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100



90 Price trajectory for +300 bps
changes in par bond yield

80
0 1 2 3 4 5
Passage of time

FIGURE 5.32 Price cone for a 5-year-maturity coupon-bearing Treasury.



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Price Price cone for 5-year
coupon-bearing Treasury
120
Price cone for a 1-year
Treasury bill
Maturity
110



100



90



80
0 1 2 3 4 5
Passage of time

FIGURE 5.33 Price cone for a 5-year Treasury and 1-year Treasury bill.



Transitioning now from bonds to equities, consider Figure 5.34. As a
rather dramatic contrast with the figure for bonds, there is no predetermined
maturity date and, related to this, no convergence toward par with the pas-
sage of time. In fact, quite the contrary; the future price possibilities for an
equity are open-ended, both on the upside and the downside. However, and
as depicted, a soft floor exists at the point where the book value of assets
becomes relevant. As one implication of this greater ambiguity, a variety of
methodologies may be used to generate some kind of forecast of what future
price levels might become. These methods include price forecasts based on
an equity™s valuation relative to other equities within its peer group, analy-
ses of where the equity ought to trade relative to key performance ratios
inclusive of its multiple of price to book value (total assets minus intangi-
ble assets and liabilities such as debt) or price-earnings (P/E) ratio (current
stock price divided by current earnings per share adjusted for stock splits),
and the application of technical analysis (analysis that seeks to detect and
interpret patterns in past security prices).
Figure 5.35 shows currencies. Not too surprisingly, the figure more
closely resembles the profile for equities than that for bonds, and this is
explained by the more open-ended nature of potential future price values.
As with equities, a soft floor is inserted where an embedded credit call might
be said to exist that reflects some value of a country™s economic and politi-
cal capital. Again, a variety of methodologies might be used to forecast a




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232 FINANCIAL ENGINEERING, RISK MANAGEMENT, AND MARKET ENVIRONMENT



Price
Equity



Purchase price


Soft floor for equity price positioned at the
book value of assets (adjusted for debt)
0




0
Passage of time

FIGURE 5.34 Price cone for an equity.



future exchange rate value, including consideration of interest rate parity or
purchasing power parity models. Another way a cone might be created is
with reference to a given exchange rate™s implied volatility. In short, a for-
ward series of implied volatilities could be used to generate an upper and
lower bound of potential exchange rate values over time. In fact, this
method of generating cones could be used for any financial instrument where
an implied volatility is available.
For another perspective of evaluating the different issues involved with
price and total return calculations across cash flows and products, consider
Table 5.7.
In the table, there are two “Yes” indications for bonds, one for equi-
ties, and none for currencies. As a very general statement about the total
return profile of investment-grade bonds versus equities and currencies, over
the long run, the total returns of bonds tends to be less volatile relative to
the returns of equities, and the total returns of equities tends to be less
volatile relative to the returns of currencies. This pattern can be linked
directly to the frequency and variety of cash flows generated by a given prod-
uct (where frequency and variety relate to cash flow diversification) and to
the relative predictability of all the cash flows.
Finally, the exercise of defining upper and/or lower bounds to financial
variables of interest can be applied in a number of creative and meaningful
ways. Its usefulness stems from assisting an investor with thinking about the
parameters of what a best- and worst-case scenario actually might look like.




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Risk Management



Price
(Exchange rate)
Currency


Purchase price


Soft floor for currency value
(Embedded credit call)
0




0
Passage of time

FIGURE 5.35 Price cone for currencies.


TABLE 5.7 Comparison of Total Return Components for a One-Year Horizon
Products

Bonds Equities Currencies

Cash flow
End price Yes No No
Cash flows Yes Yes N/A
Reinvestment
of cash flows No No N/A



To provide an example outside of the broader strokes of product types, con-
sider the effect of different prepayment speeds on the outstanding balance
of principal for an MBS. Figure 5.36 embodies a set of scenarios to be
considered.
As shown, prepayment speeds can have a very important impact indeed
on the valuation of an MBS, and these speeds can vary from month to
month. Just as these types of illustrations can be useful with evaluating the
risk of a particular security, they also can be used to evaluate the risk pro-
file of entire portfolios. Another popular way to conceptualize the risks of
a portfolio is with scenario analysis.
“Scenario analysis” refers to evaluating a particular strategy and/or port-
folio construction by running it through all of its paces, all the while taking




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234 FINANCIAL ENGINEERING, RISK MANAGEMENT, AND MARKET ENVIRONMENT



Remaining balance (%) 0% PSA

50% PSA

120% PSA

200% PSA




0 5 10 15 20 25 30

Passage of time

FIGURE 5.36 Outstanding principal balances for a generic “current coupon” 30-year
pass-thru.


note of how total return evolves. For example, for a proposed bond port-
folio construction, a portfolio manager might be interested in observing how
total returns look on a six-month horizon if the yield curve stays relatively
unchanged, if the yield curve flattens, or if the yield curve inverts. The total
returns for these different scenarios then can be compared to the prevailing
six-month forward yield curves and to the portfolio manager™s own personal
forecast (should she have one), and the proposed portfolio construction then
can be evaluated accordingly. A variety of instrument types can be layered
onto this core portfolio, including futures and options, so as to incorporate
the latter. Additional scenarios (or “stress tests” as they are sometimes called)
also might be performed that include different assumptions for volatility.
Scenario analysis can help give investors a working idea of the risks and
rewards embedded in a particular strategy or portfolio structure before the
plan is actually put into place. Of course, regardless of the number of what-
if scenarios applied, the actual experience may or may not correspond exactly
to any one of the scenarios. In this regard the value of scenario analysis lies
in helping to identify boundary conditions.
In a more macro context of risk, consider the challenge of linking envi-
ronmental dynamics with financial products. Let us assume that a company



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Risk Management



is headquartered in country X with a rather large and important subsidiary
in country Y. Further, assume that the currencies in country X and Y are dif-
ferent and that the company repatriates its profits on an annual basis to its
home base. It would be rather straightforward to envision a scenario
whereby the subsidiary in country Y has a very profitable year but where
those profits would quickly diminish after the relevant exchange rate were
applied. This reflects a situation where the currency of country Y depreci-
ated in a significant way relative to the currency of country X.
If the company had elected at the start of the year to hedge its currency
exposures on an ongoing basis when and where practical, likely its profitability
would have been at least partially protected. Accordingly, this strategy is
often called an economic hedge. The motivation for the strategy would be
to protect against a macro-oriented business level exposure (as opposed to
a more micro-oriented portfolio- or product-level exposure). Other examples
include an energy-sensitive industry, such as an airline, using oil futures to
hedge or otherwise protect against high fuel costs, or a rate-sensitive indus-
try, as with banking, using interest rate futures to hedge or protect against
adverse moves in rates.


Summary
Probability plays a central role in attempts to characterize an investment™s
total return. In the absence of uncertainties, probability is 100 percent. As
layers of risks are added, a 100 percent probability is whittled down to some-
thing other than complete certainty. In the classic finance context of a trade-
off between risk and reward, riskier investments will generate higher returns
over a long run relative to less risky investments, assuming there is some
diversification within respective portfolios.
As another perspective on the inter-relationship between probability and
products, consider Figure 5.37. With probability on one axis and time on
the other, it shows profiles of a sample bond, equity, and currency.
As shown, a product™s price is known with 100 percent certainty at the
time it is purchased, and there is a relatively high degree of certainty that its

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