This dissertation consists of two essays. In the first essay I investigate the optimal consumption-portfolio choice of an agent who exerts effort to earn labor income and has the option to retire from work. The decision to retire is irreversible: the agent cannot join the labor force again, once the retirement option has been exercised. I show that the optimal time to retire is when the wealth level reaches a threshold. As the wealth level approaches the threshold, the investor decreases consumption and increases investment in the risky assets. The investment in the risky assets jumps down at retirement. The threshold level of wealth is higher when the agent can choose how much effort to exert than when a constant amount of effort has to be exerted.
The issue of using margin policies as a tool to control stock volatility is highly debated among academics and practitioners. In particular, the empirical literature is divided on the issues of the effects of margin requirements on asset prices and volatility. In the second essay I investigate the effects of portfolio constraints such as margin requirements on stock price, stock returns volatility and interest rate. I consider a pure exchange, continuous time economy with portfolio constraints and investors with heterogeneous risk aversion. The investor with portfolio constraints is assumed to have logarithmic utility with constant risk aversion while the unconstrained investor has time varying risk aversion. I show that in equilibrium, equity Sharpe ratio is higher, interest rate and stock returns volatility are lower in an economy with portfolio constraints as compared to an economy without constraints. I perform welfare analysis and show that unconstrained agent is better off while constrained agent is worse off when the constraint binds.