Hedge fund industry has grown to be a key player in the financial markets. Just as large investment banks, the failure of this industry will greatly destroy the liquidity and stability of the whole system. However, contrast to regulated mutual funds, hedge funds are private and lightly regulated entities who are not obliged to disclose their activities to the general public. Hedge funds risk taking activity using ways such as short selling and excessive leverage and their increasingly correlated strategies pose substantial threats to the financial stability of the great economy.

In the First Chapter, we propose a simple framework which adopts the theory of acceptable risks and calculate capital requirements using the limited available data on hedge funds. We model the risky cash flow asset less liability (or Net Asset Value) directly using either a Gaussian process or a Variance Gamma process and apply the method to demeaned NAV data on $3622$ hedge funds from January 2005 to April 2009. Funds are analyzed for their required capital and the value of the option to put losses back to the taxpayers.

The previous study has considered funds individually with no correlation between them. Focusing only on individual funds ignores the critical interactions between them and can cause the regulators to overlook important changes in the overall system. Because many hedge funds employ similar investment strategies they produce correlated returns. The failure of these correlated large funds will greatly affect the markets systematically either in a direct or an indirect way. In the Second Chapter, we propose a systemic approach with correlated largest market participants and we study the $30$ largest funds as of April 2009 with total Asset Under Management over $$620$ Bn. We demonstrate the systemic capital charges to be held by the broad economy, as well as the capital charges at the fund level accounting for the residual idiosyncratic risk component.

Hedge fund investment strategies often include the use of leverage in order for them to build up large positions. Extensive use of leverage has increased funds liabilities especially during market downturns and has posted a great systemic risk to the economy in large. In the Third Chapter, we recognize that with limited and incomplete information on hedge funds balance sheet positions, the public usually does not know how much leverage there is in a particular fund or how to distinguish its assets and liabilities from the observed returns. We estimate hedge fund leverage using a regression-based exercise on the individual fund level. The estimated leverage information is then combined with publicly known return and other fund information to separate from fund cash flows its asset side and liability side. The two sides of the cash flows are then modeled as exponentials of two correlated L'evy processes following \cite{EberleinMadan:2010}. Capital implications are then derived from the above setup.