This dissertation consists of three essays on investments. The first essay examines the incidence, determinants, and consequences of hedge fund share restriction changes. This paper finds that nearly one in five hedge funds change their share restrictions (e.g., lockup) over the period of 2007-2012. Share restriction changes are not random. Fund’s asset illiquidity, liquidity risk, and performance are related to share restriction changes. A hazard model indicates that funds who actively manage liquidity concerns live longer by adjusting share restrictions. The paper examines whether changes in share restrictions create an endogeneity bias in the share illiquidity premium (Aragon, 2007) and find that 18% of the premium can be explained by the dynamic nature of contract changes. The second essay examines why mutual funds appear to underperform hedge funds. Utilizing a unique panel of mutual fund contracts changes, this paper explores several possible channels, including: alternative investment practices (e.g., short sales and leverage), performance-based compensation, and the ability to restrict the funding risk of fund flows. This paper documents that over our sample period, mutual funds were more likely to shift their contracting environment closer to that of hedge funds. However, this shift provided no benefit to mutual funds and the paper finds no causal link between these contract changes and improvements in performance. Rather, this paper casts doubt on the binding nature of investment restrictions in the mutual fund industry. The third essay examines whether the 52-week high effect (George and Hwang, 2004) can be explained by risk factors. The paper finds that it is more consistent with investor underreaction caused by anchoring bias: the presumably more sophisticated institutional investors suffer less from this bias and buy (sell) stocks close to (far from) their 52-week highs. Further, the effect is mainly driven by investor underreaction to industry instead of firm-specific information. The 52-week high strategy works best among stocks whose values are more affected by industry factors. The 52-week high strategy based on industry measurement is more profitable than the one based on idiosyncratic measurement.

The purpose of this thesis is to use the martingale approach to solve dynamic international portfolio problems. This thesis consists of three essays in dynamic international portfolio allocation. In demonstrating that foreign consumption plays an important role in international portfolio allocations, in Chapter 2, we present the first essay where we provide the optimal consumption plan and portfolio allocation for a representative investor with continuoustime and complete market assumptions in a simple two-country setting. Due to the demand for foreign consumption, the optimal portfolio allocation requires suitable foreign bonds to hedge against the changes in the foreign investment opportunity set and the exchange rate. The empirical results not only show that the optimal portfolio allocation with domestic and foreign consumption is different from that without consumption or with domestic consumption only, but also demonstrate the need for the foreign bonds to hedge against the change in the exchange rate risk. We present the second essay in which we extend the research of the investor's portfolio allocation problem into a continuous dynamical international market where the investment barrier of international portfolio exists. With deterministic market prices of risks, CRRA utility function and the existence of a simple investment barrier, the investor optimally hedges against the investment opportunity by allocating funds into three portfolios which are constructed by unconstrained bank accounts, equities and bonds. The first portfolio is the so called mean-variance portfolio, the second is the hedge portfolio, and the third is the synthetic portfolio which mimics the expected excess return of the constrained security in foreign country. This issue displays in Chapter 3. The third essay is presented in Chapter 4. Here we develop a continuous-time intertemporal portfolio allocation model in an international mildly segmented market. With deterministic market prices of risks and CRRA utility function, the domestic investor in the segmented market optimally hedges against the stochastic interest rates by allocating funds into two portfolios. The restricted mean-variance portfolio is derived from the traditional mean-variance portfolio without foreign constrained securities. The hedge portfolio is comprised of domestic bonds with a specific horizon for hedging against the change in the domestic interest rate. The numerical results indicate that when the volatility of the stochastic discount factor increases due to the less diversification caused by market segmentation, the less risk-averse investor benefits accordingly. Chapter 5 summarizes the main findings of the three studies and concludes the thesis by suggesting some future research venues related the current subject. / The purpose of this thesis is to use the martingale approach to solve dynamic international portfolio problems. This thesis consists of three essays in dynamic international portfolio allocation. In demonstrating that foreign consumption plays an important role in international portfolio allocations, in Chapter 2, we present the first essay where we provide the optimal consumption plan and portfolio allocation for a representative investor with continuoustime and complete market assumptions in a simple two-country setting. Due to the demand for foreign consumption, the optimal portfolio allocation requires suitable foreign bonds to hedge against the changes in the foreign investment opportunity set and the exchange rate. The empirical results not only show that the optimal portfolio allocation with domestic and foreign consumption is different from that without consumption or with domestic consumption only, but also demonstrate the need for the foreign bonds to hedge against the change in the exchange rate risk. We present the second essay in which we extend the research of the investor's portfolio allocation problem into a continuous dynamical international market where the investment barrier of international portfolio exists. With deterministic market prices of risks, CRRA utility function and the existence of a simple investment barrier, the investor optimally hedges against the investment opportunity by allocating funds into three portfolios which are constructed by unconstrained bank accounts, equities and bonds. The first portfolio is the so called mean-variance portfolio, the second is the hedge portfolio, and the third is the synthetic portfolio which mimics the expected excess return of the constrained security in foreign country. This issue displays in Chapter 3. The third essay is presented in Chapter 4. Here we develop a continuous-time intertemporal portfolio allocation model in an international mildly segmented market. With deterministic market prices of risks and CRRA utility function, the domestic investor in the segmented market optimally hedges against the stochastic interest rates by allocating funds into two portfolios. The restricted mean-variance portfolio is derived from the traditional mean-variance portfolio without foreign constrained securities. The hedge portfolio is comprised of domestic bonds with a specific horizon for hedging against the change in the domestic interest rate. The numerical results indicate that when the volatility of the stochastic discount factor increases due to the less diversification caused by market segmentation, the less risk-averse investor benefits accordingly. Chapter 5 summarizes the main findings of the three studies and concludes the thesis by suggesting some future research venues related the current subject.