Level III | Essay #9 2012

The material on derivatives is worth between 5% and 15% of your overall score and last year (2012) was the first time in four years that it appeared in the morning section. This might have thrown some candidates if they were not expecting an essay question, so I thought I would go over one of the questions in this week’s post.
The essay questions, along with the guideline answers, are available on the Institute’s website for your practice.
Together, questions #8 and #9 were worth 25 points or about 7% of the overall exam. Problem #8 covered the use of equity futures in changing a portfolio’s beta, using equity and bond futures to adjust portfolio allocation, and pre-investing with futures. Problem #9 covered options with delta hedging and some conceptual material on how gamma changes closer to expiration. These are formula intensive sections but the calculations really are not that hard once you work through them.
The first thing you should notice when starting #9 is that the three parts (A,B,C) are worth 12 points. Unless you have saved some time elsewhere in the morning, you should try to get through these in no more than 10-15 minutes. Don’t spend 30 minutes on a question that is only worth 12 points! Use your time wisely.
You may want to underline or highlight key figures as you’re reading to make it easier to pick out data when you come to questions. Here things that jump out to me are 2,000 shares of equity, x-price of 1,300 Euros, premium of E19.09, etc.

  1. A put is a right to sell while a call is a right to buy, so being on the other side of the transaction (the writer of the option) would be the obligation to do the reverse (i.e. put is obligation to buy while call is obligation to sell). Knowing your ultimate exposure, you can figure out how to hedge it through an equity position. In this case you need to create an offsetting short position so you take the number of shares times the option delta times the current price.
  2. You need more in-depth knowledge of how options price here with the convex relationship between price and the underlying. You’ve seen this concept with mortgage-backed securities in the fixed income topic area so it shouldn’t be totally new. Remember, delta is the change in option price relative to stock price while gamma is the change in delta relative to the underlying. Long options (calls) have positive gamma (change in price is less for a decrease in underlying than the change for an increase in the underlying) while short options (puts) have negative gamma (change in option price will be greater for a decrease in underlying equity relative to the change from an increase in the underlying).
  3. The toughest part here is continuous compounding and the fact that you need to do six calculations for just five points. Don’t stare at the problem too long if you do not know it. Just get something down and move on to make sure you get the easy points in the exam. You will get partial credit if you hit on some of the points for which the graders are looking, so write something down!
    1. First, start with the trader’s net cash position which is the number of shares long times the price, minus the premium collected for the options sold.
    2. Even if you can’t remember how to do the continuous compounding, do the equation anyway and move on to the next steps. You can still get credit for doing the remaining calculations even if the result is off because of a prior mistake (and here the difference between continuous compounding is only $0.05).
    3. From here it’s just a matter of subtracting the short call position from the long equity position and finding the relative return.

Of the 12 total points, you could have gotten 6 or 7 easily by just knowing the conceptual material and working through the equations quickly. The remaining points would have been a little harder and may have taken more time than they were worth if you really didn’t know the material. This is a great example of making sure you get the easy points and not spending too much time where it’s not going to pay off.
If you know that you don’t know something or it’s going to take a while to figure it out, move on and come back to it if you have time.
Two more weeks to the exam. Make sure you are ready for the first two questions (individual and institutional portfolio management) and get a few mock exams done.
‘til next time, happy studyin’
Joseph Hogue, CFA

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