What Is the Risk-Free Rate? A Model and Empirical Tests in a Market with Frictions

I study the properties of implied interest rates from futures and put-call parity relations, and compare it to other market rates commonly used by academics and practitioners. I show that in a market with borrowing and short-selling costs, the price of futures and put-call parity relations is a¤ected by demand pressure. I apply the model to the futures market and obtain a closed-form solution for futures prices that is a function of the risk-free rate and a latent demand factor. My model-implied risk-free rate estimated using S&P 500 index futures compares favorably with other commonly used candidates. I also estimate the model-implied demand factor and verify that is related to observable proxies for demand pressure in the futures market. I also show empirically that relative mispricing is positive (negative) when buying (selling) pressure is high and is di¢ cult to borrow (short-sell the underlying). These results extend to futures and put-call parity relations in other indices as well. Job Market Candidate, Department of Finance, Stern School of Business, New York University, 44 W 4th St., New York, NY 10012, [email protected], www.stern.nyu.edu/~lnaranjo. I owe my gratitude to my advisor, Marti Subrahmanyam, for his invaluable guidance and unconditional support. I also would like to thank the other members of my committee –Menachem Brenner, Stephen Brown, Joel Hasbrouck and Stijn Van Nieuwerburgh–and Bryan Kelly, Farhang Farazmand, JongSub Lee, and Rik Sen for their feedback and encouragement. All errors are mine.