builders and residential developers will find to be of material interest in their initiatives to access capital and put it into place, investing in new, for-sale, single-family homes in 2016. In it, Patrick Simmons, director of strategic planning for Fannie's Economic & Strategic Research Group, focuses on a single mathematical value, the rate of change in homeownership rates among adults aged 25- to 34-year-old.
By definition, the rate of change of a rate is a second derivative. When a rate of deterioration changes, slowing, and a pattern forms so that the deterioration gets less and less and less over time, one might project an inflection point. This would be the moment where the rate of deterioration, or decline (say, in homeownership rates among young adults), slows into a flat rate of zero change, and, perhaps, changes after that zero rate of change into a positive rate of change.
Fannie economist Simmons plays out such a scenario as he looks at the 25- to 34-year-old age group.
In the five-year, 2007 to 2012 span, homeowner-occupants, according to the Census American Community Survey, dead-weighted downward by an annual average of 300,000, and the homeownership rate for the age group fell by more than 10 percentage points from its peak in 2006.
Importantly, Simmons theorizes, the rate of decline has been slowing, a molasses-like drama unfolding as the absolute drop in homeownership rates, counter-balanced by the absolute growth in population for the age-group, has moderated.
The big question here forks into two scenarios. One outlook is for a continued, flat rate of change in homeownership rates for the age-group, neither improving much, nor getting worse. Here's what New Strategist Press editorial director Cheryl Russell calculates for that scenario:
If the homeownership rate has hit bottom and remains there, then the number of homeowners in the age group will rise by 74,000 a year. That's a big reversal from the average annual loss of 231,000 homeowners aged 25 to 34 since 2006.
That's a big swing, completely a function of demographics, as population growth in the age group swells, and an absolute number of homeowners in the 25 to 34 year-old group would grow if the homeownership rate is stable.
The other, very plausible scenario, is that a deteriorating rate of change flattens and eventually flips into an improving rate of change, perhaps thanks to jobs and income growth, better credit access, more affordable new home choices, a normalized resale market, etc. Here's Simmons' take on what that might look like mathematically:
If rates were to recover just slightly (Scenario 3), young homeowners would increase by approximately 111,000 per year, a pace of growth twice that observed during the boom.
Again, an annual loss of 231,000 homeowners aged 25 to 34, vs. an annual gain of 111,000 per year. That's a swing of 342,000 young adults.
As New Strategist's Russell suggests, that's a big if.
It all comes down to what happens with that second derivative. For home builders and residential developers, it also comes down to a question of whether you wager invested resources on one scenario or another, or whether your program is capable of winning, whichever of the three scenarios--1. further deterioration, 2. stabilization, 3. improvement--plays out.