Investment Theory and Risk Management, + Website

Liability-Driven Investment

Let's switch gears a bit and think about hedging the risk of not being able to meet our liabilities. This risk arguably poses the greatest challenge to pension plans. In a recent paper, Robert Novy-Marx and Joshua Rauh (2010) estimate that liabilities exceed assets across the pension plans of the 50 states in the United States by approximately $1.27 trillion using Muni rate discounting and $3.26 trillion using Treasury discounting. Either way, there is a serious underfunding of these liabilities. Pension boards are grasping for investment strategies that hedge the risk of not meeting their liabilities, hence, the concept of liability-driven investment (LDI). As we shall see further on, LDI strategies change the objective function from one of solving for the mean variance efficient portfolio of assets to finding the mean variance efficient portfolio that maximizes the surplus return. The surplus return is the weighted return on assets over the growth rate of liabilities. Thus, the problem is set up with a slightly different optimization objective but is otherwise solved as before. Let's develop this problem in detail, solve it, and then examine the properties of the solution as a hedging strategy.

The mathematics of this particular problem can get complicated and I defer treatment of the problem to Michael Bazdarich's paper (2006). I present instead an applied version of the problem that we'll study as a spreadsheet exercise. But first, let's set the ...