Category Archives: Assignments

Preparation for tomorrow’s Final Exam review for Finance 4335

Here are some suggestions for preparing for tomorrow’s Final Exam review for Finance 4335:

1. Be sure to read and review my blog posting entitled “Hints about the final exam in Finance 4335… from earlier today.

2. I have posted the final exam formula sheet which will appear as part of the final exam booklet. Furthermore, the Standard Normal Distribution Function (“z”) Table will also appear as part of the final exam booklet.

3. Read and review the Finance 4335 Fall 2017 course synopsis.

4. For tomorrow’s review session, review problem sets 3-11 (solutions for which are available at http://risk.garven.com/?s=solutions+for+problem+set) and the Spring 2017 Final Exam Booklet and Solutions and come to class with any questions you may have concerning any of this material.

See y’all tomorrow!

No class on Tuesday, November 21

I have decided to cancel class on Tuesday, November 21.  On Tuesday, November 28, we will complete our coverage of the Why is Risk Costly to Firms? lecture note (specifically, the asset substitution and managerial incentives topics which appear on pp. 26-43).

The final problem set for the semester (Problem Set 11) is now due on Tuesday, November 28 (instead of Tuesday, November 21).  The final scheduled class meeting for Finance 4335 is Thursday, November 30; class on that day will be devoted primarily to a review session for the final exam, which is scheduled for Tuesday, December 12, 2:00 p.m. – 4:00 p.m. in Foster 402.

Happy Thanksgiving!

Problem set 10 change

As per our discussion in class today, I just modified Problem Set 10 so that it considers the effect of the corporate tax policy change that is currently under consideration; i.e., the lowering of the corporate tax rate from 35% to 20%.  This is addressed in part D of the new version of Problem Set 10.  If you have previously downloaded Problem Set 10, throw that copy away and replace it with the version that I just uploaded to the course website at http://fin4335.garven.com/fall2017/ps10.pdf.

Clarification of expectations for and hints concerning Problem Set 9

A student asked me whether it’s okay to use an Excel spreadsheet to solve problem set 9.  While I  generally encourage students to use  Excel for the purpose of validating their work (especially for computationally challenging problem sets such as the present one), I also expect students to demonstrate understanding and knowledge of the logical framework upon which any given problem is based.  In other words, I expect you to show and explain your work on this problem set just as you would have to show and explain your work if this was an exam question.

As I am sure you are already well aware, you can obtain most of the “correct” answers for problem set 9 by simply downloading and opening up the Credit Risk Spreadsheet in Excel and performing the following steps:

  1. For part A, open the Firm 1 worksheet, replace the “.4” in cell B3 with “.3”.  Then the answers for the three questions are in cells F4, F3, and F5 respectively.
  2. For part B, open the Firm 2 worksheet, replace the “.4” in cell B3 with “.5”.  Then the answers for the three questions are in cells F4, F3, and F5 respectively.
  3. For part C, assuming that  you are able to follow the logic presented in my On the economics of financial guarantees blog post from yesterday afternoon, the fair insurance premiums appear on both of the worksheets, and presumably you also understand from our study of financial derivatives that the expected return on a default-free bond is the riskless rate of interest.

The problem with simply plugging and chugging the spreadsheet template is that one can mechanically follow the steps outlined above without necessarily understanding the credit risk problem.  The key takeaway from our study of credit risk is that limited liability causes prices of bonds issued by risky (poor credit quality) firms to be lower than prices of bonds issued by safe (good credit quality) firms.  In the case of this problem set, firms 1 and 2 are identical in all respects expect for asset risk, and because of limited liability, this implies that in the absence of a financial guarantee, firm 2’s bonds are riskier than firm 1’s bonds. Thus, firm 2’s bonds have a lower market value (and a correspondingly higher yield, or expected return) than firm 1’s bonds, and firm 2 can expect to have to pay more than firm 1 for a financial guarantee which transfers the default risk from investors over to a financial guarantor.  In a competitive market, the fair premium for such a guarantee is given by the value of the limited liability put option.

By all means, make use of the Credit Risk Spreadsheet to validate your answers for the problem set.  But start out by devising you own coherent computation strategy using a piece of paper, pen or pencil, and calculator. Since you know that the value of risky debt is equal to the value of safe debt minus the value of the limited liability put option, one approach to solving this problem set would be to start out by calculating the value of a riskless bond, and the value of the limited liability put option.  The value of a riskless bond is V(B) = B{e^{ - rT}}, where B corresponds to the promised payment to creditors.  The value of the option to default (V(put)) can be calculated by applying the BSM put equation (see the second bullet point on page 8 of http://fin4335.garven.com/fall2017/lecture16.pdf); this requires 1) calculating {d_1} and {d_2}, 2) using the Standard Normal Distribution Function (“z”) Table to find N({d_1}) and N({d_2}), and 3) inputting your N({d_1}) and N({d_2}) values into the BSM put equation, where the exercise price corresponds to the promised payment to creditors of $500,000, and the value of the underlying asset corresponds to the value of the firm, which is $1,000,000.  Once you obtain the value of the safe bond (V(B)) and the value of the option to default (V(put)) for each firm, then the fair value for each firm’s debt is simply the difference between these two values; i.e., V(D) = V(B) – V(put).  Upon finding V(D) for firm 1 and firm 2, then you can obtain these bonds’ yields to maturity (YTM ) by solving for YTM in the following equation: V(D) = B{e^{ - YTM(T)}}.

Since the value of equity corresponds to a call option written on the firm’s assets with exercise price equal to the promised payment to creditors, you could also solve this problem by first calculating the value of each firm’s equity (V(E)) using BSM call equation (see the second bullet point on page 7 of http://fin4335.garven.com/fall2017/lecture16.pdf and substitute the value of assets ($1,000,000) in place of S and the promised payment of $500,000 in place of K in that equation).  Once you know V(E) for each firm, then the value of risky debt (V(D)) is equal to the difference between the value of assets (V(F) = $1,000,000) and V(E).  Upon calculating V(D) in this manner, then obtain these these bonds’ yields to maturity (YTM ) by solving for YTM in the following equation: V(D) = B{e^{ - YTM(T)}}.

On the economics of financial guarantees

On pp. 13-19 of the Derivatives Theory, part 3 lecture note and in Problem Set 9, we study how credit enhancement of risky debt works. Examples of credit enhancement in the real world include federal deposit insurance, public and private bond insurance, pension insurance, mortgage insurance, government loan guarantees, etc.; the list goes on.

Most credit enhancement schemes work in the fashion described below. Creditors loan money to “risky” borrowers who are at risk for defaulting on promised payments. Although borrowers promise to pay back $B at t=1, they may default (in whole or in part) and the shortfall to creditors resembles a put option with t=1 payoff of -Max[0, B-F]. Therefore, without credit enhancement, the value of risky debt at t=0 is

V(D) = B{e^{ - r}} - V(Max[0,B - F]).

However, when credit risk is intermediated by a guarantor (e.g., an insurance company or government agency), credit risk gets transferred to the guarantor, who receives an upfront “premium” worth V(Max[0,B - F]) at t=0 in exchange for having to cover a shortfall of Max[0,B - F] that may occur at t=1. If all credit risk is transferred to the guarantor (as shown in the graphic provided below), then from the creditors’ perspective it is as if the borrowers have issued riskless debt. Therefore, creditors charge borrowers the riskless rate of interest and are paid back what was promised from two sources: 1) borrowers pay D = B - Max[0,B - F], and 2) the guarantor pays Max[0,B - F].

economics_of_deposit_insurance

Credit risk teaching note and spreadsheet

I’d like to call your attention to my credit risk teaching note @ http://fin4335.garven.com/fall2017/creditrisk.pdf and my credit risk spreadsheet @ http://fin4335.garven.com/fall2017/creditrisk.xls. This teaching note provides a brief synopsis of today’s presentation of the credit risk topic, and the spreadsheet provides the code required in order to produce the table on page 8 of the teaching note.