The backgrounds of the webpages are based on actual assignments, research and other thoughts. Read on if you want to know a little more. -- Andy

Home Page Background Formulae

I have described the formulae on the home page as the work I'm most proud of that nobody cares about. I was tasked with valuing share units that were based on relative total shareholder return (TSR).

Unlike most of the relative TSR awards, these were measured against an index, not a percentile ranking among a list of companies (e.g., peers or underlying company shares included in an index). For these units, performance was measured at the end of three years as a ratio of the company total shareholder return to the index return minus 1. The threshold payout was made if the result was -4%, target if the result was 0% (company return was equal to the index return), and maximum if the result was at least 8%.

Since performance was measured against only one time series, I thought that a closed form solution could be found rather than use the brute force of a Monte Carlo simulation. So, I used some fancy Black-Scholes math and solved for the closed form solution.

The model I developed runs the valuation three different ways to see if the same answer is obtained: (1) a Monte Carlo simulation, (2) and discrete lognormal distribution based on predefined z-scores and (3) the closed-form solution I solved for. All three matched providing me with confidence that the formulae are correct.