Private Constant Returns and Public Shadow Prices

Private investment and public equity returns

Because of external financing costs, private business owners often need to self-finance new investment projects. These self-financing needs create an incentive for business owners to hold financial assets whose payoffs are positively correlated with self-financing needs. If this effect is aggregated, expected returns on financial assets should be negatively correlated with aggregate private inv...

Measuring private equity returns and benchmarking against public markets

Private equity is still a relatively young asset class, with some unique characteristics. One feature is the very irregular timing of cashflows, and a consequence of this is that private equity relies on measures of returns that are not standard in other asset classes. As such, new investors can be unclear or unaware of the differences between the common methods for measuring private equity per...

Planning, Prices and Increasing Returns

Shadow prices for continuous processes

In a financial market with a continuous price process and proportional transaction costs we investigate the problem of utility maximization of terminal wealth. We give sufficient conditions for the existence of a shadow price process, i.e. a least favorable frictionless market leading to the same optimal strategy and utility as in the original market under transaction costs. The crucial ingredi...

Shadow prices in territory division

We consider a geographic optimization problem in which we are given a region R, a probability density function f(·) defined on R, and a collection of n utility density functions ui(·) defined on R. Our objective is to divide R into n sub-regions Ri so as to “balance” the overall utilities on the regions, which are given by the integrals ̃ Ri f(x)ui(x) dA. Using a simple complementary slackness a...