The Risk and Risk-free Rate of T-bills

We argue 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. We employ two factors to model the expected risk-free rate that the market expects the current monetary policy to move towards the neutral rate over a certain period. Expecting that the T-bill risk (i.e., the macrorisk) largely reflects a country’s inflation risk, we measure the risk as a 5-year payment’s risk to be comparable across assets. To solve the model factors, we use repeated trials to minimize the prediction errors. Our models thus split US and Canada T-bill yields into the risk and risk-free rate, on average explaining 98.7% of the returns. The models assuming independence of the two returns show similar power in predicting T-bill returns, which can significantly simplify the formulas. We also find that the inclusion of a risk constant over maturity, which has a small value of several basis points, significantly reduces the prediction errors. The risk and the risk-free rate is the gateway to corporate the risk of various assets in the country.