All posts by jgarven

Credit Risk Spreadsheet from today’s class meeting of Finance 4335

Linked below is the Credit Risk Spreadsheet that I built from scratch from today’s class meeting of Finance 4335. In cells A16:B21, the comparative statics of the probability of default are listed. Other things equal, the probability of default is negatively related to the value of the firm’s assets (V(F)), the rate of interest (r), and the time to maturity for the firm’s bonds (T). On the other hand, the probability of default is positively related to the firm’s financial leverage (as measured by B) and the risk of the firm’s assets (as measured by sigma).

Credit Risk Spreadsheet.xlsx

Teacher evaluations for the courses (including Finance 4335) in which you are enrolled this semester

By now, you should have received an email inviting you to complete teacher evaluations for the courses (including Finance 4335) in which you are enrolled this semester.

At Baylor, your professors are given annual evaluations concerning quality of teaching, research, and service. These evaluations are based in part upon teacher evaluations provided by students. Thus, by completing teacher evaluations, you provide the University with important and valuable information that may affect not only faculty compensation and promotion/tenure decisions, but also provide faculty with useful information concerning ways to improve teaching. Thus, I encourage you to not only complete your teacher evaluation for Finance 4335, but also for the other courses in which you are enrolled.

Helpful hints for Problem Set 9

A student asked me whether it’s okay to solve Problem Set 9 by using Excel. 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.

By all means, create your own spreadsheet model of Problem Set 9 to validate your answers for this problem set. But start out by devising you own 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; this requires 1) calculating {d_1} and {d_2}, 2) using the Standard Normal Distribution Function (“z”) Table to find 1-N({d_1}) and 1- N({d_2}) , and inputting these probabilities into the BSM put equation, where the exercise price corresponds to the promised payment to creditors and the value of the underlying asset corresponds to the value of the firm’s assets (keep in mind that the (risk neutral) probability of default corresponds to  1- N({d_2}) for reasons explained during yesterday’s class meeting). 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)}}; the credit risk premium is equal to the difference between the yield to maturity and the riskless rate of interest.

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 and substitute the value of assets (V(F)) in place of S and the promised payment of $B 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) and the value of equity V(E) Then YTM and credit risk premium follow in the manner described in the previous paragraph.

Credit risk spreadsheet (based upon yesterday’s credit risk class problem)

For what it’s worth, I have posted a spreadsheet (based upon yesterday’s credit risk class problem; see the PDF document linked below) the which calculates the fair market values for 1) the uninsured deposits held by banks 1 and 2, 2) the limited liability put options for these banks, 3) these banks’ (risk neutral) probabilities of bankruptcy? 4) the yields to maturity on these bank’s uninsured deposits, and 5) the credit risk premiums for these banks’ uninsured deposits.

Finance 4335 Class Problem – Credit Risk.pdf

Federal Financial Guarantees: Problems and Solutions

Besides insuring bank and thrift deposits, the federal government guarantees a number of other financial transactions, including farm credits, home mortgages, student loans, small business loans, pensions, and export credits (to name a few).

In order to better understand the problems faced by federal financial guarantee programs, consider the conditions which give rise to a well-functioning private insurance market. In private markets, insurers segregate policyholders with similar exposures to risk into separate risk classifications, or pools. As long as the risks of the policyholders are not significantly correlated (that is, all policyholders do not suffer a loss at the same time), pooling reduces the risk of the average loss through the operation of a statistical principle known as the “law of large numbers”. Consequently, an insurer can cover its costs by charging a premium that is roughly proportional to the average loss. Such a premium is said to be actuarially fair.

By limiting membership in a risk pool to policyholders with similar risk exposures, the tendency of higher risk individuals to seek membership in the pool (commonly referred to as adverse selection) is controlled. This makes participation in a risk pool financially attractive to its members. Although an individual with a high chance of loss must consequently pay a higher premium than someone with a low chance of loss, both will insure if they are averse to risk and premiums are actuarially fair. By charging risk-sensitive premiums and limiting coverage through policy provisions such as deductibles, the tendency of individuals to seek greater exposure to risk once they have become insured (commonly referred to as moral hazard) is also controlled.

In contrast, federal financial guarantees often exaggerate the problems of adverse selection and moral hazard. Premiums are typically based upon the average loss of a risk pool whose members’ risk exposures may vary greatly. This makes participation financially unattractive for low risk members who end up subsidizing high risk members if they remain in the pool. In order to prevent low risk members from leaving, the government’s typical response has been to make participation mandatory. However, various avenues exist by which low risk members can leave “mandatory” risk pools. For example, prior to the reorganization of the Federal Savings and Loan Insurance Corporation (FSLIC) as part of the Federal Deposit Insurance Corporation (FDIC) during the savings and loan crisis of the 1980s and 1990s, a number of low risk thrifts became commercial banks. This change in corporate structure enabled these firms to switch insurance coverage to the FDIC, which at the time charged substantially lower premiums than did the FSLIC. Similarly, terminations of overfunded defined benefit pension plans enable firms to redeploy excess pension assets as well as drop out of the pension insurance pool operated by the Pension Benefit Guarantee Corporation (PBGC).

Although financial restructuring makes it possible to leave mandatory insurance pools, the costs of leaving may be sufficiently high for some low risk firms that they will remain. Unfortunately, the only way risk-insensitive insurance can possibly become a “good deal” for remaining members is by increasing exposure to risk; for example, by increasing the riskiness of investments or financial leverage. Furthermore, this problem is even more severe for high risk members of the pool, especially if they are financially distressed. The owners of these firms are entitled to all of the benefits of risky activities, while the insurance mechanism (in conjunction with limited liability if the firm is incorporated) minimizes the extent to which they must bear costs. Consequently, it is tempting to “go for broke” by making very risky investments which have substantial downside risk as well as potential for upside gain. The costs of this largely insurance-induced moral hazard problem can be staggering, both for the firm and the economy as a whole.

Ultimately, the key to restoring the financial viability of deposit insurance and other similarly troubled federal financial guarantee programs is to institute reforms which engender lower adverse selection and moral hazard costs. Policymakers would do well to consider how private insurers, who cannot rely upon taxpayer-financed bailouts, resolve these problems. The most common private market solution typically involves some combination of risk-sensitive premiums and economically meaningful limits on coverage. Federal financial guarantee programs should be similarly designed so that excessively risky behavior is penalized rather than rewarded.

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].