SFM. STRATEGIC FINANCIAL MANAGEMENT Solution Booklet for DERIVATIVES(F&O) By CA. Gaurav Jain. 100% Conceptual Coverage With Live Trading Session

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1 1 SFM STRATEGIC FINANCIAL MANAGEMENT Solution Booklet for DERIVATIVES(F&O) By CA. Gaurav Jain 100% Conceptual Coverage With Live Trading Session Complete Coverage of Study Material, Practice Manual & Previous year Exam Questions Registration Office: 1/50, Lalita park, Laxmi Nagar Delhi 92 Contact Details: , Mail Id: Web Site: FB Page:

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7 7 Solutions Futures QUESTION NO. 1A Step 1Computation of Profit/Loss on Share of X Ltd Purchase Price : 10,000 x 22 Sale Price : 10,000 x (22-22 x 2%) Loss 4400 Step 2Computation of Profit/Loss on Nifty Sale Price: 400 x Purchase Price: 400 x ( x 1.5%) Profit 6600 Step 3 Computation of Overall Profit and Loss in Profit on Nifty 6600 Loss on X Ltd. Share 4400 Overall Net gain in the set of transaction 2200 QUESTION NO. 1B In this case, the total value of ` 2,80,000 and the lot is 200, so, the NIFTY futures on the transaction date was (i.e., 2,80, ). Now, on the settlement date, the NIFTY is So, it has reduced by 22 points. The loss to the investor is: Loss = ( ) x = ` ` 1000 = ` 5400 In case, he has sold the futures contract, his profit would have been: Profit = ( ) x ` 1,000 = ` ` 1000 = ` 3400 It may be noted that in both the cases i.e. whether the investor is buying Future Contract or Selling Future Contract. The brokerage of ` 1,000 would be payable. QUESTION NO. 2A Initial Margin (IM) = ` 10480( ) Maintenance Margin (MM) = ` 7860( x 0.06) Note : Initial Margin & Maintenance Margin are same for same for both long & short positions. 1. Status of investor who has gone long: Day Settlement Price Opening Balance Mark to Market C/F Deposit Closing Balance Net profit (loss) on the contract: = (500) Or Simply ( ) 100 = -500 Additional Analysis: Why margin call of Rs 3000 at the end of Day 4 : See at the end of Day 4 our balance falls below maintenance margin of `7860 i.e it falls to = Now we know that whenever balance falls below Maintenance Margin we have to maintain the

8 8 balance upto the initial margin. Hence we have-made a margin call of`3000 ( ). 2. Status of the investor who has gone short: Day Settlement Price Opening Balance Mark to Market C/F Deposit Closing Balance Net profit (loss) on the contract: = = 500 Or Simply ( ) x100 = 500 QUESTION NO. 2B Initial Margin= μ + 3 s Where μ = Daily Absolute Changes = Standard Deviation Accordingly Initial Margin = ` 10,000+ ` 6,000 = ` 16,000 Maintenance margin = ` 16,000 x 0.75 = ` 12,000 Day Change in Future Values (`) Margin A/c (`) Deposit (`) 4/2/ /2/09 50 ( ) = /2//09 50 ( ) = /2/09 50 ( ) = /2/09 50 ( ) = /2/09 50 ( ) = /2/09 50 ( ) = /2/09 50 ( ) = /2/09 50 ( ) = /2/09 50 ( ) = QUESTION NO. 3A Fair Future Value = Spot Price e rt = 1800 e.08x(3/12) = ` Therefore Fair Future Value for 100 lots will be 100 x =

9 9 QUESTION NO. 3B Using Normal Compounding: (As Per Suggested) Fair Futures Price = Spot Price (l + r) n => = Spot Price [ ]6 => = Spot Price [ ] 6 => = Spot Price [l.0067] 6 => = Spot Price => Spot Price = ` 200 QUESTION NO. 4A Fair Future Value = (Spot Price - Present Value Of Dividend) e rt Where Spot Price = 80; Present Value of Expected Dividend. =Dividend e - rt = 3(e) = 3e = = Therefore Fair Future Value = ( ) e 0.10 x 6/12 = x = QUESTION NO. 4B Fair Future Value = (Spot Price - Present Value Of Dividend) e rt = (` ) e. 09 x 12/l2 = ` = ` Where Present Value of Dividend = ` 40 e (-.09 6/12) ( /12) + 40 e = ` 40 e ` 40 e -.09 = ` = ` = ` QUESTION NO. 5A Fair Future Value = Spot Price e (r-y)t [ where y = dividend yield] = 1200 e = 1200 e.005 = = QUESTION NO. 5B The duration of future contract is 4 months. 3%+3% +4%+3% The average yield during this period will be = = 3.25% 4 As per Cost to Carry model the future price will be F = Se (r d) t Where S = Spot Price rf = Risk Free interest D = Dividend Yield t = Time Period Accordingly, future price will be = 2200 e ( ) 4/12 = 2200 e ( ) = = QUESTION NO x 3/l2 ( )3/12

10 10 We know that: Future Value = [Spot Price + PV Storage Cost] e rt Where Present Value of Storage Costs payable after 6 months = e 6/12.10 = Value of Future = (100 x )e 6/12.10 = ` i.e /gm. When Future is available at `520 per gram Actual Value of Futures (` 520) > Fair Future Value (` ) Therefore Value in Future Market is Overpriced. Sell Gold in Future Market, Buy gold in Spot/ cash Market. When Future is available at `490 per gram Actual Value of Futures (` 490) < Fair Future Value (P s ) Therefore Value in Future Market is Under-priced. Buy Gold in Future Market, Sell Gold in Spot/ Cash Market. Actual Future Price Fair Future Price AFP FFP Case Valuation Future Market Spot Market Invest / Borrow AFP > FFP Overvalued Sell Buy Borrow AFP < FFP Undervalue d Buy Sell Invest QUESTION NO. 7A OR 5802 = ( ) e (.15 c) 1 => = e (.15 c) => e.10 = e (.15 c) => c = 5% QUESTION NO. 7B Fair Futures Price = [Spot Price + Present Value Of Storage Costs - Present Value Of Convenience Yield] (l + r) n Or 10,800 = [10, Present value of convenience yield] (l +. 12) 1 Or Present value of convenience yield = $ per ton. QUESTION NO. 8A 6 months forward price may be found as follows: Fair Future Value = Spot Price e rt = ` 180 x e.12x.5 = ` = ` Decision: Actual Future Price = `195 ; Fair Future Price = ` Since Fair Future Price is less than Actual Future Price. Arbitrage Opportunity is possible. Stock is Overvalued in Future Market. For Arbitrage Gain: (i) Buy the Stock in the Spot / Cash Market (ii) For this Borrow the necessary amount (iii) Then Sell the Stock in the Future Market. Gain or Loss on Expiration: Repayment including 12% c.c taken for borrowing and buying stock in the spot market. [180 e.12 6/12 = 180 x e.06 => ] Sell the Stock in the future market as per contract and collect Net Gain The arbitrage opportunity will continue to exist. So long as the actual market price is more than ` [Which was our Fair Future Price]

11 11 QUESTION NO. 8B Fair Future Price = (Spot Price -Present Value of Dividend Income) e r t = ( ) x e.12 6/12 = x e.06 = x = ` Working Notes: PV of dividend income = 2 x e -12 x 4/12 = 2 e = 2 x = On 100 Shares Total Dividend will be ` Decision : Actual Future Price Fair Future Price AFP FFP Valuation Future Market Spot Market Under Buy Sell Over Sell Buy Or Decision: When Actual Value is ` 7400 Since Actual Future Value < Fair Future Value, Stock is Undervalued in the Future Market. For Arbitrage Gain, Sell the Stock in the Spot Market; Buy it in the Future Market. When Actual Value is Rs 7800 Since Actual Future Value > Fair Future Value. Stock is overvalued in the Future Market. For Arbitrage Gain: Buy the Stock in the Spot Market, Sell the Stock in the future market Additional Analysis: Gain Or Loss : on Expiration i.e at the end of 6 months (i) When the Contract Value is ` 7400 Sell the Stock in the Spot Market at ` 7500 and Invest the proceed at risk free Rate of l2% c.c for 6 months and collect at the end of 6 months ` 7500 e.12 6/12 Or i.e Loss on Dividend Income to be received otherwise [200 e 2/12.12 Or 200 e.02 Or ] Purchase Stock in the Future Market as Contracted Gain [Here we have assumed that arbitrageur holds 100 shares of the given stock initially] (ii) When the Contract Value is ` 7800 Repayment including 12% c.c for borrowing and buying stock in the spot market (` 7500 e.12 6/12 Or ) Dividend to be received on Stock Purchased [200 e 2/12.12 Or 200 e.02 Or ] Sell the Stock in the future market as contracted and collected Gain QUESTION NO. 8C Refer class notes QUESTION NO. 9A Hedge Required for SBI under Nifty=2,00,000 x.8= 1,60,000 He is Long on SBI Stock Hence for Hedging he has to go short on Nifty. He has taken Short Position of Nifty to the extent of 1,00,000. Hence he is partially hedged. For

12 12 complete hedge he has to take short position of Nifty to the extent of 1,60,000. Hence Additional Hedge required = 1,60,000-1,00,000 = 60,000 QUESTION NO. 9B SL No. Company Name Trend Amount (`) Beta Index Value (`) Position (i) Right Ltd Rise 50 lakh ,50,000 Short (ii) Wrong Ltd. Depreciate 25 lakh ,50,000 Long (iii) Fair Ltd. Stagnant 20 lakh Long QUESTION NO. 10A No. of futures contracts to be Sold Or Purchase to reduce Or increase beta can be find out by using the following: = Total Value of Portfolio (Existing Beta Desired Beta) value of Stock Index Therefore (a) No. of Stock Index Futures (SIF) contacts to be sold to reduce beta = 13,00,00,000 ( ) = 375 contracts (b) No. of Stock Index Futures (SIF) contacts to be buy to increase beta = 13,00,00,000 ( ) = contracts Working Note: Stock Shares Owned Stock Purchase d Total Value (Lacs) Weights Beta Portfolio Beta 1 1,00, ,00, ,00, Total Note: (i) If we want to reduce beta we have to sell Index Futures and (ii) If we want to increase beta we have to purchase Index Futures. QUESTION NO. 10B (Refer Class Notes) QUESTION NO. 10C (Refer Class Notes) QUESTION NO. 11 (Refer Class Notes) QUESTION NO. 12A Number of Contract to be traded by another formula may also be found = Total Value of Portfolio (Desired Beta Existing Beta) = 10,00,000 ( ) = contracts Value of Stock Index

13 13 QUESTION NO. 12B (Refer Class Notes) Number of index future to be sold by the Fund Manager is: Crore = = 4605 contracts Justification of the answer: Loss in the value of the portfolio if the index falls by 10% is = Crore = 9.90 Crore 100 Gain by Short Covering of Index Future is = ,00,00,000 This justifies the answer cash is not part of portfolio. = 9.90 Crore QUESTION NO. 12C (i) Future Price of the 4 month BSE Index = 5000 e = = 5050 ( ) (4/12) Price/Value of the one future contract = ` = ` 2,52,500 (ii) Number of future index contracts to be sold for complete hedge = Current Value of Portfolio Existing Beta of Portfolio = 10,10, = 6 Value of One Future Contract It is given that Index after three months turn out be 4500.But for calculating Gain/Loss we need Index Value for 4 months. Therefore Future Price of BSE (Index) after 4 months will be = 4500 e ( ) (1/12) = Therefore, Gain from the shot (selling) futures position is = ( ) 50 6 = QUESTION NO. 12D QUESTION NO. 12E (Refer Class Notes) (Refer Class Notes) QUESTION NO. 13 In order to hedge its position trader would go short on future at current future price of ` per kg. This will help the trader to realize sure ` after 6 months. Quantity of wheat to be hedged kgs Contract Size 2000 kgs No. of Contracts to be sold 220 Future Price ` Exposure in Future Market (` ) ` 81,40,000 After 6 months the trader would cancel its position in future market by buying a future contract of same quantity and will sell wheat in spot market and position shall be as follows. Price of Future Contract ` Amount bought ` 77,22,000 Gain/Loss on Future position ` 4,18,000

14 14 Spot Price ` Amount realized by selling in spot market ` 77,00,000 Effective Selling Amount ` 81,18,000 Effective Selling Price (Per Kg) ` QUESTION NO. 14 To compute the return on investment we shall first compute profit on short sale which will be as follows: =Beginning value - Ending value - Dividends - Trans. Cost - Interest Accordingly beginning value of investment = 5.60 x = Mr. V s investment = Margin Requirement + Commission = = = Ending value of investment = = (Closing out position) Dividend = = 2500 Transaction cost = = 3000 Thus, Profit = = 5500 The rate of return on investment will = 5500/ = 20.56% QUESTION NO. 15 (Refer Class Notes) Practice Questions QUESTION NO. 1 The equilibrium price for different futures would be: 1 month futures: F = S e rt = ` 250 e = ` months futures: F = S e rt = ` 250 e = ` months futures: F = S e rt = ` 250 e = ` Working Note: The time period (t) of these futures is 1 month, 2 months and 3 months, i.e..083 y`,0.167 years, and 0.25 yea` The Spot Price (S) is ` 250 and the Risk Free Rate ( r ) is 12% p.a c.c QUESTION NO. 2 Fair Futures Price = SP e rt => = 92 e r.25 => = e r.25 => e.04 = e r.25 => 0.04 = r.25 => r = 16% ( approx) Therefore, Continuously Compounded Risk Free Rate is 16% p.a QUESTION NO. 3 Value of Forward Contract = [ Spot Price - Present Value of Dividend Income ] x e rt = [100 x ] x e 6/12.10 = ` Working Note:

15 15 Dividend Proceeds = 100 x 1.50 = ` 150 Present Value of Dividend Proceeds = 150 x e (.33)(0.10) = QUESTION NO. 4 Fair Future Value = [Spot Price - Present Value Of Dividend Income] x e rt = ( ) e.15 2/12 = ` Working Note: Present Value Of Dividend Income = ` 10 e / 365 = ` 9.95 QUESTION NO. 5 Fair Future Value = [Spot Price - Present Value Of Dividend Income] x e rt = ( ) e =51.14 Working Notes: PV of dividends = 0.75e / e / e /12 = QUESTION NO. 6 Given Information: Maturity Period: 3 Months; Future Value = 540 per gram; Spot Price = ` 530 per gram; Storage Cost = ` 3 per gram to be incurred at the end of 3 months (a) Computation of Continuously Compounded Risk Free Rate: Future Value = (Spot Price + PV of Storage Cost) e rt. =>540 = [ e -.25 r ) e.25 r =>540 = 530e.25r + 3 =>537 = 530e.25r => e.25r = (Or ) => e.25r = e.01 (nearest) =>.25r =.01 => r =.04 i.e. 4% [approx] (b) Fair Future Price if r = 8%: Fair Future Value: = [ x e ][ x.98020] x = Decision: Fair Future Value (FFP) = ` Actual Future Value (AFV) =` 540 Since Actual Future Value is less than Fair Future Value Futures is Undervalued. For Arbitrage Gain: Sell in the Spot Market and Buy in the Future Market. QUESTION NO. 7 Fair Future Value = [Spot Price + PV Storage Cost] x e rt = [ 60, ] x e = 60,294 x e 0.06 = 60, = ` 64,022 or 640 per gram Working Note: PV of Storage Cost :Storage Cost for 100 gms = 3 x 100 = ` 300. Present Value = 300 e -rt = e = 300 e = = `

16 16 Decision: Actual Future Price Fair Future Price AFP FFP Case Valuation Future Market Spot Market Invest / Borrow AFP > FFP Overvalued Sell Buy Borrow AFP < FFP Undervalue d Buy Sell Invest QUESTION NO. 8 The profit to the investor when Sensex is 5600 Profit =(5,600-5,500) 200 = ` 20,000 The Loss to the investor when Sensex is 5450 Loss= (5,450-5,550) 200 = ` 10,000 Additional Analysis: If investor has a long position i.e buying position and price increases investor will make profit and if price falls he will make loss. QUESTION NO. 9 In this case, the investor creates a long position. It means that he buys the NIFTY futures. His profit or loss is as follows The Buying Value = 1700 x 200 x 5 = ` 17,00,000 Selling Value=1730 x 200 x 5 = ` 17,30,000 Profit = ` 30,000 QUESTION NO. 10 X bought one futures contract costing him ` 5,38,000. At market lot of 200, this means he paid ` 2690 per Nifty future. On the futures expiration day, index closed at Hence, he would have made a profit of (` 2,720 - ` 2,690) x 200 = ` Note: Initial margin is like a security deposit and hence not a expense. QUESTION NO. 11 Profit/Loss position on Nitika Ltd in Cash Market: Buying Value: 500 x 210 = Selling Value:500 x ( 210 x5 % ) = Loss 5250 Profit/Loss position on Nitika Ltd in Future Market : Selling Value = Buying Value ( 195 x3 % ) = Profit 1755 Overall Profit/Loss position on the above set of transaction : In Cash Market In Future Market: Loss Additional Analysis:

17 17 By entering into a Future Contract or By Taking ar. opposite position in two different market he has reduced his loss to 3495.Otherwise loss of investor without hedging would have been Hedging is a technique of taking an equal and opposite position in Stock Market so that loss that may arise in one market would be compensated by a gain in another market. QUESTION NO. 12 (a) Fair Futures Price = Spot Price x e r t = 72 x e = 72 x e.06 = 72x = `76.45 (b) If Actual Future Price = ` 75; Since Actual Future Price (` 75) < Fair Future Price ( ` ). Futures Value is under-valued in the Future Market. Under such condition we should Buy Y Ltd. from the Futures Market and Sell Y Ltd. in the Spot/ Cash Market. Proof: Profit on Expiration Sell Spot and get ` 72 and Invest ` 12% p.a.c.c for 6 months = ` Buy in the-futures Market as per contract = ` Gain/Profit = ` 1.45 (c) If Actual Future Price = ` 77 Since Actual Future Price (` 77) > Fair Future Price ( ` 76.45) Futures Value is over-valued in the Future Market. Buy Y Ltd. in the Spot/Cash Market and Sell Y Ltd. in the Future Market. Proof: Profit on Expiration Borrow ` 72 and Buy the stock. Borrowing 12% p.a.c.c for 6 months. Repayment of ` 72 including interest Sell Y Ltd. as Future Contract = (76.45) = Gain/Profit 0.55 OR AFP FFP Case Valuation Future Market Cash Market AFP > FFP Overvalued Sell Buy AFP < FFP Undervalue d Buy Sell QUESTION NO. 13 Fair Futures Price = Spot Price e r t = 40 e /12 = 40 e.06 = = `40.05 Decision: Actual Future Price = 42 andequilibrium or Fair Future Price = Since Actual Future Price (` 42) > Fair Future Price ( ` ). Future Price of A Ltd is Overvalued, Under such condition we should enter into a contract of Selling Future at ` 42. We should further Buy the share in Cash Market at ` 40 to cover our exposure open in Future Market. Amount required for buying the share (i.e ` 40) should be 5 %.

18 18 QUESTION NO. 14 Fair Future Price = 300( )3 = ` Since Actual Future Price (` 312) is greater than Fair Future Price (` ), Arbitrage Opportunity is possible as X Ltd share is overvalued. Action To Be Taken By Arbitrageur Sell X Ltd Share in Future Market at ` 312 Buy X Ltd Share in Cash Market at Rs 300 Borrow ` 300 for 3 month Profit calculation at the end of3 month Sell X Ltd. Share in Future market as per contract ` Pay Borrowed Amount with interest 300( ) 3 (` ) Risk Less Profit + ` 4.74 QUESTION NO. 15 Fair Future Price (FFP) = Spot Price x e (r-y) t = 9000 x e ( ) 0.25 = 9000 x e.02 = ` Since, actual forward price is 9125 is less than FFP, the NIFTY forward should be bought as it is Undervalued. QUESTION NO Nov.Opening Balance Nil + Initial Margin Paid`800 per contract x15 contracts ` 12,000 + Profit / Loss Today15 contracts x 50 shares/contract x `5/shares ` 3,750 = Closing Balances ` 15, Nov.Opening Balance From previous day ` 15,750 + Profit/Loss Today 15 contracts x 50 shares/contract x `7/share ` 5,250 = Balance before Withdrawals ` 21,000 Profit withdrawn Half of (21,000-12,000) ` (4,500) = Closing Balance ` 16, Nov Opening Balance From previous day ` Profit/Loss Today 15 contracts x 50 shares/contact x (- ` 15)/ Share ` (11,250) = Balance before Margin Call ` 5,250 + Margin Call Paid To bring Balance back to initial margin ` 6,750 (since balance fell below maintenance Margin of 15 x 600 = 9,000) = Closing Balance Rs. 12, Nov.Opening Balance From previous day ` 12,000 + Profit/Loss Today15 contracts x 5000 shares/contact x (- `3)/ Share ` (2250) = Balance before Margin Call ` 9,750 + Margin Call Paidnone(Since Balance is above maintenance-margin of 9,000) = Closing Balance Rs. 9, Nov.Opening Balance From previous day ` 9,750 + Profit/Loss Today15 contracts x 5000 shares/contact x ( `3)/ Share ` 4,500 = Closing Balance Rs. 14,250 QUESTION NO. 17 Yes, the Speculator is over hedged. He is over hedged because its overall exposure in Pentsware Ltd.,

19 19 in relation to the market was 2 lakh 1.03 = and He has hedged his position to the time of 2,50,000. Hence, he is over hedged by: `( 2,50, ) = ` QUESTION NO. 18 The correct hedging strategy is Short Nifty Futures of ` ( ` 2,00,000 x.50 ) with February expiration QUESTION NO. 19 Number of Contracts to be traded = Existing Portfolio Beta Value of spot position requiring hedge =.8 50,00,000 = 5.84 Contract Value of underlying one future Contract Note : (i) Since we have not been given the Value of Future Index, Value of Current Index of ` 6840 has been assumed to be Value of Future Index (ii) Value of Spot Position requiring hedging is taken as `5 million as Unit Trust wants to hedge its portfolio of shares worth `5 million as given in question i.e it is a case of complete hedge i.e we want to reduce our Beta to Nil using Future Index (iii) Number of Contract to be traded by another formula may also be found: = Total Value of Portfolio (Existing Beta Desired Beta) = 50,00,000 (.8-0) = 5.84 contracts Value of Stock Index Additional Analysis: Why Desired Beta has been taken to be Zero: Because we want to hedge completely.since nothing has been said about the extent of hedging, we have assumed it to be a complete hedge question. QUESTION NO. 20 Fair Future Value = [ e ] e = QUESTION NO. 21 The company can hedge position by selling future contracts as it will receive amount from outside. Number of Contracts = $ 4,00,000 = 40 Contracts $ 1,000 Gain by trading in futures = (`45 - `44.50) 4,00,000 = `2,00,000 Net Inflow after 3 months = ` x `4,00, ,00,000 = `1,80,00,000 Effective Price realization = ` 1,80,00,000 $ 4,00,000 = ` 45 per US$

20 20 Practice Question Options QUESTION NO. 1 Type of option American Put option Exercise Price Expiry Date Option Premium Put Buyer Put Writer Underlying Asset ` 4500 per share 30th December ` 20,000 (` 200 X 100 shares) Mr. X Mr. A Tata Shares QUESTION NO. 2 The Profit loss profile of the investor is as follows: Case of Call Option: Market price Strike Price Action Gross Profit Premium Net profit/loss Lapse Lapse Lapse Exercise Exercise Case of Put Option: Market price Strike Price Action Gross Profit Premium Net profit/loss Exercise Exercise Exercise Lapse Lapse Additional Analysis: Remember Buyer of the option whether Call Buyer and Put Buyer can never have loss more than the amount of premium paid by them. QUESTION NO. 3 Given: Current Stock Price = ` 100; Strike Price = ` 100; Option Premium = ` 5; Option = Call Option. Break Even Point for Call Buyer: Market Price- Exercise Price Call Premium = 0 Market Price = 0 => Market Price = 105 Profit and Loss (i.e. pay off) of Call Option Buyer if stock price remain subdued at ` 100 will be: (Market Price at Expiry-Strike Price)- Premium = ( ) 5 = -5 QUESTION NO. 4

21 21 Value of Call option on Expiry: Stock Price Exercise Price Action Value Max IMP EP 0] Lapse Lapse Lapse Exercise Exercise 4 QUESTION NO. 5 Value of Put Option on Expiry: Stock Price Exercise Price Action Value Max (EP-MP, 0) Exercise Exercise Lapse Lapse Lapse 0 QUESTION NO. 6 (i) Theoretical Minimum price of a Call Option = Current Market price Present Value of Strike Price =Current Market Price Strike Price x e -rt = x =3.66 Working Notes : e - rt = 1 e rt = 1 e = = Theoretical Minimum price of a Put Option = PV of Strike Price Current Market = = Working Notes : e - rt = 1 = 1 1 = e rt = QUESTION NO. 7 e If there are put options on EUR/USD, and call options the put/call ratio would be 0.4 implying a bullish market. 2. If there is one put traded for every two calls, then put/call ratio is.5 QUESTION NO. 8 Spot Price (Current Price) = ` 75 Expected price at One Year Time: Low Price : ` 50 and High price : ` X (Assume) Current Price of Option or Value Of Option or Option Premium = ` 15 Risk Free Interest rate = 10% p.a. Exercise Price = ` 70 Hedge Ratio i.e. Number Of share To Be Purchased () = C1 C2 S1 S2 = X 70) Amount of Borrowing Required (B) = 1 1+r ( S1 C2) = ( x 50 0) = Now Value of Call Option (Premium) = Current Market Price X Number of Share Purchased Borrowings= S B => 15 X 50 (1)

22 22 =75 50 => = X 70 = X = X 50 Therefore, Expected Price on Expiry Will be :` 90 (approx.) QUESTION NO. 9 Value of Call on Expiry Maturity Price Max [MPS EP,0] Probability Expected Value of Premium Value as Call as on Expiry 7.92 Option Premium as on today = 7.92 X ) = or 7.99 X e-12x25 = ` Working Notes: When c.c. is not used : P = R d u d When c.c. is used : P = 100 e 12X = Spot Price (1+Interest Rate) Lower Price Higher Price Lower Price = 100 (1 +.03) = 100 X =.72 or =.7247 (1-p) =.28 [As the probability of any event will always be equal to 1] or 3 = (8 p) [1 (1-p)] => 3= 8 p p => p = 0.72 QUESTION NO. 10 According to Put Call Parity Theory we have Value of Call + Present Value of Strike Price = Value of Put + Current Market Price => e /12 = Value of Put + 70 => Value of Put = QUESTION NO. 11 The following diagram shows the possible value of call option after 6 months: 50 Price after 6 months Price after next 6 month Value of Put on Maturity Max (EP-MP, 0) Max (EP-MP, 0) Max (EP-MP, 0) Max (EP-MP, 0) When Spot Price ` 50: Let probability of price rise be p for the first 6 months:

23 23 P = 50x e X = = Probability of price fall for the first 6 months will be (1-p) i.e. ( ) =.3718 When Spot Price `60: Let probability of price rise be p for the Nwxt 6 months: P = 60x e X = = When Spot Price is ` 40: Let Probability of price rise for next 6 months: P = 40x e X = = Probability of price fall for the next 6 months will be (1-p) i.e ( ) =.3718 Additional Analysis: if the % increase and decrease is same for all the period, then probability of price rise and fall will be same as can be seen from above. Market Price at expiration Exercise Price Value of Put Max (EP-MP, 0) Probability Expected Value x x x x.3718 Value of put as on expiration date: Value of Put as on today = x e.10 = x = QUESTION NO. 12 Market Price of Stock (MPS) ` Option premium = Intrinsic Value + Time Value of Option. Exercise Price (EP) ` Premium ` Nature of Option Intrinsic Value Call: MPS EP ; Put : EP- MPS Long Call Long Put Short Put Short Call Short Put Long Put QUESTION NO. 13 Time Value of Option

24 24 QUESTION NO. 14 QUESTION NO. 15 Nature EP MP Result Action I V (a) Put in the money Exercise 82 (b) Call Out of money Lapse 0 (c) Call at the money Lapse 0 (d) Put at the money Lapse 0 (e) Put in the money Exercise 90 (f) Call In the money Exercise 22 (g) Call In the money Exercise 4 (h) Put In the money Exercise 3 Exercise Price Market Price Premium Status IV TV In In At Out Out 0 7 Value of Call Option = ` 2.74 d1 = 2 d2 = 1.945