Three Essays on Portfolio Optimization with Market Frictions

Abstract

In this thesis, I investigate the effect of market frictions towards the optimal policy of three different investors. The first chapter is devoted to the investor who gains a utility from the stream of consumption. The investor can participate in the bond and stock market and optimize the investment policy to maximize the utility from her consumption stream. However, albeit the stock pays the cash dividend, it is not perfectly liquid. That is, whenever the investor trades, the rebalancing process entails a proportional transaction costs. Not only the illiquidity, but the investor also considers the sudden shift in the investment opportunity, namely, the regime switching. I find that the regime switching transaction costs and dividend could strengthen the argument of \cite{jang2007liquidity}, in particular, under reasonably calibrated parameters, the counter-cyclical transaction costs could raise the liquidity premium whereas the counter-cyclical dividend provides liquidity. For a further analysis, I calculate the expected transaction costs and the expected holding time. The numerical analysis implies counter-cyclical illiquidity could raise the expected transaction costs but lowers the expected holding time.

The second chapter is devoted to another form of the market friction: the leverage constraint. This setting is very similar to the previous chapter because this model also has the regime switching and the transaction cost. However, the investor maximizes the terminal wealth, and there is no cash dividend. The leverage constraint also takes a place so that the investor has a limited ability to borrow in a purpose of investing in a risky asset. Similar to the previous chapter, I calculate the liquidity premium. However, unlike most of conventional transaction costs models, the liquidity premium shows a heterogeneity in different wealth groups. The rich investor requires more liquidity premium whereas the poor investor needs a small compensation. I also calculate the cost of mismanagement in its simplest form. That would be the binding solution, or the myopic solution. By calculating the cost of myopia, I find that the poor investor suffers from mismanagement. Also, the myopic investor with the small level of wealth tends to invest less in the risky asset.

The final chapter tries to ask a question that ``does market friction important for the different type of the investor, particularly the household?". I incorporates first two chapters in more realistic settings of the household finance. First, the investor can allocate her wealth to bond and the mortgage. The mortgage market suffers from the transaction costs whereas the bond market is perfectly liquid. The investor receives labor income in form of a cash. When the investor decides to buy a house, she faces a realistic constraint: LTI, LTV, and a novel DSR (Debt Service Ratio). Atop of LTI and LTV, I observe how a simplified version of DSR can change the investor's policy, value, and the default probability.