| The goal of this study is to provide a quantitative framework for modeling illiquid investments in private markets and restricted funds. As such, we divide the study into two halves. First, we attempt to mimic private equity behavior by a quasi-replication strategy with a portfolio of publicly traded assets, as illustrated in an application to endowment investing. We also study its behavior and fair valuation by an earnings-based stochastic model (Chapter 1 and 2). Second, we build a stochastic model for portfolios with non-traded assets and deliver numerical results on optimal portfolio choice under lock-up type of illiquidity. We also examine the option value of various fund redemption restrictions via a binomial pricing model (Chapter 3 and 4).;We believe there is a relatively strong link between private and public markets and our study is among the first few studies to exploit this linkage to partially hedge or manage illiquid equity exposures and apply it to fund-of-funds investing. We are also able to formulate a portfolio optimization model for making optimal consumption and investment decisions while having locked-up capital. With a stochastic risk premia for both stock index and non-tradable asset in the portfolio, we show that illiquidity can be beneficial or detrimental depending on risk premium levels as well as the portion of illiquid wealth. In particular, an indifference pricing approach illustrates how much unrestricted wealth makes the certainty equivalent of a liquidity constrained portfolio. Finally, we are able to quantify the cost of redemption restrictions in fund investment after a detailed fund survival analysis. Expected fund returns and volatility, recovery rate in case of default and lockup periods are among parameters that drives changes in cost of illiquidity. |
