First random thought: a person who was very ignorant about future house prices would nevertheless be almost certain that real (inflation-adjusted) house prices will be lower than today at some time in the future.
If we want a null hypothesis about house prices, I think the best null hypothesis would be that the log of real house prices follows a martingale. That means they are equally likely to rise (say) 10% next year as they are to fall 10% next year. And equally likely to rise 20% next year as fall 20% next year. Etc. For any year, regardless of anything. I think that is what someone who admitted total ignorance would assume.