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Parenthetically, there is also a systemic risk, which is defined as the risk
associated with the general health or structure of a financial system. It is
almost invariably discussed in terms of the system™s inability to handle large
quantities of market, credit, or settlement risk.
By what methodology does someone calculate precise values for
“expected expenses,” “expected losses,” or “capital to support market risk
and credit risk and other risks”? The most simple and yet most accurate
answer to this question is that it varies by firm. Obviously enough, each firm
has different objectives, different levels of risk tolerance, and different areas
of expertise when it comes to markets and risk management. Accordingly,
some risk calculations (if they even exist at all in some firms) may appear to
be simplistic or naïve, while other risk calculations may appear to be overly
complex or confusing. One organization that has made tremendous efforts
to both create risk measurements and educate about their relevance has been
the Bank for International Settlements (BIS) headquartered in Switzerland.
As banking certainly tends to be a regulated industry, we take up the matter
of reporting requirements and related methodologies in Chapter 6.
No matter how quantitative or objective the capital allocation process
may appear, it undoubtedly reflects at least some underlying linkages to some
qualitative and subjective biases. These biases may be geographic (as in
where the company is headquartered), industry-specific (if the company is
an investment bank as opposed to a hedge fund), or even shaped by the per-
sonality of the company™s key managers. Whatever the biases, the capital
allocation process is often a fluid one, and perhaps ought to be for certain
industry types so as to keep up with market opportunities as they arise.




Managing risk




Now that we have discussed how risks can be quantified and allocated, we
turn to how risks can be managed on a day-to-day basis. For some investors,
it all begins with one fundamental consideration: probability. Accordingly,
investment-related decisions are made on the basis of how a particular
choice appears relative to available data, and those data typically are based
on previous experiences. However, such an orientation can be made even



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more meaningful when it can be combined with a forward-looking approach,
as with scenario analysis. Once a probability assessment is made, decisions
inevitably follow. Finally, we examine a few basic approaches to hedging
products and cash flows.
At its very essence, the managing of risk consists of probability, time,
and cash flows. Figure 5.24 helps to illustrate this in the context of three
different securities: a Treasury bill, a 30-year single-A rated corporate bond,
and a share of equity. Probability is labeled as “uncertainty” to be consis-
tent with lower uncertainties (greater probabilities) residing closer to the ori-
gin. As shown, a one-month Treasury bill sits pretty close to the origin since
its credit is that of the U.S. government, it has but one cash flow (principal
at maturity), and if held to maturity its total return is known with certainty
at time of purchase. At the other extreme we have an equity, which is last
in line from a credit perspective, and there is little certainty as to its future
price value.


Equity
30-year single-A corporate bond
Uncertainty of¦
Uncertainty of¦
Drift and default (with less seniority than bonds)
Drift and default
Dividend reinvestment rates
Coupon reinvestment rates
Price (at any time)
Price (if sold prior to maturity)


Uncertainty




1-month Treasury bill




Cash flows
Time




FIGURE 5.24 A conceptual mapping of uncertainties.



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Risk Management



Uncertainties:
Cash flows
• None
+



O
Time




FIGURE 5.25 Six-month Treasury bill.


To further illustrate the relationships among probability, time, and cash
flows, the next figures use a layering approach. We begin with something
that™s 100 percent certain, possesses one single cash flow, and ceases to exist
after 180 days: a six-month Treasury bill (see Figure 5.25).
As shown in Figure 5.25 it can be said with 100 percent certainty (to
the extent that anything can be 100 percent certain in life or in finance) that
there is no credit risk, no reinvestment risk, and no price risk (if the Treasury
bill is held to maturity). Accordingly, it can be said with 100 percent cer-
tainty at the time of purchase exactly what the total return of the Treasury
bill will be in six months™ time.
Figure 5.26 considers a two-year Treasury. Again there is no credit risk
and no price risk (if the Treasury bill is held to maturity), but we can no
longer say that there is 100 percent certainty of knowing total return at time
of purchase. The reason is reinvestment risk; we do not know the rates of
reinvestment for the coupon cash flows that are received between purchase
and maturity dates. While this might seem to be a minor point, keep in mind
that for a 20-year bond, well over one-half of its lifetime total return can
easily come from its reinvested coupon income.7
Now let us change our two-year Treasury into a two-year double-B rated
corporate bond. The incremental risk of credit is highlighted Figure 5.27.
What can we say about the three cases presented thus far? While we
do not have enough information to comment on specific total return values,
we certainly can make some general observations. If we let ptb represent the




7
For a 20-year bond with an 8 percent coupon, a reinvestment rate of 10 percent
could lead to the reinvestment of coupon cash flows contributing more than 60
percent to the security™s overall total return at maturity.




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Uncertainties:
• Reinvestment of coupon income
• Total return prior to maturity
Cash flows

+ Reinvestment risk




O
Time




FIGURE 5.26 Two-year Treasury bond.


Uncertainties:
• Reinvestment of coupon income
• Credit drift and default
Credit risk • Total return prior to maturity
Cash flows

+ Reinvestment risk




O
Time




FIGURE 5.27 Two-year double-B corporate bond.



probability of knowing a Treasury bill™s total return at time of purchase
(holding it to maturity), ptb 100 percent. If we let p2yt represent the prob-
ability of knowing a two-year Treasury™s total return at time of purchase,
at the very least we know that p2yt is less than ptb. In fact, it has to be less
than ptb since the two-year Treasury bond embodies more risk (via the added
risk of reinvesting coupons). It then stands to reason that p2c (representing
a two-year corporate bond) must be less than p2t. Putting these side-by-side,
we have ptb p2t p2c.




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Risk Management



Earlier it was stated that managing risk could be seen in the context of
cash flows, probability, and time. In the last two examples, time was held
constant at two years. Not surprisingly, uncertainty only increases with time.
Investors who think it is difficult to forecast what reinvestment rates might
be over the next two years should try to imagine how tough it is to forecast
reinvestment rates for the next 20 years. Rating agencies make distinctions
between a company™s short-term debt ratings and its long-term debt ratings.
When the two ratings differ, typically the longer-term rating is lower.
Accordingly, we can safely say that p2t p20t and that p2c p20c.
If we can safely say that p2t p20t and p2c p20c, can we say that p20t
p2c? No, at least not on the basis of what we have seen thus far. The uncer-
tainty related to the reinvestment risk of a 20-year Treasury may be greater
than the uncertainty related to the credit risk of a double-B corporate bond,
but we are comparing apples (reinvestment risk) with oranges (credit risk).
But hey, apples and oranges are both fruits that grow on trees, so let us not
be so quick to end the conversation here. In fact, consider Figure 5.28. As
shown, price volatilities between corporate and Treasury coupon-bearing
securities appear to cross with seven-year Treasuries and five-year triple-B
rated corporates.



Price volatility




The intersection of
the price volatility of
a 7-year Treasury
note and a 5-year
triple-B rated
corporate security.

CCC
5
10
15
BBB
20
AAA

Coupon-bearing
Treasuries 5-year coupon-bearing
(by maturity in years) corporate security
(by rating)

FIGURE 5.28 A conceptual mapping of risk profiles.




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