The Risk and Risk-free Rate of T-bills

This study argues that a payment’s risk approaches zero as maturity approaches zero, and that the central bank’s short-term rate best captures the risk-free rate of various assets. Expecting that the T-bill risk largely reflects a country’s inflation risk or macrorisk, we measure the risk as a one-year payment’s risk to be comparable across assets. We argue that the risk-free rate reflects the expected inflation effect, that the inflation risk reflects the unexpected inflation effect or the opportunity cost of alternative nondepreciating investment, and that a GDP growth rate lower than the risk-free rate is actually negative. To simplify the formulas, we also examine if the two returns can be computed independently. We employ two factors to model the risk-free rate, which the market expects the current monetary policy to bring towards the neutral level over a certain period. The 4-factor models include a risk constant over maturity to capture the depreciation cost of inter-bank short-term lending. To solve the model factors, we use repeated trials to minimize the prediction errors. Our models thus split T-bill returns into the risk and the risk-free rate. The 4-factor independence model outperforms all the other models, on average explaining 99.3% of the US T-bill returns. The T-bill metrics is the gateway to the risks of various corporate assets. We have to develop the 4-factor independence model into software to analyze the noise of inflation risk that follows a blended normal distribution (Nie, 2023).