Course FM Manual by Dr. Krzysztof Ostaszewski, FSA, CERA, FSAS, CFA, MAAA 2014 Edition Errata Posted October 9, 2014 The solution of Problem 5 in Practice Examination 18 should be: Let us write p for the risk-neutral probability of the stock going up. Then, based on the value of the call option, we must have 30 − 25 50 − 25 5 − 5p + 25p 5 + 20 p 20 = (1− p ) ⋅ + p⋅ = = , 1.07 1.07 1.07 1.07 so that p = ( 20 ⋅1.07 − 5) / 20 = 0.82. Therefore, the value of the one-year European put with a strike price of 40 is ( ) 0.82 ⋅ ( 0 / 1.07 ) + (1− 0.82 ) ⋅ ( 40 − 30 ) / 1.07 ≈ 1.68224299. Answer B. Posted June 2, 2014 Some printing of the manual may have items on page misplaced due to displacement of a graph. You can find a correct version of page 36 at: http://math.illinoisstate.edu/krzysio/Page36.pdf Posted May 14, 2014 The answer choice in Problem 2 in Practice Examination 2 is B, not C, as indicated. Posted April 19, 2014 In the solution of Problem 30 in Practice Examination 8, the beginning of the sentence following the first displayed equation should be: The exchange rate is then 0.80 dollars per franc instead of The exchange rate is then 0.80 francs per dollar Posted April 9, 2014 In the solution of Problem 25 in Practice Examination 19, the last part of the second displayed formula should be 750 + 350 ⋅1.04− n. Furthermore, the last displayed formula should be 5 P = 750 + 350 ⋅1.04 − n = 750 + 350 ⋅ ⋅1.04 −15 ≈ 819.41. 14 The correct answer choice is E. Posted March 20, 2014 In the solution of Problem 26 in Practice Examination 4, the calculated value for alpha has a decimal point in a wrong spot, it should be: α= 0 1.05 7 0.95 = −7 ⋅1.05 ≈ 71.3592233, 1.03⋅ ( 0.95 − 1.05 ) 1.03 1.05 1.03 0.95 and the resulting amount invested in a riskless bond is approximately $71.36. The solution and answer choice are unaffected, because the question asked about the number of shares, which is calculated correctly. Posted March 12, 2014 Analysis of answer E in Problem 1 in Practice Examination 17 should be: For E, s3 = (1+ i ) + (1+ i ) + 1 > (1+ i ) + 1+ 1 = s2 + 1, so that the numerator in E is smaller 2 than the numerator in C, while the denominator in E is clearly larger than the denominator in C. This makes E smaller than the correct answer C, so E is not true. Posted March 5, 2014 The last sentence of the solution of Problem 1 in Practice Examination 17 should be: For answer D, note that for any positive interest rate s3 = (1+ i ) + (1+ i ) + 1 > (1+ i ) + 1+ 1 = s2 + 1, 2 so that answer D, 1+ a2 + s2 a3 + s3 , is smaller than answer C, a2 + s3 a3 + s3 , and D is therefore incorrect. Posted January 15, 2014 In the solution of Problem 22 in Practice Examination 1, the value of present value of annuity due should be: a10 10% ≈ 6.75902382. This changes the subsequent calculation to 15.5 − 12 x= ≈ 40.04129432% 15.5 − 6.75902382 and answer choice is B. Posted January 15, 2014 The first displayed formula in the solution of Problem 11 in Practice Examination 1 should be 2 ⎛ i( 2 ) ⎞ 2 i = ⎜ 1+ ⎟ − 1 = (1+ 0.04 ) − 1 = 8.16%. 2 ⎠ ⎝ Posted November 2, 2013 For Problem 13 in Practice Examination 12, the answer choices should be: A. $65 or more B. Less than $65 but more than $55 C. Less than $55 but more than $45 D. Less than $45 but more than $35 E. Less than $35 and the solution should be: Given that the futures price is $660, spot price is $645, cost of carry is 2% (effectively, a negative dividend), if we write r for the current risk-free force of interest, we must have −δ t 660 = F = Se ⋅ ert = 645 ⋅ e0.02⋅1 ⋅ er⋅1 = 645 ⋅ e0.02 ⋅ er .   Forward price Ex-dividend spot price Accumulated at risk-free rate 660 = er+0.02 , and 645 ⎛ 660 −0.02 ⎞ r = ln ⎜ ⋅ e ⎟ = ln 660 − ln 645 − 0.02 ≈ 0.2989518%. ⎝ 645 ⎠ An ounce of gold costs now $645, but whoever owns it will have to pay storage cost, and the price with that storage cost included is $645 ⋅ e0.02 . An investor who buys an ounce of gold pays that and at the end of one year will either have one ounce worth $700 with probability pUP or once ounce worth $600 with probability 1− pUP , where probabilities are risk-neutral. Since these probabilities are risk-neutral, we must have $700 $600 $645e0.02 = pUP ⋅ r + (1− pUP ) ⋅ r . e e Therefore, 660 645er+0.02 − 600 645 ⋅ 645 − 600 pUP = = = 0.6, 700 − 600 100 and 1− pUP = 0.4. One year from now, the futures price will be either 660 FUP = 700 ⋅ er+0.02 = 700 ⋅ ≈ 716.28, 645 or 660 FDOWN = 600 ⋅ er+0.02 = 600 ⋅ ≈ 613.95. 645 The European call with the strike price $650 will pay $716.28 - $650 = $66.28 in the up state, and 0 in the down state, resulting in the price of the European call being 645 0.02 pUP ⋅ 66.28 ⋅ e− r = 0.6 ⋅ 66.28 ⋅ ⋅ e ≈ 39.65. 660 Answer D. Based on this,