Recently, Scott Sumner and Arnold Kling blogged about asset bubbles. Scott Sumner post is about bubble deniers and how cognitive bias affects our assessment of about predicting bubbles. Arnold Kling takes one central point out of the Sumner argument - how to define a bubble. I think he views Prof. Sumner's post narrowly but his own definition is fabulous. That got me thinking about predicting asset bubbles. Let me explain it. The underlying principle Mr. Kling uses is this:

Asset profitability = rental rate + appreciation - interest cost

The logic is, so long as the asset profitability is positive at given price, the price is justified and hence not in a bubble territory. Let me distill the equation a bit more. I am simplifying here but, rental rate represents income from asset, appreciation represents rate of price appreciation and interest cost represents cost of capital. We also need to remember that that the equation deal in expectations. So asset profitability is expected asset profitability, rental rate is expected rental rate and so on. Further, to be consistent with units, we have to use rates (first derivatives) everywhere. Thus we have,

Asset Profitability = rental rate + Rate of appreciation - weighted average cost of capital (or WACC)

Hence, the limiting condition for asset profitability is,

Rental rate + Rate of Appreciation > WACC

Mr. Kling suggests that prices are in bubble territory when

Rate of Appreciation > WACC (given Rental rate > = 0)

**Interpreting the asset bubble condition**

Please examine the equation for bubble condition. There is no variable called price. Is it a surprise that the equation, as distilled does not involve absolute prices or price income ratio or other related variable at all? Well the equation leads us to very important conclusions.

First, we understand the influence of interest rate on asset bubbles. We understand why raising interest rate pricks bubbles. It increases the RHS of the bubble condition. Now raising interest rate or cost of debt by 1% will increase cost of equity by more than 1%. Thus WACC will increase in relative proportion. We must note that WACC is very difficult to determine at a macro level - for the entire market. WACC also increases when risk perception of the environment increases thus popping bubbles. That may be the reason why extraneous events that affect the risk perception for capital pops bubbles and cools asset prices.

Second, asset prices move within a spectrum. Do note the way equation is derived. It shows us how asset price rise, initiated by fundamentals, moves into bubble territory. At one end of the spectrum are assets that depreciate - like machinery. The decision to buy them depends on how much rental rate (or income from that assets) exceeds the WACC. If the rental rate covers the depreciation(1) then assets become profitable. At the other end of the spectrum are assets where Rate of Appreciation is greater than WACC. I expect price of every asset moves within such a spectrum, from the rental rate covering for WACC and depreciation on lower side to the bubble zone where rate of appreciation exceeds WACC.

Third, asset bubbles can be identified by relative prices. The equation helps us understand if the prices we pay are bubble prices or genuine prices for our point of view. We cannot determine if the market as a whole is in a bubble territory or not. To know if markets as whole are in bubble we again go back to two principles. First is the notion that it is difficult for a market participant to estimate market WACC. Second represents the ability to stack assets in order of hierarchy based on rental rate. For any given WACC we can determine relative price hierarchy and thus estimate if rate of appreciation is higher than WACC.

**Note:**

(1) Here we must understand the difference between financial definition of depreciation and effective depreciation that includes maintenance and upkeep costs. Firms use factory maintenance programs to reduce the effective rate of depreciation.