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in moves out of risky assets (namely, Eurodollar-denominated securities that
are dominated by bank issues) and into safe assets (namely, U.S. Treasury



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206 FINANCIAL ENGINEERING, RISK MANAGEMENT, AND MARKET ENVIRONMENT



securities), Treasury bill yields would be expected to edge lower relative to
Eurodollar yields and the TED spread would widen. Examples of events that
might contribute to perceptions of market uncertainty would include a weak
stock market, banking sector weakness as reflected in savings and loan or
bank failures, and a national or international calamity.
Accordingly, one way for investors to create a strategy that benefits from
an expectation that equity market volatility will increase or decrease by more
than generally expected is via a purchase or sale of a fixed income spread
trade. Investors could view this as a viable alternative to delta-hedging an
equity option to isolate the value of volatility (V) within the option.
Finally, here is an example of an interrelationship between products and
credit risk. Studies have been done to demonstrate how S&P 500 futures con-
tracts can be effective as a hedge against widening credit spreads in bonds.
That is, it has been shown that over medium- to longer-run periods of time,
bond credit spreads tend to narrow when the S&P 500 is rallying, and vice
versa. Further, bond credit spreads tend to narrow when yield levels are
declining. In sum, and in general, when the equity market is in a rallying
mode, so too is the bond market. This is not altogether surprising since the
respective equity and bonds of a given company generally would be expected
to trade in line with one another; stronger when the company is doing well
and weaker when the company is not doing as well.


CASH FLOW INTERRELATIONSHIPS
Chapter 2 described the three primary cash flows: spot, forwards and
futures, and options. These three primary cash flows are interrelated by
shared variables, and one or two rather simple assumptions may be all that™s
required to change one cash flow type into another. Let us now use the tri-
angle approach to highlight these interrelationships by cash flows and their
respective payoff profiles.
A payoff profile is a simple illustration of how the return of a particu-
lar cash flow type increases or decreases as its prices rises or falls. Consider
Figure 5.16, an illustration for spot.
As shown, when the price of spot rises above its purchase price, a pos-
itive return is enjoyed. When the price of spot falls below its purchase price,
there is a loss.
Figure 5.17 shows the payoff profile for a forward or future. As read-
ers will notice, the profile looks very much like the profile for spot. It
should. Since cost-of-carry is what separates spot from forwards and
futures, the distance between the spot profile (replicated from Figure 5.16
and shown as a dashed line) and the forward/future profile is SRT (for a
non”cash-flow paying security). As time passes and T approaches a value




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207
Risk Management



Return

Positive
returns




0 O Price


Negative Price at time of
returns purchase




FIGURE 5.16 Payoff profile.

Equal to SRT.
Convergence between
forward/future profile
Return and spot profile will
Profile for spot occur as time passes.
Positive
returns


Spot price at
time of initial trade

0 O
O Price


Negative Forward price at time of initial trade
returns



Profile for forward/future

FIGURE 5.17 Payoff profile for a forward or future.

of zero, the forward/future profile gradually converges toward the spot pro-
file and actually becomes the spot profile. As drawn it is assumed that R
remains constant. However, if R should grow larger, the forward/future pro-
file may edge slightly to the right, and vice versa if R should grow smaller (at
least up until the forward/future expires and completely converges to spot).




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208 FINANCIAL ENGINEERING, RISK MANAGEMENT, AND MARKET ENVIRONMENT



Figure 5.18 shows the payoff profile for a call option. The earlier pro-
file for spot is shown in a light dashed line and the same previous profile
for a forward/future is shown in a dark dashed line. Observe how the label
of “Price” on the x-axis has been changed to “Difference between forward
price and strike price” (or F K). An increasingly positive difference
between F and K represents a larger in-the-money value for the option and
the return grows larger. Conversely, if the difference between F and K
remains constant or falls below zero (meaning that the price of the under-
lying security has fallen), then there is a negative return that at worst is lim-
ited to the price paid for the option. As drawn, it is assumed that R and V
remain constant. However, if R or V should grow larger, the option profile
may edge slightly to the right and vice versa if R or V should grow smaller
(at least up until the option expires and completely converges to spot).
A put payoff profile is shown in Figure 5.19. The lines are consistent
with the particular cash flows identified above.
With the benefit of these payoff profiles, let us now consider how com-
bining cash flows can create new cash flow profiles. For example, let™s cre-
ate a forward agreement payoff profile using options. As shown in Figure 5.20,
when we combine a short at-the-money put and a long at-the-money call
option, we generate the same return profile as a forward or future.
Parenthetically, a putable bond has a payoff profile of a long call
option, as it is a combination of being long a bullet (noncallable) bond and



Distance is
equal to SRT
Profile for spot
Return

Positive Distance is equal to
returns value of volatility
Price of option at
time of initial trade

Difference between
0 forward price and
strike price
O
Negative
returns
Inflection point where F = K

Profile for
forward/future

FIGURE 5.18 Call payoff profile.



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209
Risk Management




Return

Positive
returns




0 K“F



Negative
returns




FIGURE 5.19 Put payoff profile.




+ =



Long call option Short put option Long forward/future

FIGURE 5.20 Combining cash flows.


a long put option. A callable bond has a payoff profile of a short put option
as it is a combination of being long a bullet bond and a short call option.
Since a putable and a callable are both ways for an investor to benefit from
steady or rising interest rates, it is unusual for investors to have both puta-
bles and callables in a single portfolio. Accordingly, it is important to rec-
ognize that certain pairings of callables and putables can result in a new cash
flow profile that is comparable to a long forward/future.
Let us now look at a combination of a long spot position and a short for-
ward/future position. This cash flow combination ought to sound familiar
because it was first presented in Chapter 4 as a basis trade (see Figure 5.21).
Next let us consider how an active delta-hedging strategy with cash and
forwards and/or futures can be used to replicate an option™s payoff profile.
Specifically, let us consider creating a synthetic option.



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The distance between
where these two payoff
profiles cross the price
line is equal to SRT, cost-
of-carry.




+ =



Long spot Short forward/future Basis trade

FIGURE 5.21 A basis trade.


Why might investors choose to create a synthetic option rather than buy
or sell the real thing? One reason might be the perception that the option is
trading rich (more expensive) to its fair market value. Since volatility is a
key factor when determining an option™s value, investors may create a syn-
thetic option when they believe that the true option™s implied volatility is too
high”that is, when investors believe that the expected price dynamics of the
underlying variable are not likely to be as great as that suggested by the true
option™s implied volatility. If the realized volatility is less than that implied
by the true option, then a savings may be realized.
Thus, an advantage of creating an option with forwards and Treasury
bills is that it may result in a lower cost option. However, a disadvantage of
this strategy is that it requires constant monitoring. To see why, we need to
revisit the concept of delta.
As previously discussed, delta is a measure of an option™s exposure to
the price dynamics of the underlying security. Delta is positive for a long call
option because a call trades to a long position in the underlying security.
Delta is negative for a long put option because a put trades to a short posi-
tion in the underlying security. The absolute value of an option™s delta
becomes closer to 1 as it moves in-the-money and becomes closer to zero as
it moves out-of-the-money. An option that is at-the-money tends to have a
delta close to 0.5.
Let us say that investors desire an option with an initial delta of 0.5. If

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