You own the following portfolio, which is a significant part of your wealth: Face Coupon paid...

 

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You own the following portfolio, which is a significant part of your wealth: Face Coupon paid Market Value Value Security US Treasury Bill Corporate Bond Rated Aa Corporate Bond rated B Corporate Bond $20,000 $67,500 $19,192 Term(Years) Annually 1 $7,500 $60,359.2 8 $112,500 $89,968.9 10 $37,500 $39,753.2 5 0 10% 12% 15% Yield to maturity 12.14% 16.17% 13.28% Cash Find: a) Calculate the Macaulay duration of each of the securities and the Macaulay duration of the portfolio? b) Using Excel Solver shows how much would need to be invested in each instrument to obtain a portfolio Macaulay duration of 3.25 years. There are the following constraints. 1 The total investment should not change. 2 The same amount needs to be held in cash 3 A total of $100,000 market value needs to be invested in the T Bill and $20,000 in the Aa Bond. 4 Yield is maximized. c) Is default risk a major concern for this portfolio? d) The Baa rated bond has just been re-rated by one of the rating agencies and this has the impact of reducing its yield to maturity by 5 basis points. If at the same time there is a general change in interest rates so that yields fall across the whole of the yield curve by 20 basis points (including the rerated bond), what is the new value of the portfolio? You own the following portfolio, which is a significant part of your wealth: Face Coupon paid Market Value Value Security US Treasury Bill Corporate Bond Rated Aa Corporate Bond rated B Corporate Bond $20,000 $67,500 $19,192 Term(Years) Annually 1 $7,500 $60,359.2 8 $112,500 $89,968.9 10 $37,500 $39,753.2 5 0 10% 12% 15% Yield to maturity 12.14% 16.17% 13.28% Cash Find: a) Calculate the Macaulay duration of each of the securities and the Macaulay duration of the portfolio? b) Using Excel Solver shows how much would need to be invested in each instrument to obtain a portfolio Macaulay duration of 3.25 years. There are the following constraints. 1 The total investment should not change. 2 The same amount needs to be held in cash 3 A total of $100,000 market value needs to be invested in the T Bill and $20,000 in the Aa Bond. 4 Yield is maximized. c) Is default risk a major concern for this portfolio? d) The Baa rated bond has just been re-rated by one of the rating agencies and this has the impact of reducing its yield to maturity by 5 basis points. If at the same time there is a general change in interest rates so that yields fall across the whole of the yield curve by 20 basis points (including the rerated bond), what is the new value of the portfolio?

Answer rating: 100% (QA)

a To calculate the Macaulay duration of each security and the portfolio well use the following formula Macaulay Duration Present Value of Cash Flows T... View the full answer