Topics in Quantitative Finance and Actuarial Science

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This proposal continues the main themes of my previous research. It explore issues in risk sharing and investment finance. I now three specific topics that I have identified. The first is an investment topic that relates to the financial crisis. The second is mortgage default insurance. Despite its growing importance there is little academic research on this topic. The third is optimal portfolio selection which is one of the most basic problems in finance. The first topic concerns closed end funds. A closed end bond fund consist of a portfolio of bonds of other firms. The owner of these bonds sells common shares in the market. The performance of the shares of the closed end bond fund depends on the returns of the bond portfolio. The returns on closed end bond funds are typically higher than those of comparable open ended bond funds and this result is explained by the fact that closed end bond funds typically borrow money as well. When an institution borrows money it increases its leverage. This research will model the impact of leverage on the expected return and risk of the closed end bond fund's shares. Initially the model will only deal with solvency issues. These funds underwent significant changes during the financial crisis and their short term borrowing capacity dried up. This effect will be modelled by including liquidity risk as well as insolvency risk. Mortgage default insurance is paid for by the borrower and the lender receives the benefits if the borrower defaults. The claim amount is equal to the difference between the outstanding principal and the then value of the property. Mortgage insurance is an important feature of housing finance and its importance was highlighted during the sub prime crisis in the United States. Mortgage insurance is also important in Canada where 70% of the business is conducted by Canada Mortgage and Housing Corporation and the remainder by the private sector. Mortgage insurance has a very long and variable underwriting cycle where long periods of benign experience are followed by periods of extreme stress. One challenge is to manage the risk by building up an adequate capital cushion. This project will develop a model of the mortgage insurance risk. This risk depends on borrower attributes, loan characteristics, the underlying collateral as well as macroeconomic variables such as house prices, interest rates and unemployment rates. We will also explore the robustness of the model to extreme circumstances and construct scientific stress tests that will be useful to regulators. Picking an optimal portfolio is one of the most basic problems in investment. Recently I have shown that the principal eigenvector of the correlation matrix of security returns can be used to construct an efficient portfolio with positive weights . This method also provides a natural way to select an expected return vector. We plan to explore the empirical performance of this approach using real data. Graduate students will be heavily involved in all aspects of this research. The results of this research have the potential to improve practice and lead to more informed policy and more enlightened regulation.