NPTEL DEPARTMENT OF INDUSTRIAL AND MANAGEMENT ENGINEERING IIT KANPUR QUANTITATIVE FINANCE END-TERM EXAMINATION (2015 JULY-AUG ONLINE COURSE)

Size: px

Start display at page:

Download "NPTEL DEPARTMENT OF INDUSTRIAL AND MANAGEMENT ENGINEERING IIT KANPUR QUANTITATIVE FINANCE END-TERM EXAMINATION (2015 JULY-AUG ONLINE COURSE)"

Heather Dana Boone
5 years ago
Views:

1 NPTEL DEPARTMENT OF INDUSTRIAL AND MANAGEMENT ENGINEERING IIT KANPUR QUANTITATIVE FINANCE END-TERM EXAMINATION (2015 JULY-AUG ONLINE COURSE) READ THE INSTRUCTIONS VERY CAREFULLY 1) Time duratio is 2 hours 2) The total marks is ) This questio paper cosists of TWO sectios. 4) Sectio#1-Subjective: 3 questios havig multiple subparts each. There is step markig for all questios. You have to show all workig ad calculatios to get the full marks. If your fial aswer is icorrect eve though your approach is right, marks will be provided for workig show. There is o egative markig i this sectio. 5) Sectio#2-Objective: 15 questios. Correct aswer: 4 marks. Icorrect aswer: -1 marks. No marks for questios left uatteded. 6) Write all aswers i the aswer sheets provided. Do ot use separate aswer sheets for objective questios. Please write the optio umber (A, B, C. etc.) very clearly i the same aswer sheets provided ad give explaatio wherever it is asked. 7) Questios are self-explaatory. Make ecessary assumptios wherever required. 8) Oly o-programmable calculators are allowed. PART#1 Subjective Questio # 1: [Marks#30 (10*3)] 1. Hospitality Hotels forecasts mothly labour eeds. a) Give the followig mothly labour figures, make a forecast for Jue usig a threeperiod movig average ad a five-period movig average. Moth Actual Values Jauary 32 February 41 March 38 April 39 May 43 b) What would be the forecast for Jue usig the aïve method? c) If the actual labour figure for Jue turs out to be 41, what would be the forecast for July usig each of these models? d) Compare the accuracy of these models usig the mea absolute deviatio (MAD), mea squared error (MSE).

2 2. The maager of a small health cliic would like to use expoetial smoothig to forecast demad for laboratory services i their facility. However, she is ot sure whether to use a high or low value of α. To make her decisio, she would like to compare the forecast accuracy of a high ad low α o historical data. She has decided to use α = 0.7 for the high value ad α = 0.1 for the low value. Give the followig historical data, which do you thik would be better to use? Week Demad (labour requiremet) A compay uses expoetial smoothig with tred to forecast mothly sales of its products, which show a tred patter. At the ed of week 5, the compay wats to forecast sales for week 6. The tred through week 4 has bee 20 additioal cases sold per week. Average sales have bee 85 cases per week. The demad for week 5 was 90 cases. The compay uses α =.20 ad β =.10. Make a forecast icludig tred for week 6. Questio # 2: [Marks#30 (15+15)] a) Near market closig time o a give day, you lose access to stock prices, but some Europea call ad put prices for a stock are available as follows: Strike Price Call Price Put Price $40 $11 $3 $50 $6 $8 $55 $3 $11 All optios have the same expiratio date. After reviewig the iformatio above, Joh tells Mary ad Peter that o arbitrage opportuities ca arise from these prices. Mary disagrees with Joh. She argues that oe could use the followig portfolio to obtai arbitrage profit: Log oe call optio with strike price 40; short three call optios with strike price 50; led $1; ad log some calls with strike price 55. Peter also disagrees with Joh. He claims that the followig portfolio, which is differet from Mary s, ca produce arbitrage profit: Log 2 calls ad short 2 puts with strike price 55; log 1 call ad short 1 put with strike price 40; led $2; ad short some calls ad log the same umber of puts with strike price 50. Which of the followig statemets is true? (i) Oly Joh is correct. (ii) Oly Mary is correct. (iii)oly Peter is correct. (iv) Both Mary ad Peter are correct. (v) Noe of them is correct.

3 b) A isurace compay sells sigle premium deferred auity cotracts with retur liked to a stock idex, the time-t value of oe uit of which is deoted by S (t). The cotracts offer a miimum guaratee retur rate of g%. At time 0, a sigle premium of amout is paid by the policyholder, ad (π * y) % is deducted by the isurace compay. Thus, at the cotract maturity date, T, the isurace compay will pay the policyholder: You are give the followig iformatio: (i) The cotract will mature i oe year. (ii) The miimum guaratee rate of retur, g%, is 3%. (iii) Divideds are icorporated i the stock idex. That is, the stock idex is costructed with all stock divideds reivested. (iv) S (0) = 100. (v) The price of a oe-year Europea put optio, with strike price of $103, o the stock idex is $ Determie y%, so that the isurace compay does ot make or lose moey o this cotract. Questio # 3: [Marks#30 (15+15)] a) For a two-period biomial model, you are give: (i) Each period is oe year. (ii) The curret price for a o-divided-payig stock is 20. (iii) u = , where u is oe plus the rate of capital gai o the stock per period if the stock price goes up. (iv) d = , where d is oe plus the rate of capital loss o the stock per period if the stock price goes dow. (v) The cotiuously compouded risk-free iterest rate is 5%. Calculate the price of a America call optio o the stock with a strike price of 22. b) You are cosiderig the purchase of 100 uits of a 3-moth 25-strike Europea call optio o a stock. You are give: (i) The Black-Scholes framework holds. (ii) The stock is curretly sellig for 20. (iii) The stock s volatility is 24%. (iv) The stock pays divideds cotiuously at a rate proportioal to its price. The divided yield is 3%. (v) The cotiuously compouded risk-free iterest rate is 5%. Calculate the price of the block of 100 optios.

4 PART#II - Objective 1) You have three (3) fiacial assets with the followig set of iformatio Asset (i) A B C Average retur A B C If SS is allowed, the at MVP the weights of A, B ad C are (A) (6/12, 4/12, 3/12) (B) (3/12, 6/12, 4/12) (C) (4/12, 3/12, 6/12) (D) oe of the above 2) For, problem # 1, give above, the retur at MVP is (A) 4.00 (B) 6.67 (C) 6.83 (D) oe of the above 3) For, problem # 1, give above, the variace, V(MVP), at MVP is (A) V (MVP) < 4.00 (B) 4.00 V(MVP) < 9.00 (C) 9.00 V(MVP) < (D) V(MVP) ) If we ivest i equal proportio i stocks ad the sigle idex model is true, the (A) P P P ( i) (B) P m P 2 i P P p 2 ( i) i ( i) i 1 (C) (D) oe of the above 5) (This questio has Multiple Aswers) Idetify the first two steps i a profitable arbitrage, give the followig: Yield o U.K. govermet oe-year ote: 8% Yield o U.S. govermet oe-year ote: 5% Exchage rate (spot): 1.60 USD/Poud Exchage rate (oe year forward): 1.70 USD/Poud (A) Sell short US securities (B) Sell USD i spot foreig exchage market for pouds (C) Sell short UK securities (D) Sell pouds i spot foreig exchage market for USD (E) There is o arbitrage 6) Ala has just etered ito a derivative positio with a dealer. The dealer makes a positive payoff whe the price of uderlyig asset is less tha $35 ad higher tha $45 at expiratio. Which of the followigs describes the optio strategy that the dealer has etered ito? I purchased stragle II writte stragle III butterfly-spread

5 IV Bull call spread (A) I, III (B) II, III (C) II, IV (D) III, IV (E) Noe of these 7) The curret (spot) rate for cor is 1.60 per bushel. The 6 moth forward price is $1.50 per bushel. The cotiuously compouded aual rate is r =.035. Farmer Brow, has total fixed ad variable costs of 1.44 per bushel, ad plas to produce 100,000 bushels for $144,000. A six moth (T =.5) put with a strike price of 1.52 per bushel is available at a price of What are the miimum ad maximum profits for Farmer Brow i six moths if he is hedged with a purchase of this put? A) Miimum = 4, 212, Maximum = 19, 678 B) Miimum = 6222, Maximum = 19, 678 C) Miimum = 4, 212, o maximum D) Miimum = 6, 242, o Maximum E) oe of the above 8) The presidet of State Uiversity wats to forecast studet erollmets for this academic year based o the followig historical data: 5 years ago; 15,000, 4 years ago; 16,000, 3 years ago; 18,000, 2 years ago; 20,000, Last year; 21,000. What is the forecast for this year usig expoetial smoothig with α = 0.4, if the forecast for two years ago was 16,000? A) B)17850 C)19420 D)18960 E) Questios 9 to 12 are based o the data give below: Suppose Mr. X is i a world where there are oly two assets Gold ad Stocks. He is iterested i ivestig his moey i oe of the two assets or both. Cosequetly he collects the followig data o returs o the two assets over the last six years. Gold Stock Market Average Retur 8% 20% SD 25% 22% Correlatio ) Mr. X is costraied to pick oe, which oe he would choose ad why? 10) Mr. Y, a fried of Mr. X argues that he is wrog. He says that Mr. X is igorig the big payoffs that he ca get o gold. How would Mr. X go about alleviatig his cocer? 11) How would a portfolio composed of equal proportios i gold ad stocks do i terms of mea ad variace? 12) Mr. X came to kow that GPEC (a cartel of gold-producig coutries) is goig to vary the amout of gold it produces with stock prices i the coutry. (GPEC will produce less gold whe stock markets are up ad more whe it is dow). What effect will this have o his portfolios? Explai

6 13) No-diversifiable risk meas it has the followig property (A) Ca be made zero (0) (B) caot be made zero (0) (C) Ca be made a miimum of fiftee (15) (D) ca be made a maximum of te (10) 14) Which is ot a valid assumptio for CAPM (A) Presece of trasactio cost (C) Persoal tax ot preset (B) Ulimited SS (D) rfl same as rfb 15) If we first subtract the tred value (T) for each quarter from the origial value (Y), the average the values for a give quarter over successive years, the for short-term data we get: A) Useasoal data B) Seasoal compoet C) Cyclical compoet D) De-seasoalised data

Course FM/2 Practice Exam 1 Solutions

Course FM/2 Practice Exam 1 Solutios Solutio 1 D Sikig fud loa The aual service paymet to the leder is the aual effective iterest rate times the loa balace: SP X 0.075 To determie the aual sikig fud paymet,