EC3333 MidTermPaper2011Fall_answer

EC3333 MidTermPaper2011Fall_answer - EC3333 NATIONAL...

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EC3333 NATIONAL UNIVERSITY OF SINGAPORE EC3333 FINANCIAL ECONOMICS I: MID-TERM (SEMESTER I : AY2011-2012) Time Allowed: 1.5 Hours INSTRUCTIONS TO CANDIDATES 1. This examination paper contains 3 questions and comprises 6 printed pages including this front page. The last page provides a formula which you may find useful. 2. Answer all questions. 3. Total marks are 30 . 4. Use question paper t o a n sw e r . W r i t e d ow n y o u r Matriculation Number, Name and Tutorial Group Number (e.g. W1, W2 etc.) on your question paper. 5. This is a CLOSED BOOK examination.
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EC3333 2 1. (16 marks) There are 3 assets for an investor to form his/her portfolio. A T-bill has a rate of return of 1%; Risky asset A’s rate of return has an expectation of 3% and a standard deviation of 1%; Risky asset B’s rate of return has an expectation of 5% and a standard deviation of 2%. The rates of return of assets A and B are independent. (a) Please derive the mathematical expression for the efficient frontier. (3 marks) 0004 . 0 ) 1 ( 0001 . 0 ) 1 ( 02 . 0 05 . 0 05 . 0 ) 1 ( 03 . 0 ) 1 ( ) 1 ( 2 2 2 2 2 2 2 A A B A A A r A A A B A A A B A A A Er Er Er r r r 0004 . 0 )] 05 . 0 ( 50 1 [ 0001 . 0 )] 05 . 0 ( 50 [ ) 1 ( ) 05 . 0 ( 50 2 2 2 2 2 2 2 Er Er Er B A A A r A (b) Please solve for expected rate of return of the minimum-variance portfolio constructed from the two risky assets. (3 marks) . 034 . 0 05 . 0 5 1 03 . 0 5 4 5 4 0004 . 0 0001 . 0 0004 . 0 ) , cov( 2 ) , cov( : 5 1 5 4 0 0004 . 0 ) 1 ( 2 0001 . 0 2 2 2 2 2 Er r r r r e Alternativ d d B A B A B A B A B A A A A r
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EC3333 3
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EC3333 MidTermPaper2011Fall_answer - EC3333 NATIONAL...

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