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Helpful study hints for the final exam in Finance 4335…

As you prepare for the Finance 4335 final exam you would do well to review key resources, including the Finance 4335 Course Overview, the Final exam formula sheet, and problem sets, class problems, and sample exams available on the course website.

By now, I assume that my Finance 4335 students

  • Understand how to calculate and rank order risks based on expected utility;
  • Understand how to apply the standard normal and binomial probability functions;
  • Comprehend that one is risk averse/risk neutral/risk seeking if the risk premium \lambda is positive/zero/negative;
  • are aware that the risk premium \lambda can be calculated in either of the following two ways: 1) by setting expected utility (E(U(W))) equal to the utility of the certainty equivalent of wealth (WCE ), solving for the WCE, and subtracting WCE from E(W), or 2) multiplying half of variance by the Arrow-Pratt Coefficient, evaluated at E(W) (\lambda = .5\sigma _W^2{R_A}(E(W)));
  • Understand that the risk premium (\lambda) is positively related to the degree of risk aversion, as measured by the Arrow-Pratt Coefficient {R_A}(W) = - U''/U' – thus, a decision-maker with logarithmic utility (U = ln W) is more risk averse than a decision-maker with power utility (U = Wn);
  • Have learned that in a world where investors’ portfolios comprise combinations of the riskless asset and the market portfolio, only systematic is priced; i.e., E({r_i}) = {r_f} + {\beta _i}[E({r_m}) - {r_f}];
  • Understand that riskless arbitrage ensures the formation of so-called “arbitrage-free” prices for financial derivatives such as futures/forward and options;
  • Are aware that option pricing principles can value the option to default and determine the credit risk premium that investors demand from limited liability firms that issue debt.
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Finals week office hours for Finance 4335

I will be available for virtual office hours for Finance 4335 on Wednesday, May 8, from 3-5 pm. To join, enter “zoom.garven.com” in your web browser’s address field. If you need to schedule a different time during finals week, feel free to text your request for a meeting at 254-307-1317.

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Friendly reminder: Optional problem set 10 due tomorrow

As we wind down the spring semester in Finance 4335, here’s a friendly reminder for Finance 4335.

There is one more problem set left for Finance 4335, which is Problem Set 10 (Corporate Risk Management), and it is due via Canvas before the start of tomorrow’s class meeting. However, completing this problem set is optional. If you choose to complete and turn it in via Canvas, the grade you earn on it will replace your lowest problem set grade for the semester, provided its grade is higher than your lowest grade received on Problem Sets 1-9.

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Source for today’s coverage of the “underinvestment” problem

During today’s Finance 4335 class meeting, the logic behind the so-called underinvestment problem (where, in the absence of risk management, it may be “rational” to reject a positive net present value investment project) is explained in the How Insurance Solves the Underinvestment Problem assigned reading. That assigned reading is an unpublished appendix based on the following published (peer-reviewed) journal article:

Garven, James R. and Richard D. MacMinn, 1993, “The Underinvestment Problem, Bond Covenants, and Insurance,” Journal of Risk and Insurance, Vol. 60, No. 4 (December), pp. 635-646.

This journal article received a “best paper” award from the journal editors in the year it was published, and according to Google Scholar, it has been cited 96 times in works by other scholars.

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Extension of Problem Set 9 deadline and plans for tomorrow’s Finance 4335 class meeting

I have extended the deadline for Problem Set 9 from tomorrow (Thursday, April 25) to Tuesday, April 30. This decision was inspired by a question from a Finance 4335 student, which also led me to publish a related blog post earlier today titled "Pricing Credit Risk Class Problem and Solutions…".

In tomorrow’s Finance 4335 class, we will begin by reviewing the solutions for the first part of the class problem included in the above-referenced blog post (also previously covered during last Thursday’s class meeting). We will complete our discussion of the credit risk topic by covering the second part of the class problem. The rest of the class tomorrow will be devoted to further discussing the topic of corporate risk management, which began in yesterday’s Finance 4335 class meeting.

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Problem Set 8 helpful hints

Here are some helpful hints to consider for Problems 1 and 2 on Problem Set 8 (Problem Set 8 is due by 11 am this Tuesday):

  • Problem 1, Part A: Since the call option described in Problem 1, Part A is initially out-of-the-money (i.e., since S = $18 and K = $20), there will be terminal nodes at which the call option expires in-the-money and others at which it expires out-of-the-money.  By solving the b = \ln (K/S{d^n})/\ln (u/d) equation and rounding to the nearest integer greater than b (referred to in the CRR equation below as the parameter “a“), this indicates the minimum number of up moves required such that this call option expires in–the–money.  Once you have this information, you can consider only those terminal nodes at which the call option expires in-the-money (which are nodes a through n) and calculate the call option price by applying the CRR call option pricing equation:  C = {e^{ - rT}}\left[ {\sum\limits_{j = a}^n {\frac{{n!}}{{j!\left( {n - j} \right)!}}{q^j}{{\left( {1 - q} \right)}^{n - j}}\left( {{u^j}{d^{n - j}}S - K} \right)} } \right]
  • Problem 1, Part B: Apply the put-call parity equation (C+Ke^{-rT} =P+S) to solve for the put option price.
  • Problem 2, (Scenario A): requires solving for call and put option prices using the Black-Scholes-Merton option pricing formulas.  See the Part 2 option pricing lecture note, page 18, for a numerical illustration of how to do this.
  • Problem 2, Scenario B requires finding the current price of the underlying asset, where the call, put, and exercise prices are all given.  Solve the put-call parity equation (C + K{e^{ - rT}} = P + S) for S.
  • Problem 2, Scenario C requires finding the exercise price, where the call, put, and underlying asset prices are all given.  Solve the put-call parity equation for K.
  • Problem 2, Scenario D requires finding \sigma for a call option worth $2.38 and a put option worth $3.60.  Feel free to use the Black-Scholes spreadsheet from the course website, or better yet, create your own Excel spreadsheet in which you solve for the call and/or the put by varying \sigma (this can be accomplished either via trial and error or better yet, by using either Solver or Goal Seek).  An important lesson you’ll learn from this part of problem 2 is that call and put option prices are positively related to \sigma .