# Problem Set 10 Due Date and Required Submission Procedure

Problem Set 10 is due (as a file attachment to an email sent to risk@garven.com) by no later than 5 p.m. on Monday, May 1.  I won’t accept it for credit unless it is submitted electronically prior to 5p.m. on Monday.  I will subsequently post solutions for Problem Set 10 that same evening.

# Hints about the final exam in Finance 4335…

The final exam for Finance 4335 is scheduled for 2-4 p.m. on Wednesday, May 3, in Foster 203. The exam consists of two parts:

• The first part features five multiple-choice questions worth 5 points each. The questions are mostly on the topic of decision theory; e.g., risk neutrality, risk aversion, risk loving, maximizing expected utility, calculating expected payoffs on gambles, etc.
• The second part consists of three problems worth 24 points each. The topics covered include demand for insurance, applying the Black-Scholes-Merton option pricing formula to evaluate risk of default by a limited liability corporation, and evaluating whether the firm should hedge, given tax asymmetries (the tax asymmetry problem will be covered in tomorrow’s class meeting and is the subject of Problem Set 10).

The “good” news is that you automatically receive 3 points for signing your name on this exam booklet; thus, the total points possible for this exam are 100.

I have posted the Formula Sheet which will appear as part of the Final Exam booklet; it may help you study for the exam by looking over the various formulas.

# How Trump’s tax plan conveys incentives for individual taxpayers to incorporate themselves

Here’s a graphic appearing in today’s WSJ comparing top marginal individual tax rates with top marginal corporate tax rates since 1980 and under the Trump proposal. Given the prospective disparity between top marginal individual and corporate tax rates, I predict that the rate of incorporations by individual taxpayers may soon skyrocket! Discuss…

# A Federal Guarantee that is Sure to Go Broke

See the (November 2014) Wall Street Journal article entitled “A Federal Guarantee Is Sure to Go Broke” and related article from November 2015 entitled “Moody’s Predicts PBGC Premiums Will Become Unaffordable“.

Think of PBGC as essentially the FDIC of private pensions. Thus, the analysis that we did during last Friday’s class meeting and that I provided in my “On the economics of financial guarantees” blog post concerning how FDIC guarantees bank deposits applies here; in the diagram from that posting, simply replace “FDIC” in the diagram with “PBGC”, and in place of “Bank” and “Depositors”, substitute “Company offering private pension to Workers” and “Workers”.

Quoting from the above referenced WSJ article:

How is the PBGC insurance program doing on its 40th anniversary? Well, it is dead broke. Its net worth is negative \$62 billion as of the end of September. That is even more broke than it was a year ago, when its net worth was negative \$36 billion… The PBGC has total assets of \$90 billion but total liabilities of \$152 billion. So its assets are a mere 59% of its liabilities. Put another way, its capital-to-asset ratio is negative 69%.

Why does the government have such a pathetic record at guaranteeing other people’s debts? It isn’t that Washington wasn’t warned. “My son, if you have become surety for your neighbor, have given your pledge for a stranger, you are snared in the utterance of your lips,” reads Proverbs 6: 1-2.

# 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. 19-25 of the Derivatives Theory, part 2 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 $Max[0,B - F]$.

# Where College Seniors Are Falling Short

I thought y’all would want to know; I imagine that this article from today’s WSJ may corroborate your own experiences, as well as the experiences of many of your friends!

Even as employers look to hire more graduates from the Class of 2017 than the previous year, the current crop of job-seeking seniors are ill-prepared for the job hunt and many coveted positions, a survey finds.