Tut Topic 8 QA-new - good PDF

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Tutorial 8 – Q&A Conversion – long stock, short call, long put ( C – P = S – PV(E) i. C – P – S + PV(E) = 0 )Long Stock* P/LShort call X 0 Long PutShort call + Long Put = Short Stock (Synthetic)Long Stock P/L Long put + Long stock = Long Call (Synthetic)*Short call X 0 Long PutLong Stock P/L...

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Tutorial 8 – Q&A Conversion – long stock, short call, long put (C – P = S – PV(E) i.e. C – P – S + PV(E) = 0 ) Long Stock* P/L Short call 0

X Long Put Short call + Long Put = Short Stock (Synthetic) Long Stock Long put + Long stock = Long Call (Synthetic)

P/L *Short call 0

X Long Put

Long Stock P/L Short call 0

X

Short call + Long stock = Short put (Synthetic) Long Put*

Reverse Conversion – short stock, long call, short put (C – P = S – PV(E) i.e. – C + P + S – PV(E) = 0 ) Long call + Short Put = Long Stock (Synthetic) P/L Long call X

Short Put

0

Short Stock*

P/L

Long call* X

Short Put

0 Short put + Short stock = Short call (Synthetic) Short Stock

P/L

Long call X

Short Put*

0 Long call + Short stock = Long put (Synthetic) Short Stock

1. a.) suppose an European put option has a price higher than that dictated by the put-call parity. (i) Outline the appropriate arbitrage strategy. Answer: Put option overpriced so short (sell) the put option. Then implement synthetic long put to create arbitrage strategy. Therefore, arbitrage strategy: short put, long call, short stock P/L

Long call X

Short Put*

0 Long call + Short stock = Long put (Synthetic) Short Stock

(ii)

Name the option/stock strategy used to proof the put-call parity. Answer: Reverse conversion

(iii)

What would the extent of your profit in (i) depend on? Answer: Profit will depend on the extent of mispricing.

2.

Telekom Bhd. (TB) shares are currently at RM15.00, 3-month call and put option with RM15.00 exercise price are being quoted at RM0.75 and RM0.19 respectively. The rf rate is 12% per year. (i) Using put-call parity, prove mathematically that there is mispricing. Answer: Going by put-call parity, stock is undervalued (it should be RM15.14), call is overvalued (it should be 0.61), put is undervalued (it should be 0.33). Will use: 3-month TB 15 call option price = 0.75 3-month TB 15 put option price = 0.19

PV(E) = PV(15) = 15 x (1+0.12)(-3/12) = 14.58 C – P = S – PV(E) S = C – P + PV(E) S = 0.75 – 0.19 + 14.58 S = 15.14 Stock is undervalued (since 15 < 15.14) C – P = S – PV(E) C = S – PV(E) + P C = _______ – _______+ _______ C = 0.61 Call is _____________ (since 0.75 > 0.61). C – P = S – PV(E) P = C – S + PV(E) P = _______– _______ + _______ P = 0.33 Put is _____________ (since 0.19 < 0.33). (ii) Identify the strategy and show the diagram based on the mispriced share. Answer: Long stock, _______put and _______ call (conversion strategy). Long Stock* P/L X 0 Long put Short call Long put + Short Call = Short Stock (Synthetic)

(iii) Outline the arbitrage strategy and show the arbitrage assuming you invested in one lot/contract. Answer: Conversion strategy with overall resulting position a horizontal line. Assuming 3 months later, TB share is at RM14.00 Cash market Now: Buy underlying asset @15 = RM15 x 100 = RM1,500

Long Put option (15) Now: buy one put option @ 0.19 Premium paid = RM0.19 x 100 = RM19

Short Call option (15) Now: sell one call option at 0.75 Premium received = RM0.75 x 100 = RM75

3 months later: Sell underlying asset @RM14 Loss = (15 – 14) x 100 = RM100 Interest paid = 0.12 x 3/12 x 1,500 = RM45

3 months later: Automatic exercise and cash settle: Gain from exercise = (15 – 14) x 100 = RM100

3 months later: Expired worthless

Net loss from underlying = 100 + 45 = RM145

Net gain from put option = RM100 – RM19 = RM81

Net gain from call option = RM75

Net profit = 81 + 75 – 145 = RM11

Assuming 3 months later, TB share is at RM16.00 Cash market Now: Buy underlying asset @15 = RM15 x 100 = RM1,500

Long Put option (15) Now: buy one put option @ 0.19 Premium paid = RM0.19 x 100 = RM19

Short Call option (15) Now: sell one call option at 0.75 Premium received = RM0.75 x 100 = RM75

3 months later: Sell underlying asset @RM16 Gain = (16 – 15) x 100 = RM100 Interest paid = 0.12 x 3/12 x 1,500 = RM45

3 months later: Expired worthless

Automatic exercise and cash settle: Loss from exercise = (16 – 15) x 100 = RM100

Net gain from underlying = 100 – 45 = RM55

Net loss from put option = RM19

Net loss from call option = RM100 – RM75 = RM25

Net profit = 55 – 19 – 25 = RM11

3. On 1 July 1998, your company went long a forward contract with Citibank, KL to purchase 30 million Japanese Yen on 30 March 1999. Then on 1 September 1998, your company shorted

30 million Japanese Yen worth of futures contracts on SIMEX maturing on 30 March 1999. Assuming the exchange rate on both contracts are the same, graph each position and show the overall position. Answer: long forward has payoff equivalent to long underlying, short futures has payoff equivalent to short underlying. Thus, the net position = zero (no profit, no loss). Long forward P/L X 0

Net position = 0

Short futures

4. Maybank stock is currently selling at RM10.80. 3-month RM10.00 call and put options on the stock are being quoted RM1.50 and RM0.90 respectively. Assume the rf rate is 10% per annum. (i) Prove mathematically that there is mispricing. Answer: PV(E) = PV(_______) = _______ x (1+_______)(-3/12) = 9.76 C – P = S – PV(E) S = C – P + PV(E) S = _______– _______+ _______ S = 10.36 Stock is _______valued (since _______> _______) ; so _______ the stock C – P = S – PV(E) C = S – PV(E) + P C = _______– _______+ _______ C = 1.94 Call is _______valued (since _______< _______)) so _______ the call. C – P = S – PV(E) P = C – S + PV(E) P = _______– _______+ _______ P = 0.46 Put is _______valued (since _______> _______)) so _______ the put. (ii)

Outline the arbitrage strategy. Answer: _______ stock, _______ call and _______ put  conversion/reverse conversion

(iii)

Show graphically, that your arbitrage positions in (ii) has no net exposure. (assume mispricing based on the stock)

Answer: Graphically

(iv) Show the arbitrage assuming you invested in one lot/contract. Assuming 3 months later, Maybank share is at RM9.00 Cash market Now: Sell underlying asset @________ = RM_________ x ________ = RM1,080

Short Put option (_______) Now: sell one put option @ _______ Premium received = RM_________ x ________ = RM90

Long Call option (_______) Now: buy one call option at ________ Premium paid = RM_________ x ________ = RM150

3 months later: Buy underlying asset @RM9 Gain = (10.80 – 9) x 100 = RM180 Interest received = 0.10 x 3/12 x 1,080 = RM27

3 months later: Automatic exercise and cash settle: Loss from exercise = (10 – 9) x 100 = RM100

3 months later: Expired worthless

Net gain from underlying = _______+ _______ = RM207

Net loss from put option = _______– _______ = RM10

Net loss from call option = RM150

Net profit = _______– _______– _______ = RM47

Assuming 3 months later, Maybank share is at RM12.00

Cash market Now: Sell underlying asset @_______ = RM_________ x ________ = RM1,080

Short Put option (_______) Now: sell one put option @ _______ Premium received = RM_________ x ________ = RM90

3 months later: 3 months later: Buy underlying asset @_______ Expired worthless Loss = (_______– _______) x _______ = RM120 Interest received = _______ x _______ x _______ = RM27

Net loss from underlying = _______– _______ = RM93

Net gain from put option = RM_______

Long Call option (_______) Now: buy one call option @ _______ Premium paid = RM_________ x ________ = RM150

3 months later: Automatic exercise and cash settle: Gain from exercise = (_______– _______) x _______= RM200

Net gain from call option = _______– _______ = RM50

Net profit = _______ +_______– _______= RM47

5. Outline the appropriate derivative strategy for each of the following. (Carefully state the contract that should be used, maturity and number of contracts where necessary.) (i) Vesawit Bhd, a producer of palm oil based cooking oil would have to replenish its inventory of CPO in 3 months. It normally purchases about 250 tones every 3 months. Answer: _______ 10, 3 month CPO futures

Long futures hedge P/L X 0

Net position = 0

Short position (end-user)

(ii) A speculator expects interest rates to rise over the next 3 months. Answer: _______ 3 month KLIBOR futures

Rule: A selling (short) hedge is used by investors who want to lock in specific interest rates because they are concerned that interest rates will rise later. This is opposite for the buying hedge. Also sell high (fixed) and buy low (market) i.e. interest rates rise  price decline ( 100 – I = P)

(iii)

A trader has just been quoted 95.3 points for the 3 month KLIBOR futures contract. Using IFR, he has just determined that the correct quote should be 94.80. Answer: IFR – Implied Forward Rates Market quoted rate 95.3 _______priced (since 95.3>94.8) so to arbitrage: ___________the 3 month KLIBOR futures, ___________ the 6 mths KLIBOR, ___________the 3 mths KLIBOR Borrow 3 mths KLIBOR

24/3

Borrow 3 month KLIBOR futures

24/6

24/9

Lend 6 mths KLIBOR

(iv)Currency futures and options are available on Korean Won. A Malaysian importer has just received a shipment of refrigerators from LG of South Korea. The invoice amount is 30 million Won, payable in 90 days. Answer: _______ 3 month futures on Won for 30 million

Long Won futures (hedge) P/L X 0

Net position = 0

Short position (Malaysian importer) (v) A speculator is bullish about the Malaysian stock market and the FBM KLCI. However, he wants to establish a position that will limit his risk. Answer:

_______index call or bull call spread

P/L

Long index call X

0

(vi)A specialty chemical firm has just received 200kg of pure silver. It will use the silver over the next 6 months. The company is worried that silver prices may come down. Its output price varies with the spot price of silver. Both options and futures contracts are available on silver at a contract size of 20kg per contract. Answer: _______ 10, 6 month silver futures

Long silver position P/L X 0

Net position = 0

Short 6 month silver futures (hedge)

Not in SG 6. a.) What is the put-call parity? What ensures that the parity will/should hold?

Answer: The put-call parity describes an equilibrium relationship between an ___________and ___________on the asset. The options must be of same ___________ and ___________. Since deviations from put-call parity can be arbitraged risklessly, arbitrage will ensure that the parity holds.

b.) Outline the circumstances under which one would use a conversion strategy as opposed to a reverse conversion. Answer: Generally, given the put-call parity equation, if the right hand side (rhs) of the equation is higher than the left hand side (lhs) then a _________________ (if rhs > lhs). On the other hand, if rhs < lhs, then the ___________ strategy is used. C – P = S – PV(E) i.e. ↓rhs  stock underpriced  long stock*, short call, long put  conversion ↑rhs  stock overpriced  short stock*, long call, short put  reverse conversion c.) Differentiate between cash-flow equivalence and pricing equivalence. Answer: Cash flow equivalence describes the similarity of payoffs at maturity. Pricing equivalence describes the pricing equilibrium that must hold until maturity. Should pricing equivalence not hold, riskless arbitrage is possible. 7. An investor who is currently long MAKRO Bhd. stock, goes long a RM8.00 put and shorts a RM8.00 call on the stock. The stock I currently priced at RM8.00. Assuming the call and put premiums are equal, (i) Graph the strategy and show the overall position. Answer: Conversion strategy; overall position is the horizontal axis (since both call and put premiums are equal). Long Stock P/L Short call 0

X Long Put Short call + Long Put = Short Stock (Synthetic)

(ii)

(iii)

What is the risk profile of strategy? Answer: ___________ profit, ___________ loss. What is the objective of this strategy? Answer:

Hedge strategy intended to stay covered until option maturity. Upon maturity of options, back to long stock position. 8. A trader who is long RM12 millions of Malaysian stocks goes long FBM KLCI calls and short FBM KLCI puts (both the call and puts are at-the-money). (i) Can this be considered a hedge positions? Answer: Resulting position is ___________ long stock.

Long call + Short Put = Long Stock (Synthetic) Long call

P/L X

Short Put

0

(ii)

What must his expectation of the underlying market be? Answer: Extremely ___________.

(iii)

What is likely to happen of the market moves down? Answer: He will lose substantially, ___________the losses of the original long stock position.

(iv)

What is the delta of the option positions taken together? Answer: Delta of option position = ______.

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