RBP Probability is the implied probability of sustaining performance. In his 2008 white paper, Professor Bjorn Jorgenson of Columbia Business School tested the sensitivity of RBP Probability to some important variables. First, he confirmed the intuition: RBP Probability declines as a) stock prices rise, b) risk (as proxied by the discount rate) increases and c) operating margin declines.

These is what we'd expect, but the magnitude is not straightforward. By performing experiments in which only one variable was changed at a time, he found that the relationship between the size of the stock price change and change in RBP Probability was generally S-shaped. This implies that changes in RBP Probability are lower for a given change in stock price when RBP Probabilities are either very high or very low.

Below is Figure 1 from the white paper. In it, two curves are shown that plot the relationship between price and RBP Probability of Office Depot (NYSE:ODP). The blue curve represents the relationship between price and RBP Probability where the only variable to change is stock price. Point B on this curve represents the price and RBP Probability of Office Depot on 11/19/2007, which were $18.80 and 92.3% respectively. All other points on the blue line represent the RBP Probabilities associated with hypothetical changes in stock price.

As you can see, it is very flat at low stock prices and slopes downward rapidly as stock price increases. Further, a 1% increase in stock price results in a 2% decline in RBP Probability. Thus, the sensitivity of RBP Probability to stock price at this level is 2:1.

The red curve depicts the same relationship one year earlier, on 11/20/2006, when the company’s stock price was $41.44 and RBP Probability was 38.0%. The curve is not as steep as it was when the stock price was much lower. In fact, at this level the sensitivity of RBP Probability to stock price is a perfect 1:1, meaning that a 1% increase in stock price will result in a 1% decrease in RBP Probability.

It is important to note that in this experiment only stock price changed. In reality, all the variables that determine RBP Probability change and thus we must examine the sensitivity of RBP Probability to those variables as well. But by isolating the effect of stock price by holding all else equal we are better able to understand the general nature of this relationship.