**Basic math behind asset pricing (heavily summarised version)**Let’s use an example where half the cost of the property is the land cost, and the building needs upkeep equivalent to 3% of it’ structure cost, increasing each year at the rate of inflation. On the rental part of the equation, let’s allow for 5% vacancy rate and insurance (etc) costs equivalent to 15% of potential rental rate. In this our expected return would be:

**Cash Return (pre-tax)**= [(Weekly Rental * 52)*(1-(5%+15%)/(property price)] - [structure costs x 3%)]

And Nominal Return:

**Nominal Return**= (1+[Cash Return + (property price x CPI)]/property price) x (1+ Real Property Growth Expectation)

And adjusted for inflation:

**Real Return**= (1+Nominal Return)/(1+CPI)

In order to value the asset we need to extend our return expectations by the exponent of time, with cash flows adjusted to our discount rate. For the math to make sense the discount rate must be less than the return (otherwise the asset will be worth less than zero). While discount rates are, by their very design, subjective, we should all agree that it only makes sense for an investor to use leverage to buy an asset if the Nominal Return is higher than their cost of debt. Because interest rates are most often variable, and the variability is linked to monetary policy which is linked to inflation, it is sensible to think about the equation in Real (ie., inflation adjusted) terms. Therefore, we want to compare our Real Return over time against the Real interest rate on our debt. We can do this pretty easily by looking at the Bank Interest Margin. In Australian this has tended to float between 2% and 2.5%.

What this means, is that if the Real Return is equal to the bank interest margin then the asset exposes the investor to all the risk but an expected return of zero. If the return is less than the Bank Interest Margin it is a loss-making investment. If the return is greater than the Bank Interest Margin, this variance reflects the risk and variability premiums.

If we plug the numbers for Melbourne, we find that if the Real rate of return is between 1.92% and -0.16%. To achieve a margin at the lower bound of the Bank Interest Margin we would need to see house prices fall at least 29%. These calculations are based on 1/3 of home prices being attributable to the design and construction of the structure (on a replacement cost basis), meaning that what we actually mean by a 29%+ fall in house price is a 44% fall in the price of land (even then this wouldn’t make it a good investment; it just means that the expected return would be positive. For some comparison, under normal economic conditions we would expect Bank Bills to deliver a real return of about 0.4%, 4% for developed market equities and 5%-7% for emerging markets. Globally property risk premiums tend to be in the 3% to 5% range. For the Melbourne property market to achieve a 3% Real Risk premium prices would need to fall 37.5%, and 51% to reach a 4% Real Risk premium).