KYNEX Bulletin - April 2007

The valuation of an Asset Swap (ASW) on a convertible security consists of two parts: valuation of the recall value and valuation of the stub. The latest release of the Kynex valuation model values the ASW stub as an American style call option on a convertible bond. The ASW recall value is calculated by our interest-rate swap calculator, and has not been changed.

Asset Swaps allow an investor to take advantage of the Gamma of the option embedded in a convertible, while providing insulation against deterioration of the credit of the issuer. Since entering into an Asset Swap releases capital, the holder of an Asset Swap can be significantly more levered than the holder of the underlying bond. This can both magnify the return on the investment (in favorable circumstances) and lead to a greater negative return (in unfavorable circumstances).

While we use an American call option framework to value the ASW stub, it is important to note certain differences between a simple call option on a stock and a call option on a convertible. An Asset Swap typically expires on the first call date (or first put date) of a convertible, i.e. the bond typically does not terminate prior to the expiration of the Asset Swap. However, we have also observed several examples of Asset Swaps which expire on the maturity of the underlying bond, even though the bonds are callable and/or put-able prior to maturity. The model enforces the boundary condition that if the underlying bond is called (or put) before the expiration of the Asset Swap, the Asset Swap terminates at the same time that the underlying bond is terminated. The recall strike of an Asset Swap accretes with time (reaching par at the expiration of the Asset Swap) i.e. if the stock price does not change over time, the option goes more out of the money; hence the time value of an Asset Swap decreases faster than that of a fixed-strike option (higher negative Theta). This is a subtlety not encountered in pricing standard equity options. The accreting strike feature is also included in the Kynex valuation model.

In general, we expect an Asset Swap to be favorable in the following scenarios:

- Credit of the issuer of the convertible deteriorates considerably

- Interest rates rise meaningfully

- Volatility rises meaningfully and Gamma is realized

- Desire to not lock-up capital or hedge fund does not have enough capital

- Coupon on the convert is small and recall spread is tight

We also expect an Asset Swap might not be advantageous in the following scenarios:

- Recall spread is wide to begin with and credit tightens considerably

- Interest rates decline meaningfully

- Volatility collapses and very little Gamma is realized

- Coupon on the convert is big and recall spread is wide

We present various scenarios analyzed by us to quantify the advantages of entering into an Asset Swap vs. holding the underlying bond.

Scenarios

A few highlights are worth noting before delving into the details.

- The ASW holder does not receive any coupons but does not need to finance the “bond” portion that is swapped away. The convertible holder receives the coupons but has to finance the entire market value of the convertible. This dynamic affects the cost of carry in a significant way. For low-coupon convertibles, the ASW holder is not giving up much but the convertible holder is financing the bond at a much higher rate than the coupon received. For high-coupon convertibles, the ASW holder is giving up quite a bit and the convertible holder is able to offset the cost of financing with the coupons received.

- Since the ASW has a higher negative Theta than the convertible, the holder of the Asset Swap needs to realize volatility and/or the interest rates have to rise to overcome the higher rate of time decay.

- If an investor is concerned about the deterioration of the credit of the issuer, the underlying bond should be valued with our bankruptcy mode turned on. (The description of the Kynex convertible valuation model with bankruptcy mode is described in the Dec 2003 Kynex Bulletin.) We analyzed the relative merits in both modes i.e. bankruptcy mode turned on and off. For the bankruptcy mode, we employed a decay factor of 1, which means that the credit spread is expected to double if the stock price declines to half of its current level. When using the bankruptcy mode, you can set the decay factor to an appropriate level based on the issuer’s expected creditworthiness, etc. In practice, we found that the merit of entering into an Asset Swap (as opposed to holding the underlying bond), does not depend on whether the bankruptcy mode is on or off.

- The Kynex calculator values the underlying convertible using the risky-risky framework (risky stock growth, risky discounting of cash flows), and the Asset Swap as risk-free (risk-free stock growth, risk-free discounting).

The quantitative comparisons were performed using the Kynex Impact Analysis. The initial position consisted of 1,000 (1 million face) convertible bonds or Asset Swap on 1,000 bonds. In each case, a short stock hedge was set up to make the initial portfolio Delta-neutral. A time horizon of 1 yr was employed. The P&L from Gamma trading was calculated using the Hedge Calculator. For our investigations, we used two example bonds and Asset Swaps:

The first example is a bond with a relatively low coupon and the Asset Swap has a tight recall spread. We used the AMGN Tranche-1 0.125% 2011 convertible bond. This is a bullet bond. We created an Asset Swap, whose expiration is equal to the maturity of the bond (Feb 1, 2011), and a recall spread of 30 bps.

The second example is a bond with a higher coupon and the Asset Swap has a wide recall spread. We used the China Medical (CMED) 3.5% 2011 bond (also a bullet bond). We created an Asset Swap whose expiration is also equal to the maturity of the bond (Nov 15, 2011), and a recall spread of 300 bps.

We considered two possibilities for our analysis:

The investor enters into an Asset Swap, which releases capital, thereby making the investor more levered than a bondholder.

The Asset Swap holder invests the released capital at the risk-free rate. In this scenario, the Asset Swap holder locks up the same capital (and has effectively the same leverage) as a bondholder.

For each of the above possibilities, we valued the bond and Asset Swap with the bankruptcy mode turned on and off. Hence there were a total of four calculations for each scenario. The quantitative results for the AMGN bond/Asset Swap are summarized in Table 1 and for the CMED bond/Asset Swap in Table 2 (see below).

At the initiation of an Asset Swap, the recall spread of an Asset Swap is equal to the credit spread of the issuer. In our analysis, we therefore valued the AMGN bond and ASW with a spread of 30 bps, and the CMED bond and ASW with a spread of 300 bps. The stock price, bond price, volatility, credit spread and yield curve, etc., used for our analysis are shown in Table 3 below. Additional pertinent ancillary data are presented in Tables 4 and 5. Table 4 shows the final bond price, ASW recall value and stub value for the various scenarios. Table 5 shows the P&L (from Gamma trading of the stock) and the carry for the bond and ASW. The carry for the AMGN Asset Swap is substantially higher than for the convertible, because the bondholder has to finance the bond, and receives little income from the small coupon. The carry for the CMED Asset Swap is about the same as that of the convertible because in this case the bondholder receives a substantial income from the large coupon, which offsets the financing of the bond position.

The ratio of (recall value)/(convertible price) is a measure of how soon the Asset Swap hits its floor as the credit deteriorates. The bond price, Asset Swap recall value, and the above ratio are also presented in Table 3. The value of the ratio is 0.92 for AMGN and 0.76 for CMED. Hence the CMED Asset Swap has a longer way to go to hit the floor. This means that the CMED Asset Swap has much more negative time decay than the AMGN Asset Swap. Our analysis illustrates how the larger time decay of the CMED Asset Swap considerably reduces its rate of return, making it a less attractive investment compared to the AMGN Asset Swap.

We summarize the results of our study below.

Stock Price, Volatility, Credit Spread, and Interest Rates are Unchanged

For both AMGN and CMED (with and without the bankruptcy mode), the underlying bond outperforms the Asset Swap. This can be attributed to the higher rate of time decay of the Asset Swap relative to its underlying bond. (Recall that the upward accretion of the strike price with time causes an Asset Swap to go out of the money if all other parameters remain constant.) Basically, if volatility is not realized and/or interest rates do not increase, then an Asset Swap is not advantageous.

Stock Price Falls, Credit Spread Widens, and Implied Volatility Increases

We expect that a fall in the stock price may be correlated with a deterioration of the credit of the issuer (i.e. wider credit spread). The volatility may also typically increase. The widening of the credit spread and increase in the implied volatility are offsetting factors with respect to the change in the value of the Asset Swap.

The AMGN Asset Swap outperformed the underlying bond.

The CMED Asset Swap underperformed relative to the underlying bond. This was traced to the effect on carry (as described earlier) due to the high coupon as well as the distance between the market price and the ASW recall value. The increase in the implied volatility helps the Asset Swap holder, but (in the case of CMED) not by enough to outperform the bondholder. Both the AMGN and CMED Asset Swaps hit their respective floors in this scenario. For AMGN the floor is 87.0. The initial market price is 90, so the ASW investor suffers a loss of 3.0 before the floor kicks in. For CMED the floor is 85.4. The initial market price is 107, so the investor suffers a loss of 21.6 points before the floor kicks in. An Asset Swap investor is only protected against a widening of the credit spread after the floor is reached. Hence an investor holding the CMED Asset Swap loses substantial value if the spread widens, before the protection of the Asset Swap takes effect.

The above statements were made assuming that the Asset Swap investor is more highly levered than the bondholder. If the Asset Swap holder has the same capital as the bondholder, and invests the extra capital at the risk free rate, then in both examples the Asset Swap holder receives a better return than the bondholder.

The use of the bankruptcy mode changes the quantitative numbers but does not alter the above conclusions.

Stock Price Rises, Credit Spread Tightens, and Implied Volatility Decreases

We might expect that the results will be the opposite of the previous scenario. Both the AMGN and CMED Asset Swaps under-perform compared to their underlying bonds. The magnitude of the under-performance of the CMED Asset swap is much more than that of the AMGN. This is due to the effect on the carry (as described earlier) due to the higher coupon on the CMED convertible. The above statements assume that the Asset Swap investor is more highly levered than the bondholder. If the Asset Swap holder has the same capital as the bondholder, and invests the extra capital at the risk free rate, then the magnitude of under-performance of the Asset Swap is lesser.

The use of the bankruptcy mode changes the quantitative numbers but not the relative performances of the bonds and Asset Swaps.

Interest Rates Rise/Fall 100 bps

We hold the stock price etc., fixed in the Impact Analysis, but apply an impact of a 100bp rise/fall (parallel shift) in the interest rates. We expect that if interest rates rise, the Asset Swap outperforms the bond, and if interest rates fall, the Asset Swap will give a lower rate of return than the underlying bond.

Our findings do not completely confirm this expectation. For the AMGN bond and Asset Swap, the above behavior is observed (with both the bankruptcy mode on and off). The CMED Asset Swap, however, underperforms the bond even when interest rates rise, when the bankruptcy mode is off. This is again due to the effect on carry due to the high coupon as well as the longer distance between the market price and the ASW re-call value. When the bankruptcy mode is on, the CMED Asset Swap outperforms the underlying bond when the interest rates rise. The CMED Asset Swap underperforms the bond when the interest rates fall, both with and without the bankruptcy mode on.

The above statements assume that the Asset Swap investor is more levered than the bondholder. If the Asset Swap holder has the same capital as the bondholder (and invests the extra capital at the risk-free rate), then the return obtained by the Asset Swap holder might or might not be better than the bondholder when interest rates rise (both with and without the bankruptcy mode) depending on other factors such as carry, theta, etc.

The above findings for CMED are consistent with our expectation that an Asset Swap is not advantageous if the bond pays a large coupon and has a wide spread to begin with.

Credit Default Swap (CDS)

Another possibility for the investor to hedge against deterioration in the credit of the issuer is to buy protection via a Credit Default Swap (CDS). Please refer to our December 2006 Bulletin for more details. In this scenario, the investor holds the underlying convertible bond, and therefore does not unlock any capital. The CDS requires deal payments, which can drag down the return on the portfolio. The CDS reduces the required short stock position to be Delta-neutral since the CDS provides a hedge against credit deterioration which is correlated with stock price declines (most of the time), so in our analysis below we employed a lighter stock hedge.

We considered an example CDS on the AMGN Tranche 1 bond. The deal spread on the CDS is 30 bps (equal to the recall spread of the Asset Swap). The CDS maturity was set to March 20, 2011 (with a first coupon date of June 20, 2007). From Table 3, the hedge Delta of the bond is 48. We set the CDS notional to hedge 8%, and hedged the remaining 40% with a short stock position. The return on the bond + CDS + short stock position was calculated for a horizon of 1 year (the same as with the Asset Swap). Table 6 shows the return on the CDS (with a stock hedge of 40%, as noted above). The corresponding return obtained by using an Asset Swap (with a stock hedge of 48%) is also shown. The data for the Asset Swap was copied from Table 1 (the data where the bankruptcy mode was turned on). The returns are presented for the two scenarios

· stock price declines, spreads rise, implied volatility increases

· stock price rises, spreads tighten, implied volatility decreases

Note that the bankruptcy mode must be turned on when valuing the bond (the use of a CDS implies a probability of default). Recall that we set the decay factor to 1. We see from Table 6 that the use of a CDS (and light short stock position) does not give as good a return as the use of an Asset Swap in the first scenario (stock price declines and the spread widens). The CDS gives a better return than an Asset Swap when the stock price increases and the spreads tighten. This is because, in this scenario, the Asset Swap suffers from the reduction in the realized volatility and has large time decay. The bond + CDS portfolio does not have such large time decay.

For reference, we also constructed a CDS on the CMED bond, and display the results in Table 6. The deal spread on the CDS is 300 bps (equal to the recall spread of the Asset Swap). The CDS maturity was set to Dec 20, 2011 (with a first coupon date of June 20, 2007). For CMED, we already know that the convertible bond by itself (with Delta-neutral short stock hedge) outperforms the Asset Swap in both cases when the stock falls and credit widens and the stock rises and credit tightens. The use of a CDS (with a light stock hedge of 60 instead of 68) also outperforms the Asset Swap in both of the above scenarios.

However, there are other factors to consider when deciding to hedge with a CDS or to enter into an Asset Swap. There is no clear-cut best solution. Some points to note are:

A CDS is more liquid than an Asset Swap. Furthermore, the bond and CDS trade independently, so it is easier for the investor to change the position in the bond and/or CDS.

An Asset Swap holder is essentially locked into the position until the expiration (or recall) of the Asset Swap. To change the position, the investor must buy new convertibles and enter into a new Asset Swap agreement with a broker.

A CDS does not release capital, whereas an Asset Swap does. A hedge fund with limited capital may have no choice but to enter into an Asset Swap.

Metrics

We compare various metrics of an Asset Swap vs. the underlying bond below. For example, Asset Swaps usually have a lower Delta than the underlying bond, and are therefore hedged using a smaller short stock position. Furthermore the value of Rho is negative for a convertible bond, but is positive for an Asset Swap. Hence an Asset Swap has an implicit hedge against a rise in interest rates, as we noted in the Impact Analysis study above.

We performed sweeps with the bankruptcy mode off and also with the bankruptcy mode on. With the bankruptcy mode off, we used the AMGN bond and Asset Swap mentioned above. We performed four sets of sweeps (Spot price, Volatility, Credit Spread and an Interest Rate Shift (parallel shift of yield curve)). The graphs are shown in Figures 1 through 28 below. With the bankruptcy mode on, we employed the CMED bond and Asset Swap mentioned above. The graphs are shown in Figures 29 through 36 below.

Bankruptcy Mode Off

We discuss the case of bankruptcy mode on below, after first analyzing the results for the case of bankruptcy mode off. The input parameters for the AMGN bond and Asset Swap are the same as in Table 3, except for the credit spread. If an Asset Swap is valued by setting the credit spread of the underlying bond equal to the ASW recall spread, then we have found that the median life of the Asset Swap is zero. The advantage of entering into an Asset Swap is based on the expectation of the future credit spreads, behavior of the volatility and interest rates etc. For the purposes of comparison of the bond and Asset Swap metrics, we valued the AMGN bond with a credit spread of 150 bps.

We swept the stock price, volatility, credit spread and interest rates. For each sweep, we plotted graphs of the bond fair value and Asset Swap stub fair value, Delta, Gamma, Vega, Rho, Credit Spread 01, Theta and the median life. In all the graphs, the dark blue curve describes the bond and the pink curve describes the Asset Swap. We analyze the comparison of the metrics below.

Stock Sweep

The graphs obtained by sweeping the stock price are the most informative of the various sweeps.

· The first graph displays the bond fair value and Asset Swap stub as a function of the stock price. As expected, they both have a (smoothed out) hockey stick shape.

· The graph of Delta indicates that the Asset Swap has a lower Delta than the bond. This is consistent with the market expectation that holding an Asset Swap requires a smaller hedge than holding a bond.

· The Gamma of the Asset Swap has a peak which is slightly higher than the bond, and the location of the peak is also slightly displaced to a higher stock price. At about S=110, the two graphs coincide. At this stock price level, the median life of the Asset Swap decreases to zero, and so the Gamma of the Asset Swap equals that of the bond.

· The Vega curve is similar to the Gamma curve.

· The graph of Rho shows a significant difference in the behavior of the Asset Swap and the bond. The curves are parallel, but Rho is positive for the Asset Swap and negative for the bond. This is indicative of the fact that the Asset Swap holder is not exposed to the interest rate sensitivity of the “pure bond” part of the convertible (which is negative).

· The graph of the credit spread01 sensitivity also shows a significant difference in the behavior of the Asset Swap and the bond. The curve for the bond is negative. The curve for the Asset Swap is almost zero, indicative of the fact that the Asset Swap holder has divested himself of the credit risk of the issuer.

· The graph of Theta shows that the Asset Swap has more negative time decay than the underlying bond. Roughly speaking, the pure bond part of the convertible has a positive Theta (accretion to par), and the option part has a negative Theta. The Asset Swap holder has only the option part. Effectively, the Asset Swap holder has removed the exposure to the credit risk of the issuer, but at the price of more negative time decay.

· The median life of the bond is always equal to the time to maturity, since this is a bullet bond. The median life of the Asset Swap is also equal to the time to maturity at low stock prices, but then decreases with increasing stock price and drops to zero above about S=110. At such high values of S, the sensitivity to credit spread is very small, and the expected value of the cash flows including the value of the option embedded in the bond make it preferable to hold the convertible.

Volatility Sweep

The graphs obtained by sweeping the volatility are mostly featureless, and are included for completeness of the presentation. The median life of the Asset Swap displays a complicated dependence on the volatility, but it is difficult to draw any conclusions from this fact.

Credit Spread Sweep

The graphs obtained by sweeping the credit spread illustrate one fairly obvious point. In all the plots, the curve for the Asset Swap becomes flat as the credit spread is increased. This is consistent with our expectation that, at high spreads, the bond value declines and contributes little to the valuation of the Asset Swap. (Think of a deep out of the money option.) The Asset Swap (which is valued on a risk-free basis) is then insensitive to the precise value of the credit spread, leading to flat curves in the plots.

Interest Rate Shift

Unlike a sweep of the credit spread, an interest rate shift changes the risk-free interest rate. This affects the recall value of the Asset Swap, whereas a change in the credit spread does not. The curves for the Asset Swap therefore do not flatten out as the risk-free rate increases. The graph of the Asset Swap stub and bond fair value is the most informative. Since the Asset Swap has a positive Rho and the bond has a negative Rho, the ASW stub value and the bond fair value move in opposite directions as the risk-free rate increases.

Bankruptcy Mode On

We now discuss the case of bankruptcy mode on. As stated above, we employ the CMED bond and Asset Swap. The parameters are the same as in Table 3. We swept only the stock price. We know that when the bankruptcy mode is on, at low parity the fair value of the bond drops to zero, the bond Delta increases (in principle to infinity at zero parity), and the Gamma is negative. However, the Asset Swap stub value has a floor of zero and the Delta and Gamma behave more like those of an equity call option, i.e. Delta increases from 0 and 100 in an S-curve as the stock price increases, and Gamma is always positive. Hence we expect a significant difference in the graphs of the bond and the Asset Swap. This is confirmed in Figures 29 through 36 below. We again plotted graphs of the bond fair value and Asset Swap stub fair value, Delta, Gamma, Vega, Rho, Credit Spread 01, Theta and the median life. In all the graphs, the dark blue curve again describes the bond and the pink curve describes the Asset Swap.

We see that the median life of the Asset Swap drops to zero at about S=26. The interesting behavior is when the Asset Swap median life is nonzero, i.e. S<26. As the parity decreases to zero, the holder of an Asset Swap would decrease the stock hedge to zero, whereas a bondholder would need to increase the stock hedge. Furthermore, the bondholder would be hurt by the negative Gamma, but an Asset Swap holder does not have this problem. Furthermore, even in the region where both the bond and Asset Swap have positive Gamma (e.g. S=24, which is the stock price used in the scenario analysis above), the Asset Swap has substantially more Gamma than the bond. This explains why, in Table 5, the P&L for the CMED Asset Swap, with bankruptcy mode on, is substantially larger than the P&L for the underlying convertible.

The graph for Rho (Figure 33) indicates that the Asset Swap continues to have an implicit hedge against a rise in interest rates, and the graph for Theta (Figure 35) indicates that the Asset Swap continues to have more negative time decay than the underlying bond. Switching on the bankruptcy mode does not change these aspects of the behavior of an Asset Swap.

The graphs for the AMGN Asset Swap and bond, with the bankruptcy mode on, are similar but the differences are not as pronounced. Basically, with the bankruptcy mode on, if the median life of the Asset Swap is nonzero, then the Asset Swap has a substantially larger Gamma than the underlying convertible, as well as a smaller Delta (which goes to zero whereas the bond Delta goes to infinity at zero parity). The Asset Swap holder can realize much greater P&L from Gamma trading.

Table 1 – Return on Bond and Asset Swap for AMGN Tranche 1

Scenario	Bankruptcy Mode Off						Bankruptcy Mode On
	Bond		ASW				Bond		ASW
	Bond		No excess capital		Invest excess capital at risk-free rate		Bond		No excess capital		Invest excess capital at risk-free rate
	Return	P&L($)	Return	P&L($)	Return	P&L($)	Return	P&L($)	Return	P&L($)	Return	P&L($)
Unchanged	5.33%	11,990	3.23%	610	4.85%	10,917	5.14%	11,576	0.97%	182	4.66%	10,489
Interest Rates Rise 100 bps	– 2.17%	–4,890	37.02%	7,020	7.70%	17,322	–2.33%	–5,234	35.20%	6,677	7.55%	16,978
Interest Rates Fall 100 bps	13.32%	29,970	–28.95%	–5,489	2.14%	4,812	13.09%	29,446	–31.36%	–5961	1.93%	4,338
Stock Down 20%, Spread Widens, Implied Volatility Increases	–0.70%	–1,586	137.15%	25,953	16.11%	36,257	–6.70%	–15,070	134.75%	25,499	15.91%	35,803
Stock Up 20%, Spread Tightens, Implied Volatility Decreases	–2.25%	–5,054	–87.79%	–16,398	–2.70%	–6,082	–2.18%	–4,908	–86.90%	–16481	–2.75%	–6,180

Table 2 – Return on Bond and Asset Swap for CMED

Scenario

Bankruptcy Mode Off

Bankruptcy Mode On

Bond

ASW

Bond

ASW

No excess capital

Invest excess capital at risk-free rate

No excess capital

Invest excess capital at risk-free rate

Return

P&L($)

Return

P&L($)

Return

P&L($)

Return

P&L($)

Return

P&L($)

Return

P&L($)

Unchanged

8.95%

23,935

–23.58%

–15,029

–1.81%

–4,840

6.83%

18,723

–2.79%

–1,776

3.14%

8,412

Interest Rates Rise 100 bps

2.17%

5,795

–6.40%

–4,080

2.28%

6,109

0.56%

1,493

16.58%

10,562

7.76%

20,751

Interest Rates Fall 100 bps

16.19%

43,295

–40.68%

–25,923

–5.88%

–15,734

13.47%

36,033

–22.40%

–14,270

–1.53%

–4,081

Stock Down 20%, Spread Widens, Implied Volatility Increases

–88.54%

–236,846

–183.78%

–117,150

–39.99%

–106,962

–95.3%

–254,798

–171.4%

–109,268

–37.04%

–99,080

Stock Up 20%, Spread Tightens, Implied Volatility Decreases

2.16%

5,765

–52.81%

–33,649

–8.77%

–23,460

5.33%

14,263

–9.08%

–5787

1.65%

4,402

Table 3 – Input Parameters for P&L and Impact Analysis

Parameter	AMGN	CMED
Bond Price	90	107
ASW Recall Value	82.45	81.51
Recall Value/Bond Price	0.92	0.76
Stock Price	60	24
Volatility	19	35
Credit Spread (bps)	30	300
Yield Curve	US $Swap	US $Swap
Borrow Cost	0	0
Dividend Model	Continuous	Continuous
Bond/ASW Quantity	1000	1000
Delta Hedge	48	68
Finance/Rebate Rate	5.75/5.00	5.75/5.00
Horizon	1 year	1 year
Leverage	4	4
Bond Capital ($)	225,000	267,500
ASW Capital ($)	18,877	63,727
ASW Leverage if no excel capital	47.7	16.8

Table 4 – Bond Price and ASW Recall Value & Stub Value

Scenario	AMGN			CMED
	Bond Price	ASW		Bond Price	ASW
	Bond Price	Recall Value	Stub Value	Bond Price	Recall Value	Stub Value
Initial	90	82.45	7.55	107	81.51	25.49
Interest Rates Rise 100 bps	90.0	84.66	5.34	103.93	82.52	21.41
Interest Rates Fall 100 bps	93.48	89.39	4.08	107.69	88.45	19.24
Stock Down 20%, Spread Widens, Implied Volatility Increases	83.12	87.01	0	69.55	85.42	0
Stock Up 20%, Spread Tightens, Implied Volatility Decreases	97.20	87.33	9.87	114.02	85.43	28.60

Table 5 – Gamma Trading P&L and Carry for Bond & ASW

Scenario	AMGN		CMED
Scenario	Bond	ASW	Bond	ASW
P&L Bankruptcy Mode Off	14,680	14,680	22,147	22,147
P&L Bankruptcy Mode On	14,226	14,226	11,115	30,029
Carry	–19,580	14,828	14,218	14,396

Table 6 – Return on Portfolio using CDS or Asset Swap

Scenario	AMGN			CMED
	Bond + CDS + light hedge	ASW (from table 1)		Bond + CDS + light hedge	ASW (from Table 2)
	Bond + CDS + light hedge	No excess capital	Invest excess capital at risk-free rate	Bond + CDS + light hedge	No excess capital	Invest excess capital at risk-free rate
Stock Down 20%, Spread Widens, Implied Volatility Increases	10.22%	134.75%	15.91%	–92.5%	–171.41%	–37.04%
Stock Up 20%, Spread Tightens, Implied Volatility Decreases	–3.58%	–83.33%	–2.65%	4.94%	–9.08%	1.65%