# 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!

# Some hints for Problem Set 10

The classic capital budgeting model (such as you learned in Finance 3310) implicitly assumes that the firm has unlimited liability and faces linear taxes. When these assumptions hold, then the net present value (NPV) of a project is calculated by estimating expected values of future incremental after-tax cash flows and discounting them at an appropriate risk-adjusted discount rate. However, we showed during yesterday’s class meeting how limited liability and nonlinear taxes imply that the net present value of a project depends upon the manner in which incremental after-tax cash flows interact with cash flows from existing assets. Consequently, the after-tax value of equity is equal to the difference between the pre-tax value of equity and the value of the government’s tax claim (both of which we model as call options on the firm’s assets). Furthermore, project NPV corresponds to the difference in after-tax value of equity (assuming the project is undertaken), minus the after-tax value of equity (assuming the project is not undertaken).

Problem Set 10 provides an opportunity to apply these concepts.  Here are some hints for parts A through E of Problem Set 10 :

1. In part A, apply the option pricing framework to determine the pre-tax value of equity (V(E), where V(E) = V(Max(0,F-B)), the value of debt (V(D), where V(D) = V(B – Max(0,B-F)), and the value of taxes (V(T), where V(T) = $\tau$V(Max(0,F-TS)), assuming that this investment is not undertaken.  Helpful hint: we performed these same calculations in class yesterday for the problem described on pp. 17-18 of the http://fin4335.garven.com/fall2017/risk_costly_chapter7.pdf teaching note.
2. In order to determine whether the project should be undertaken, in part B you need to  after-tax equity value (i.e., V(E) – V(T)) which obtains under the assumption that the investment is undertaken. Once you obtain that result, the net present value (NPV) of the project is the difference between the after-tax value of equity (V(E) – V(T)) in part A (which you have already calculated) and the after-tax value of equity which obtains if the investment is undertaken. The decision to invest or not to invest depends upon whether the NPV of the investment is positive (in which case you undertake the project) or negative (in which case you do not undertake the project).

# 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 $Max[0,B - F]$. # Midterm exam 2 information… Midterm 2 will be given during class on Thursday, November 2. This test consists of 4 problems. You are only required to complete 3 problems. At your option, you may complete all 4 problems, in which case I will throw out the problem on which you receive the lowest score. The questions involve topics which we have covered since the first midterm exam. Topics covered include 1) demand for insurance, 2) moral hazard/adverse selection, 3) portfolio theory/capital market theory, and 4) financial derivatives (calls and puts specifically). By the way, I have posted the formula sheet that I plan to use on the exam at the following location: http://fin4335.garven.com/fall2017/formulas_part2.pdf. As I noted in my “Plans for next week in Finance 4335” blog posting, tomorrow’s class meeting will be devoted to a review session for midterm exam. If you haven’t already done so, I highly recommend that you review Problem Sets 5-8 and also try working the Sample Midterm 2 Exam (solutions are also provided) prior to coming to class tomorrow. # Midterm 2 Exam Synopsis (outline of topics covered since Midterm 1) In the link listed below, I provide access to the Midterm 2 Synopsis that will serve as the outline for next Tuesday’s Midterm Exam 2 review session (Midterm Exam 2 is schedule to be given during class on Thursday, November 2): Finance-4335-Fall-2017-Midterm-2-Synopsis # On the role of replicating portfolios in the pricing of financial derivatives Replicating portfolios play a central role in terms of pricing financial derivatives. Here is a succinct summary from last Thursday’s class meeting: 1. Buying forward is equivalent to buying the underlying on margin, and selling forward is equivalent to shorting the underlying and lending money. Like options, forwards and futures are priced by pricing the replicating portfolio and invoking the “no-arbitrage” condition. If the forward/futures price it too low, then one can earn positive returns with zero risk and zero net investment by buying forward, shorting the underlying and lending money. Similarly, if the forward futures price is too high, one can earn positive returns with zero risk and zero net investment by selling forward and buying the underlying with borrowed money. This is commonly referred to as “riskless arbitrage”; it’s riskless because you’re perfectly hedged, and it’s arbitrage because you are buying low and selling high. 2. The replicating portfolio for a call option is a margined investment in the underlying. For example, in my teaching note entitled “A Simple Model of a Financial Market”, I provide a numerical example where the interest rate is zero, there are two states of the world, a bond which pays off$1 in both states is worth $1 today, and a stock that pays off$2 in one state and $.50 in the other state is also worth one dollar. In that example, the replicating portfolio for a European call option with an exercise price of$1 consists of 2/3 of 1 share of stock (costing $0.66) and a margin balance consisting of a short position in 1/3 of a bond (which is worth -$0.33). Thus, the value of the call option is $0.66 –$0.33 = \$0.33.
3. Since the replicating portfolio for a call option is a margined investment in the underlying, it should come as no surprise that the replicating portfolio for a put option consists of a short position in the underlying combined with lending. Thus, in order to price the put, you need to determine and price the components of the replicating portfolio; we will begin class on Tuesday, 10/24 by determining the the relative weightings (delta and beta) for the put’s replicating portfolio.

# Problem Set 7 helpful hints

1. The least risky combination of Security A and Security B in Problem 1 is found by calculating ${w_A} = \displaystyle\frac{{\sigma _B^2 - {\sigma _{AB}}}}{{\sigma _A^2 + \sigma _B^2 - 2{\sigma _{AB}}}}$ and ${w_B} = 1 - {w_A}$.
2. It will always be the case for 2 security portfolios that by following the minimum variance portfolio weighting scheme in the previous bullet point, such a portfolio must have zero variance if ${\rho _{AB}} = 1$ or -1.
3. In part B of Problem 2, the Sharpe Ratio for security j is $\displaystyle\frac{{E({r_j}) - {r_f}}}{{{\sigma _j}}}$.