The standard deviation of dr is directly proportional to the square root of the short rate. In the CIR model, the standard deviation of dr (i.e., the basis-point volatility) is proportional to the square root of the rate. This means that as the short rate increases, the standard deviation of dr also increases, and vice versa. This relationship is represented in the CIR model by the term $\sigma\sqrt{r}$, where $\sigma$ is the constant of proportionality. This feature of the CIR model allows it to capture the observed empirical fact that interest rate volatility tends to increase when interest rates are high. This is a key advantage of the CIR model over other models of short-term rates that assume the standard deviation of dr is independent of the interest rate level, making those models less relevant during periods of high inflation and high-interest rates.

Choice A is incorrect. The standard deviation of dr is not inversely proportional to the square root of the short rate. In fact, according to the CIR model, it’s directly proportional to the square root of the short rate.

Choice B is incorrect. The standard deviation of dr is not directly proportional to the square root of $dw$. Here, $dw$ represents a Wiener process or Brownian motion which introduces randomness into our model but does not have a direct proportionality relationship with standard deviation in this context.

Choice C is incorrect. The standard deviation of dr is not directly proportional to the square root of $dt$. In this equation, $dt$ represents a small change in time and does not have a direct proportionality relationship with standard deviation as per CIR model.