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DERIVATIVES AND RISK ANALYSIS Case Solution & Answer

DERIVATIVES AND RISK ANALYSIS Case Solution

Part A: Technical Analysis

Question 1

  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%
  1. 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%
  1. Question 2

  1. 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%

 

  1. 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

 

  1. If the portfolio will be re-balanced 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

  1. 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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