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continuum we can let each strategy stand on its own as an individual trans-
action, and at the other end of the continuum we have the ability (though
only with some strong assumptions) to reduce a complex network of strate-
gies into a single value. What one firm will find most relevant and mean-
ingful may not be the same as any other firm, and the optimal risk
management profiles and methodologies may well come only with perse-
verance, creativity, and trial and error.

Credit Interrelationships
As discussed in some detail in Chapter 3, credit permeates all aspects of
finance. Credit risk always will exist in its own right, and while it can take
on a rather explicit shape in the form of different market products, it also
can be transformed by an issuer™s particular choice of cash flows. The deci-
sion of how far investors ought to extend their credit risk exposure is fun-
damental. All investors have some amount of capital in support of their
trading activity, and a clear objective ought to be the continuous preserva-
tion of at least some portion of that capital so that the portfolio can live to
invest another day. While investments with greater credit risks often provide
greater returns as compensation for that added risk, riskier investments also
can mean poor performance. Thus, it is essential for all investors to have
clear guidelines for just how much credit risk is acceptable and in all of its
Figure 5.23 provides a snapshot of some of the considerations that larger
investors may want to include in a methodology for allocating credit risk.
Generally speaking, a large firm will place ceilings or upper limits on the

Assume a total of $20 billion in a firm's capital to be allocated globally

Part of the world Asia ($5 billion)

Country Japan ($2 billion)

Industry Automotives ($0.5 billion)

Company Nissan ($0.1 billion)

Investment product type Nissan equity ($0.04 billion)

FIGURE 5.23 Allocating risk capital.

Risk Management

amount of investment funds that can be allocated to any one category, where
category might be a part of the world, a particular country, or a specific com-
pany. While the map might be excessive for some investors, it could be woe-
fully incomplete for others. For example, GE is a large company. Does the
credit officer of a large bank limit investments to GE businesses with GE
taken as a whole, or does she recognize that GE is made up of many diver-
sified businesses that deserve to be given separate industry-specific risk allo-
cations? Perhaps she creates a combination of the two different approaches
and evaluates situations on more of a case-by-case basis.
As shown in Figure 5.22, the first layer of a top/down capital allocation
process may be by “part of the world,” followed by “country,” and so on.
At each successive step lower, the amount of capital available diminishes.
Since Japan is not the only country in Asia, and since a company is unlikely
to put all of its Asian-designated capital into just Japan, the amount of cap-
ital allocated to Japan will be something less than the amount of capital allo-
cated to Asia generally. Similarly, since automotives is not the only industry
in Japan, the amount of capital allocated to automotives will be something
less than the amount of capital allocated to Japan, and so on.
Clearly, the credit risk allocation methodology that is ultimately selected
by any investor will be greatly dependent on investment objectives, capital
base, and financial resources. While there is no single right way of doing it,
just as there is no single right way of investing, at least there are well-rec-
ognized quantitative and qualitative measures of credit risk that can be tai-
lored to appropriate and meaningful applications.

In this section, we have discussed the interrelationships of risk in the con-
text of products, cash flows, and credit. We now conclude with a discussion
of ways that a firm™s capital can be allocated to different business lines that
involve the taking of various risks. Since capital guidelines and restrictions
are also a way that certain financial companies are regulated (as with insur-
ance firms and banks), we further explore the topic of capital allocation in
Chapter 6.
Generally speaking, risk limits are expressed as ceilings”upper limits
on how much capital may be committed to a particular venture (as with secu-
rities investments, the making of loans, the basic running of a particular busi-
ness operation, etc.). For especially large companies, ceilings might exist for
how much capital might be committed to a particular country or part of the
world. For smaller investment companies, ceilings might exist simply for how
much capital might be allocated to different types of securities.


Especially large companies have employees who serve as designated
credit officers. Among other responsibilities, they are regularly requested to
grant special requests for increased allocations of capital. For a business man-
ager, capital represents the lifeblood of running a successful operation, so
more capital often means the difference between having had a good year and
a fantastic year. All else being equal, if a credit manager is loath to grant an
outright increase in capital, he might otherwise be inclined to consider bor-
rowing from another ceiling. For example, if there is a limit to how much
capital can be allocated to Japan and Singapore, but the ceiling for Singapore
is far from being reached, then a portion of Singapore™s credit allocation
might be approved for Japan™s use on a temporary basis. A similar type
arrangement might be made to allow for a greater investment in automotives
versus steel, and so forth. At the investment product-type level, while
investors might find themselves up against a particular equity ceiling in
Japan, on a net basis (where long investments are permitted to cancel out
short investments) they may find that their combined equity investments in
Japan and Singapore are well below the combined equity ceilings of these
two markets. Of course, for each of the examples we™ve cited here, the
appropriate corporate officer will have to decide as to whether the requested
capital allocation is in the overall interests of the company.
This hierarchy of how capital might be allocated across various cate-
gories did not explain for the process by which the allocation decisions were
made. That is, how does a company decide that Asia will receive a 10 per-
cent allocation of capital and that Western Europe will receive an allocation
of 25 percent? How does a company determine the ceiling for investments
in the equity of a particular issuer relative to that issuer™s bonds?
To begin with, the answers to some of these types of questions may be
much more qualitative than quantitative. For example, a company that is
headquartered in Asia may be much more likely to have a higher capital allo-
cation ceiling in Asia than in Europe or the United States simply because its
people know the Asian marketplace much better. However, some global com-
panies may try to employ a more quantitative approach, using regional and
country scorings that carefully evaluate risk variables such as political and
economic stability.
Once relevant geographic considerations (part of world and country) are
completed as relates to capital allocation, quantitative measures might be
more readily applied pertaining to how much capital may be committed. For
industry, company, and product-type categories, rating agencies provide
detailed information on these types of things. Further, investors themselves
can devise various measures to quantify the risk of these classifications. For
example, RAROC (risk-adjusted return on capital) is used for risk analysis
and project evaluation where a higher net return is required for a riskier pro-
ject than for a less risky project. The risk adjustment is performed by reduc-

Risk Management

ing the risky return at the project or instrument return level rather than by
adjusting some type of capital charge. Another measure of risk relative to
capital is RORAC (return on risk-adjusted capital); it is similar to RAROC
except that the rate of return is measured without a risk adjustment and the
capital charge varies depending on the risk associated with the instrument
or project. Finally, there is RARORAC (risk-adjusted return on risk-adjusted
capital), which is a combination of RAROC and RORAC; specific risk
adjustments are made to the expected returns, and the capital charge is var-
ied to reflect differing expectations of risk in different projects or securities.
While this may seem like double counting, the adjustments on each side of
the process usually cover different risks.
The specific types of risk that might be considered with a capital adjust-
ment can be separated into systematic risk and nonsystematic risk. The for-
mer could be defined as the risk associated with movement in a market or
market segment as opposed to distinct elements of risk associated with a spe-
cific security. Systematic risk cannot be diversified away; it only can be
hedged. Within the context of the standard capital asset pricing model
(CAPM), exposure to systematic risk is measured by beta. Nonsystematic
risk is the element of price risk that can be largely eliminated by diversifi-
cation within an asset class. It may also be called security-specific risk, idio-
syncratic risk, or unsystematic risk, and in regression analysis it is equal to
the standard error.
Table 5.6 presents bonds, equities, and currencies in the context of sys-
tematic versus nonsystematic risk.
Let us now consider specific formulas that include capital- and risk-
adjusted variables. We begin with an unadjusted return on capital measure,
or simply return on capital:

Expected return on security
; or simply
Capital allocated to trade the security

TABLE 5.6 Systematic vs. Nonsystematic Risks
Systematic Risk Nonsystematic Risk

Bonds Market risk Credit risk
➣ Interest rates
➣ Volatility
Equities Market risk Credit risk
➣ S&P 500/Dow
Currencies Credit risk


Expected return

For a risk-adjusted return on capital we need to adjust expected return
downward to reflect the risks being taken with the investment being con-
sidered. Accordingly, RAROC can be stated as

Expected return Expected expenses Expected losses

The numerator is smaller due to the deduction of expected expenses and
losses; by virtue of a smaller numerator, we will have a smaller overall return.
For a return on risk-adjusted capital, we need to adjust capital upward
to reflect the risks to be supported by the investment being considered.
Accordingly, RORAC can be stated as

Expected return
Capital to support market risk Credit risk Other risks Correlations

“Correlations” (in the denominator) simply means to subtract any
overlapping capital contributions among market risk, credit risk, and any
other risks of interest or relevance so as not to engage in a double counting.
The denominator is larger due to the addition of various capital charges;
by virtue of a larger denominator, we will have a smaller overall return.
And for a risk-adjusted return on risk-adjusted capital, we need to adjust
both expected return and capital in the same way as we adjusted them above.
Accordingly, RARORAC can be stated as

Expected return Expected expenses Expected losses
Capital to support market risk Credit risk Other risks Correlations

We now have both a larger denominator and a smaller denominator,
thus rendering the value for RARORAC less than either RAROC or
As long as there are risks to be measured, each of these return ratios”
RARORAC, RAROC, and RORAC”will generate a value that is less than
expected return divided by capital. And that is the point. A predetermined
and clearly specified target (or hurdle) rate of return must be reached to jus-
tify any allocation of capital in support of that endeavor; the rate of return
must be high enough to cover the costs and capital expenditures needed to
support the particular proposal.

Risk Management


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