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and to let the issue simply continue to trade when it is at prices below par),
anything that has the effect of pulling the callable away from being in-the-
money (as with a larger value of Oc) also has the effect of reducing the
call risk. Thus, OAS narrows as volatility rises.




Quantifying
risk
Credit




Borrowing from the drift and default matrices first presented in Chapter 3,
a credit cone (showing hypothetical boundaries of upper and lower levels of
potential credit exposures) might be created that would look something like
that shown in Figure 5.14.
This type of presentation provides a very high-level overview of credit
dynamics and may not be as meaningful as a more detailed analysis. For
example, we may be interested to know if there are different forward-looking
total return characteristics of a single-B company that:



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Risk Management



Likelihood of default
at end of one year (%)

25
Single C
20

15

10

Single B 5

0
Initial credit ratings

FIGURE 5.14 Credit cones for a generic single-B and single-C security.


Just started business the year before, and as a single-B company, or
Has been in business many years as a double-B company and was just
recently downgraded to a single-B (a fallen angel), or
Has been in business many years as a single-C company and was just
recently upgraded to a single-B.

In sum, not all single-B companies arrive at single-B by virtue of hav-
ing taken identical paths, and for this reason alone it should not be surprising
that their actual market performance typically is differentiated.
For example, although we might think that a single-B fallen angel is
more likely either to be upgraded after a period of time or at least to stay
at its new lower notch for some time (especially as company management
redoubles efforts to get things back on a good track), in fact the odds are
less favorable for a single-B fallen angel to improve a year after a downgrade
than a single-B company that was upgraded to a single-B status. However,
the story often is different for time horizons beyond one year. For periods
beyond one year, many single-B fallen angels successfully reposition them-
selves to become higher-rated companies. Again, the statistics available from
the rating agencies makes this type of analysis possible.
There is another dimension to using credit-related statistical experience.
Just as not all single-B companies are created in the same way, neither are
all single-B products. A single-A rated company may issue debt that is rated
double-B because it is a subordinated structure, just as a single-B rated com-
pany may issue debt that is rated double-B because it is a senior structure.
Generally speaking, for a particular credit rating, senior structures of lower-



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202 FINANCIAL ENGINEERING, RISK MANAGEMENT, AND MARKET ENVIRONMENT



rated companies do not fare as well as junior structures of higher-rated com-
panies. In this context, “structure” refers to the priority of cash flows that
are involved. The pattern of cash flows may be identical for both a senior
and junior bond (with semiannual coupons and a 10-year maturity), but with
very different probabilities assigned to the likelihood of actually receiving
the cash flows. The lower likelihood associated with the junior structure
means that its coupon and yield should be higher relative to a senior struc-
ture. Exactly how much higher will largely depend on investors™ expectations
of the additional cash flow risk that is being absorbed. Rating agency sta-
tistics can provide a historical or backward-looking perspective of credit risk
dynamics. Credit derivatives provide a more forward-looking picture of
credit risk expectations.
As explained in Chapter 3, a credit derivative is simply a forward, future,
or option that trades to an underlying spot credit instrument or variable.
While the pricing of the credit spread option certainly takes into consider-
ation any historical data of relevance, it also should incorporate reasonable
future expectations of the company™s credit outlook. As such, the implied
forward credit outlook can be mathematically backed-out (solved for with
relevant equations) of this particular type of credit derivative. For example,
just as an implied volatility can be derived using a standard options valua-
tion formula, an implied credit volatility can be derived in the same way
when a credit put or call is referenced and compared with a credit-free instru-
ment (as with a comparable Treasury option). Once obtained, this implied
credit outlook could be evaluated against personal sentiments or credit
agency statistics.
In 1973 Black and Scholes published a famous article (which subse-
quently was built on by Merton and others) on how to price options, called
“The Pricing of Options and Corporate Liabilities.”6 The reference to “lia-
bilities” was to support the notion that a firm™s equity value could be viewed
as a call written on the assets of the firm, with the strike price (the point of
default) equal to the debt outstanding at expiration. Since a firm™s default
risk typically increases as the value of its assets approach the book value
(actual value in the marketplace) of the liabilities, there are three elements
that go into determining an overall default probability.

1. The market value of the firm™s assets
2. The assets™ volatility or uncertainty of value
3. The capital structure of the firm as regards the nature of its various con-
tractual obligations


6
F. Black and M. Scholes, “The Pricing of Options and Corporate Liabilities,”
Journal of Political Economy, 81 (May“June 1973): 637“659.




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Risk Management



Figure 5.15 illustrates these concepts. The dominant profile resembles
that of a long call option.
Many variations of this methodology are used today, and other method-
ologies will be introduced. In many respects the understanding and quan-
tification of credit risk remains very much in its early stages of development.
Credit risk is quantified every day in the credit premiums that investors
assign to the securities they buy and sell. As these security types expand
beyond traditional spot and forward cash flows and increasingly make their
way into options and various hybrids, the price discovery process for credit
generally will improve in clarity and usefulness. Yet the marketplace should
most certainly not be the sole or final arbiter for quantifying credit risk. Aside
from more obvious considerations pertaining to the market™s own imper-
fections (occasions of unbalanced supply and demand, imperfect liquidity,
the ever-changing nature of market benchmarks, and the omnipresent pos-
sibility of asymmetrical information), the market provides a beneficial
though incomplete perspective of real and perceived risk and reward.
In sum, credit risk is most certainly a fluid risk and is clearly a consid-
eration that will be unique in definition and relevance to the investor con-
sidering it. Its relevance is one of time and place, and as such it is incumbent
on investors to weigh very carefully the role of credit risk within their over-
all approach to investing.




[Image not available in this electronic edition.]




FIGURE 5.15 Equity as a call option on asset value.
Source: “Credit Ratings and Complementary Sources of Credit Quality Information,” Arturo
Estrella et al., Basel Committee on Banking Supervision, Bank for International Settlements,
Basel, August 2000.




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204 FINANCIAL ENGINEERING, RISK MANAGEMENT, AND MARKET ENVIRONMENT




Allocating
risk




This section discusses various issues pertaining to how risk is allocated in
the context of products, cash flows, and credit. By highlighting the rela-
tionships that exist across products and cash flows in particular, we see how
many investors may have a false sense of portfolio diversification because
they have failed to fully consider certain important cross-market linkages.
The very notion of allocating risk suggests that risk can somehow be
compartmentalized and then doled out on the basis of some established cri-
teria. Fair enough. Since an investor™s capital is being put to risk when invest-
ment decisions are made, it is certainly appropriate to formally establish a
set of guidelines to be followed when determining how capital is allocated.
For an individual equity investor looking to do active trading, guidelines may
consist simply of not having more than a certain amount of money invested
in one particular stock at a time and of not allowing a loss to exceed some
predetermined level. For a bond fund manager, guidelines may exist along
the lines of the individual equity investor but with added limitations per-
taining to credit risk, cash flow selection, maximum portfolio duration, and
so forth. This section is not so much directed toward how risk management
guidelines can be established (there are already many excellent texts on the
subject), but toward providing a framework for appreciating the interrelated
dynamics of the marketplace when approaching risk and decisions of how
to allocate it. To accomplish this, we present a sampling of real-world inter-
relationships for products and for cash flows.


PRODUCT INTERRELATIONSHIPS
Consider the key interrelationship between interest rates and currencies
(recalling our discussion of interest rate parity in Chapter 1) in the context
of the euro™s launch in January 1999. It can be said that prior to the melting
of 11 currencies into one, there were 11 currency volatilities melted into one.
Borrowing a concept from physics and the second law of thermodynamics”
that matter is not created or destroyed, only transformed”what happened
to those 11 nonzero volatilities that collapsed to allow for the euro™s creation?



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One explanation might be that heightened volatility emerged among the fewer
remaining so-called global reserve currencies (namely the U.S. dollar, the yen,
and the euro), and that heightened volatility emerged among interest rates
between euro-member countries and the rest of the world. In fact, both of
these things occurred following the euro™s launch.
As a second example, consider the statistical methods between equities
and bonds presented earlier in this chapter, namely, in the discussion of how
the concepts of duration and beta can be linked with one another.
Hypothetically speaking, once a basket of particular stocks is identified that
behaves much like fixed income securities, a valid question becomes which
bundle would an investor prefer to own: a basket of synthetic fixed income
securities created with stocks or a basket of fixed income securities? The
question is deceptively simple. When investors purchase any fixed income
security, are they purchasing it because it is a fixed income security or
because it embodies the desired characteristics of a fixed income security (i.e.,
pays periodic coupons, holds capital value etc.)? If it is because they want
a fixed income security, then there is nothing more to discuss. Investors will
buy the bundle of fixed income securities. However, if they desire the char-
acteristics of a fixed income security, there is a great deal more to talk about.
Namely, if it is possible to generate fixed income returns with non“fixed
income products, why not do so? And if it is possible to outperform tradi-
tional fixed income products with non”fixed income securities and for com-
parable levels of risk, why ever buy another note or bond?
Again, if investors are constrained to hold only fixed income products,
then the choice is clear; they hold only the true fixed income portfolio. If
they want only to create a fixed income exposure to the marketplace and
are indifferent as to how this is achieved, then there are choices to make.
How can investors choose between a true and synthetic fixed income port-
folio? Perhaps on the basis of historical risk/return profiles.
If the synthetic fixed income portfolio can outperform the true fixed
income portfolio on a consistent basis at the same or a lower level of risk,
then investors might seriously want to consider owning the synthetic port-
folio. A compromise would perhaps be to own a mix of the true and syn-
thetic portfolios.
For our third example, consider the TED spread, or Treasury versus
Eurodollar spread. A common way of trading the TED spread is with futures
contracts. For example, to buy the TED spread, investors buy three-month
Treasury bill futures and sell three-month Eurodollar futures. They would
purchase the TED spread if they believed that perceptions of market risk or
volatility would increase. In short, buying the TED spread is a bet that the
spread will widen. If perceptions of increased market risk become manifest

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