Investigating the Use of Volatility Derivatives to Hedge Portfolios
MSRI-UP 2011: Mathematical Finance June 21, 2011 - July 24, 2011
Location: MSRI: Baker Board Room
The trading of volatility derivatives was introduced less than two decades ago; it is a fairly new practice in the world of mathematical finance. When markets crash, stocks are often traded frantically, and volatility imminently increases. Hence, adding volatility derivatives to a portfolio should balance losses in the event of bearish market behavior. We quantify and minimize the risk of a portfolio using Markowitz’s optimization theory. One assumption of this model is that past performance of a portfolio is indicative of its future behavior. The goal of this theory is to minimize the portfolio’s risk given a fixed rate of expected return. We implement this method in MATLAB to plot the minimized portfolio risk versus portfolio returns, producing a curve known as the efficient frontier. We collect market data on stocks from various indices and sectors, as well as data on volatility derivatives. From this data, we construct portfolios with and without volatility derivatives. By comparing the efficient frontier generated by the portfolio with volatility derivatives against the efficient frontier generated without the derivatives, we can quantify the risk reduction induced. Preliminary results confirm our hypothesis, which suggests that volatility derivatives can serve as effective instruments of insurance in an investor’s portfolio.
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