Carol Vorderman’s troubles highlight two facts. One is that the housing market is unusually risky in an important sense. The other is that a highly abstract piece of economic theory actually works.

Carol’s problem is not merely that she’s lost money on her London flat. It’s that she’s suffered the loss at the same time as she’s had bad news about her labour income.

Her investment in housing has therefore been risky not just in the trivial sense that she’s lost money*, but in the sense that she‘s lost at a bad time.

This matters. To a large extent, the reason we want to have wealth - in the form of (excess) housing, cash, shares or whatever - is to tide us over in bad times, so we can maintain our spending.

Carol’s experience shows that housing is bad at doing this, as it lets us down in bad times - so much so that she can‘t even afford a complete dress.

And this in turn means that long-term returns on housing should be quite high, to compensate for the risk that house prices will fall just when our other assets are doing badly. As John Cochrane says in his book,

Carol’s problem is not merely that she’s lost money on her London flat. It’s that she’s suffered the loss at the same time as she’s had bad news about her labour income.

Her investment in housing has therefore been risky not just in the trivial sense that she’s lost money*, but in the sense that she‘s lost at a bad time.

This matters. To a large extent, the reason we want to have wealth - in the form of (excess) housing, cash, shares or whatever - is to tide us over in bad times, so we can maintain our spending.

Carol’s experience shows that housing is bad at doing this, as it lets us down in bad times - so much so that she can‘t even afford a complete dress.

And this in turn means that long-term returns on housing should be quite high, to compensate for the risk that house prices will fall just when our other assets are doing badly. As John Cochrane says in his book,

*Asset Pricing*(pdf):Other things equal, an asset that does badly in states of nature like a recession, in which the investor feels poor and is consuming little, is less desirable than an asset that does badly in states of nature like a boom in which the investor feels wealthy and is consuming a great deal...

Assets whose returns covary positively with consumption make consumption more volatile, and so must promise higher expected returns to induce investors to hold them.

Assets whose returns covary positively with consumption make consumption more volatile, and so must promise higher expected returns to induce investors to hold them.

We can quantify this. This thinking implies that the Sharpe ratio on an asset should be equal to:

- the standard deviation of consumption growth (how likely are bad times?), multiplied by:

- the correlation between consumption growth and the asset’s returns (how likely is the asset to do badly in bad times when our consumption falls?), multiplied by:

- a risk aversion coefficient (how much do we hate risk.

Now, since Q1 1955 the standard deviation of annual real consumption growth has been 2.3%, or 0.023. The correlation between this and annual real house price changes has been 0.66 - which is high, suggesting Carol's experience is not unusual. And a reasonable coefficient of risk aversion would be around 5.

Multiplying these gives us a predicted Sharpe ratio of 0.023 x 0.66 x 5 = 0.076.

What’s been the actual Sharpe ratio? House prices have risen a real 3.2% a year, whilst Treasury bills have returned a real 1.9%. So the excess return on housing has been 1.3 percentage points. The standard deviation of annual house price changes has been 8.9 percentage points.

Which gives a Sharpe ratio of 0.146.

It looks like theory under-predicts house price inflation by a factor of two. Which is pretty shabby.

Not so. For one thing, this is vastly better than theory does at explaining share prices . The equity premium puzzle, first identified by Ed Prescott and Rajnish Mehra (pdf), is at least five times greater than the housing premium puzzle.

And we can easily remove this puzzle. A risk aversion coefficient of 10 (goey but not absurd) would do the job).

A more plausible explanation, though, is that no-one owns housing in general. We own particular houses. And individual houses are of course riskier than the index. If we suppose they are twice as risky, then the Sharpe ratio halves, and theory is spot on.

- the standard deviation of consumption growth (how likely are bad times?), multiplied by:

- the correlation between consumption growth and the asset’s returns (how likely is the asset to do badly in bad times when our consumption falls?), multiplied by:

- a risk aversion coefficient (how much do we hate risk.

Now, since Q1 1955 the standard deviation of annual real consumption growth has been 2.3%, or 0.023. The correlation between this and annual real house price changes has been 0.66 - which is high, suggesting Carol's experience is not unusual. And a reasonable coefficient of risk aversion would be around 5.

Multiplying these gives us a predicted Sharpe ratio of 0.023 x 0.66 x 5 = 0.076.

What’s been the actual Sharpe ratio? House prices have risen a real 3.2% a year, whilst Treasury bills have returned a real 1.9%. So the excess return on housing has been 1.3 percentage points. The standard deviation of annual house price changes has been 8.9 percentage points.

Which gives a Sharpe ratio of 0.146.

It looks like theory under-predicts house price inflation by a factor of two. Which is pretty shabby.

Not so. For one thing, this is vastly better than theory does at explaining share prices . The equity premium puzzle, first identified by Ed Prescott and Rajnish Mehra (pdf), is at least five times greater than the housing premium puzzle.

And we can easily remove this puzzle. A risk aversion coefficient of 10 (goey but not absurd) would do the job).

A more plausible explanation, though, is that no-one owns housing in general. We own particular houses. And individual houses are of course riskier than the index. If we suppose they are twice as risky, then the Sharpe ratio halves, and theory is spot on.

** Relative to a few months ago, not relative to when she bought - a fact that doesn‘t change my story.**** Picture comes from Curly, a great public benefactor, which shows that not all Carol‘s assets are in bad shape.*
Excellent piece. I know see why twice gilts has seemed a reasonable return on my property investments (in good times).

I already knew how I suffer right now.

Posted by: David Heigham | October 27, 2008 at 01:39 PM

It is interesting that the housing market gets so much closer to the theoretical level than the equity market. the Equity market will probably be larger in terms of numbers of trades per day and the volume of assets traded, but perhaps this could be because the number of individuals in the housing market is greater so in aggregate you are getting more wisdom from a bigger crowd.

Posted by: chris strange | October 27, 2008 at 07:11 PM

Hi!

Good tips you gave there!

I love the math part!

Posted by: Johnny Coates | October 28, 2008 at 02:43 AM

Di-doo, di-doo, di-doo-di-doo.

Posted by: ejh | October 29, 2008 at 02:43 PM