This paper performs specification analysis on the term structure of variance swap rates on the S&P 500 index and studies the optimal investment decision on the variance swaps and the stock index. The analysis identifies 2 stochastic variance risk factors, which govern the short and long end of the variance swap term structure variation, respectively. The highly negative estimate for the market price of variance risk makes it optimal for an investor to take short positions in a short-term variance swap contract, long positions in a long-term variance swap contract, and short positions in the stock index
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