DERIVATIVES AND RISK ANALYSIS Case Solution
Part A: Technical Analysis
Question 1
 The annual Return on Equity in year 1 will be 6.32 %. The calculations are shown in the Table 1.1.
Table 1.1
Principal value  $ 100  million 
Maturity  5  years 
Senior Tranche  80%  
Junior Tranche  15%  
Equity  5%  
Senior Tranche rate  6.25%  
LIBOR  3.25%  
Junior Tranche rate  6.35%  
Treasury Rate  4.35%  
Coupon rate  7.25%  
5 year swap rate  4.80%  
The annual return value on equity  $6.32  
The annual return on equity  6.32% 
 The annual Return on Equity in year 2 after the default of 3 million principal value with zero recovery rate will be 3.22 %. The calculations are shown in Table 1.2.
Table 1.2
High Yield Bonds default value with Zero Recovery 
$ 3  million 
Principal value  $ 97  million 
Maturity  5  years 
Senior Tranche  80%  
Junior Tranche  15%  
Equity  5%  
Senior Tranche rate  6.25%  
LIBOR  3.25%  
Junior Tranche rate  6.35%  
Treasury Rate  4.35%  
Coupon rate  7.25%  
5 year swap rate  4.80%  
The annual return value on equity  $ 3.13  
The annual return on equity  3.22% 

Question 2
 In order to replicate the investment; the portfolio will be a mix of cash and stocks of JPM, with equally likely in order to show the same or equal risk of default because the volatility of stocks of JPM is extreme, i.e. 25%. That is the why, the portfolio will be consisted of 50% cash and 50% JPM stocks.
Table 1.3
Portfolio will consist of  
Cash  50% 
Stocks  50% 
 If the JPM’s stock will increase by 25% and decrease by 20%, then the value of the portfolio at the end of the first year will be 97.62 million dollar, which represents a decrease of around 2.38 million dollars in the value of the portfolio.
Table 1.4
125  
Stocks Value  100  
80  
Time Step  0  1  
Value of portfolio  100  97.62 
 If the portfolio will be rebalanced in year 2, with the mix of the cash and the call options. Now, the portfolio will be a mix of cash and call options with equally likely in order to show the same or equal risk of default, the portfolio value of will further decrease in the year 2 from 97.62 million dollars to 92.67 million dollars due to the effect of the 5 percent risk free rate in the market and the cash and call options will not provide dividend and other benefits within the five year’s maturity period.
Table 1.5
Portfolio will be rebalanced  
Call options  50%  
Cash  50%  
Value of portfolio  97.62  92.97 
Question 3
 The annual cash flows at the end of the year 1 by using the arbitrage opportunity will be in negative, because the annual cash flows earned from the AIG bonds are lower than the annual cash outflow to CDS bonds. The calculations are shown in below mentioned table, which also shows the annual loss of around 69,848 dollars in first year.
Table 1.6
Principal value  $ 100  million 
Maturity  5  years 
AIG Bonds  ($110.23)  
CDS Bonds  ($110.69)  
Number of bonds purchased of AIG  907,184  
Number of bonds purchased of CDS  903,457  
AIG Bonds rate  5.50%  
LIBOR  3.25%  
CDS Bonds rate  5.60%  
Treasury Rate  4.35%  
5 year swap rate  4.80%  
Annual return if AIG Purchased  $ 4,989,513  
Annual return if CDS Purchased  $5,059,361  
Difference (Loss)  $ (69,848) 
………………….
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