"Calculating" the hedge ratio...?

When I teach The Spaulding Group's prep courses for the CIPM exams, I always advise candidates to carefully consider the Learning Outcome Statements in each study session, as these statements describe the subject matter that candidates are required to master. In particular, I tell the candidates to focus on the verbs in each statement (e.g., compare, contrast, state, calculate, describe), as I see these as really the centerpiece of each statement.

At the Expert Level, there is a Learning Outcome Statement in Study Session II that reads:

Calculate the hedge ratio (delta) of an option and conclude whether the option is in-the-money, at-the-money or out-of-the money

The word "calculate" has a fairly specific meaning in my mind, but I decided to consult with Merriam Webster:

transitive verb

• 1a : to determine by mathematical processes <calculate the rate of acceleration>
• 1b : to reckon by exercise of practical judgment : estimate <calculate the likelihood of success>
• 1c : to solve or probe the meaning of : figure out calculate his expression — Hugh MacLennan>

• 2a: to design or adapt for a purpose calculated the timing of his arrival for maximum impact>

• 3a : to judge to be true or probable b : intend calculate to do it or perish in the attempt — Mark Twain>

intransitive verb

• 1a : to make a calculation
• 1b : to forecast consequences
• 2a : count, rely

In checking the list of formulae for the Expert Level, I don't see a specific formula for the hedge ratio, and I don't see one in the assigned readings. Thus, I don't think "calculate" is what is intended - at least not in the common, every day usage of the word.

Having said that, it is important to understand the characteristics of the hedge ratio (of a call option) in certain situations:

• Hedge ratio is a function of stock price, term of the option contract, the expected variance of the underlying stock's price, and the risk-free rate
  
  
• If the underlying stock's price is considerably below the option's strike price (i.e., the option is deeply "out-of-the-money"), the hedge ratio approaches zero and it is not desirable to exercise the option.
  
  
• If the underlying stock's price is "at-the-money" (i.e., the stock price and the strike price of the option are approximately equal), the hedge ratio is close to .5, as it makes little difference if the stock is acquired via market purchase or by exercising the call option
  
  
• If the option is deep "in-the-money", the hedge ratio approaches 1, and it is advantageous to acquire the underlying stock by exercising the option.

Note that all of this describes call options only (i.e., options where the holder has the right to purchase the underlying security). Put options are not currently covered in the CIPM curriculum.

Note: The graphic above illustrates Bloom's Taxonomy, upon which the Learning Outcome Statements of the CIPM curriculum are based.