2006_exam_solutions_slides

2006_exam_solutions_slides - 1 If i = 0.05 calculate to 4...

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1 Financial Mathematics MA315/715 2006 Past Exam Paper 1. If i = 0.05, calculate to 4 decimal places; (a) 10 a && (b) (2) 15 a (c) ( ) 5 Da (d) (4) a (e) 4 s (f) 9 ( ) Ia [10 marks] Comment: You have been asked to round to 4dp so don’t forget to do it. 1. 10 9 ) 1 8.1078 a a a = + = && (2) (2) 15 15 ) 10.3797 1.012348 10.5079 i b a a i = × = × = ( ) 5 5 5 ) 6 ( ) 6 4.3295 12.5664 13.4106 c Da a Ia = - = × - = (4) (4) 1 1 ) 20.3712 0.049089 d a i = = = 4 4 ) 4.3101 1.024797 4.4170 i e s s δ = × = × = ( ) ( ) 9 9 ) 33.2347 1.024797 34.0588 i f Ia Ia δ = × = × = [10] 2. State the three most popular explanations for the term structure of interest rates. [3 marks] Comment: very badly answered question – do NOT forget to learn the ‘wordy’ parts of the course i.e. definitions, ads and disads, proofs etc…. 2. Expectations Theory [1] Liquidity Preference Theory [1] Market Segmentation [1] Comment: You were asked to STATE, therefore do not need to waste time with a full explanation. Remember to read questions carefully to decide what is expected. 3. Company shares with a current dividend yield of 5% have a share price of £25 per share. Calculate the forward price of a 3-year forward contract on the asset if the risk free effective rate of interest is 6% per annum. State any assumptions that you make. [3 marks]
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2 3. Assume : Dividends are paid continuously Principal of No Arbitrage Now 0 0.05 3 25 0.06 0.0583 D T S i δ = = = = = Then ( ) 3(0.058 0.05) 0 25 £25.63 T D K S e e δ - - = = = per share [3] Comment: do NOT forget the ASSUMPTIONS, note you have been given i = 6% NOT δ = 6% 4. Assuming; 1 2 4 1,4 6% 6.25% 6.5% 5% y y y f = = = = (a) Calculate the 5-year spot rate (b) Calculate the 2-year forward rate in 2 years time [4 marks] 4. a) 4 1 1,4 (0,5) (0,1) (1,4) (1 ) (1 ) A A A y f = × = + × + 5 4 5 5 (1 ) 1.06 1.05 5.20% y y + = × = [2] b) (0,4) (2,2) (0,2) A A A = 4 4 2 4 2,2 2,2 2 2 2 (1 ) 1.065 (1 ) 6.75% (1 ) 1.0625 y f f y + + = = = + [2] 5. A 10-year loan stock has a coupon of 12% per annum payable half yearly in arrear and is redeemable at par. (a) Write down an expression for the price per £100 nominal of the loan stock. (b) If an investor requires a gross redemption yield of i , state for what values of i the loan stock will be priced at less than £100 per £100 nominal. [4 marks] 5. (2) 10 10 12 100 P a v = + and require P < 100 (2) 10 10 12 100 100 a v + < P = 100 if yield = coupon rate i.e. 12% p.a. convertible half yearly i.e. P < 100 if (2) 12% i > i.e. P < 100 when (2) 2 (1 ) 1 2 i i > + - i.e. if i > 12.36% [4] 6. Order by magnitude (from smallest to largest) the following; (a) % 5 = i (b) % 5 = d (c) (2) 5% i = (d) (12) 5% i = (e) % 5 = δ [5 marks]
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