Boundary Value Problems and Equity Valuation

One of my favorite classes in college was boundary value problems. It was essentially about solving differential equations under certain constraint. For example, if you stick one end of a steel rod into a giant bath of boiling water, the temperature of that end must adapt to equal the boiling point of water. That would be out fixed boundary. The heat from the water bath would gradually travel lengthwise to the rest of the rod and effect its temperature as well. Since the rest of the rod is exposed to the normal environment, an equilibrium is reached when the temperature is such that the heat supplied by the hot bath equals the heat dissipated to the normal environment.

As Dow has crossed its historical highs and S&P is nearing such a feat, there is a palpable nervousness among investors and pundits alike. Today, the entire financial market is immersed in the fixed boundary of zero interest rate. Slowly but surely, the asset value levitating effect is permeating to the rest of the investment world.

The business of private equity is essentially capital arbitrage. They take advantage of cost of capital differential between equities and bonds. When fixed financing is abundantly available at a cheap rate, private equity transactions will be most active. That equities, despite reaching new heights, are cheap compared to bonds is evident by the increasing PE activities. The large deals like Dell and Heinz of course catch most of the attention. But smaller deals is also happening. Today, teen retailer Hott Topic is being acquired by Sycamore Partners.

Normally, bond investors tend to be more conservative as bonds have limited upside and 100% downside, while stock investors are more sanguine as stocks have unlimited upside. Today, the opposite is true. Bond market is trading at the level it is at not because bond folks have lost their minds, it is because the boundary conditions imposed are so overwhelming. In mathematics, fixed boundary is assumed to lessen the complexity of the ensuing equation. In the real world, powerful forces tend to have powerful side effects. This is why equity investors are so nervous.