Sunday, April 14, 2013

Why US stock prices are thriving?

I have been trying to explain for a long time why stock prices in the US have been increasing regardless the troubling recovery of the economy. This morning, I was browsing the Bagliano & Bertola (2004) book (a rather comprehensive with a fascinating subject if you ask me) when I saw an equation regarding the capital gains the profits and the short term interest rate. Extending this equation can very well justify the blooming US stock exchange. Let me elaborate on that.

In equilibrium state the sum of operational-profits-to-assets and the capital gains equal the short term interest rate rate of government debt securities. It makes sense: if bond rate is higher demand for these securities increases, so does their price and subsequently interest rate falls; if the returns of the government debt is lower than the sum of profits-to assets and capital gains, demand decreases, price falls and subsequently interest rate increases. The following illustrates what happens when the short term interest rate of government debt is zero.


What does the last equations tells us? That the change in stock prices equals the negative profit. In the following mathematical operations I induce uncertainty in the form of conditional expectation:


What the algebra reveals is that under the zero rate scenario, stock prices increase when losses (negative profit) are expected to be recorded, otherwise stock prices decrease when profitability is expected!!! It may seem peculiar at first- as a matter of fact, it is- but keep in mind that interest rates are zero, a fact that is anyway out-of-the-ordinary. First of all, as long as interest rates decrease asset prices increase; a fundamental behaviour of assets. Intuitively, consider this: macro-scopicallyif short term rates are zero and expected profitability of business activity is negative funds can be placed in the stock exchange in order for a chance to make some "profit" to exist (here, "profit", in brackets, imply capital gains and not operational profit). Others participate in stock exchange with little, others with no and others with 100% hedging- it does not make any difference at all, but it is a fact.

Currently, stock exchange is flourishing because investment coordinators expect to record losses. If they were expecting positive operational profits, investment would be rising and unemployment would be declining as well.

Although it is a humble attempt of mine to explain the latest stock exchange developments despite the negative economic outlook, it is hard to doubt the math. And yet, my intuitive explanation remains weak.

[1]Bagliano, Fabio- Cesare; Bertola, Giuseppe (2004); “Models for Dynamic Macroeconomics”. Oxford University Press, New York.