act2020 midterm 1 - 07
TRANSCRIPT
ACT 2020, MIDTERM #1ECONOMIC AND FINANCIAL APPLICATIONS
FEBRUARY 8, 2007HAL W. PEDERSEN
You have 70 minutes to complete this exam. \\Then the invigilator instructs you tostop writing you must do so immediately. If you do not abide by this instruction youwill be penalised. All invigilators have full authority to disqualify your paper if, intheir judgement, you are found to have violated the code of academic honesty.
Each question is worth 10 points. Provide sufficient reasoning to back up your answerbut do not write more than necessary.
This exam consists of 8 questions. Answer each question on a separate page of theexam book. Write your name and student number on each exam book that you useto answer the questions. Good luck!
Question 1. Bill and Jim enter into a binding contract involving the exchange ofan asset in nine months time. The current market price of the asset is $100. Thecontinuously compounded interest rate is r = 0.045. The contract calls for Jim tosell the asset to Bill at that time at a price G that is set today. The price G is set sothat a fair valuation of the contract requires Jim to pay Bill $2.20 today. If the priceof the asset in nine months time is $98 what is Jim's total profit or loss at the timethe asset is sold?
Question 2. John has just purchased a home for $200,000. The insurance policy willcover any losses due to fire subject to a deductible of $10,000. The one-year premiumon the insurance policy is $3,000 which is due at the start of the policy year.
(1) [5 points] Let NI denote the market value of John's home at the end of the policyyear.1 Draw a chart of the net value of John's home and insurance policy versus AIat the end of the policy year. Assume r = 0 for simplicity.
(2) [3 points] Explain in what sense there is a put option implicit in this transaction,possibly drawing an appropriate chart.
(3) [2 points] Explain in what sense there is a call option implicit in this transaction,. possibly drawing an appropriate chart.
llf there is a devastating fire the market value of John's home could be close to zero. If there isno fire and the real estate market soars then the market value of John's home could be more thanJohn's purchase price of $200,000.
2 ACT 2020 - r.I1DTERM # 1
Question 3. Your client currently owns one share of XYZ Corporation and has aninvestment horizon of six months. The current market price of one share of XYZCorporation is $25. Your client is considering writing one European call option onXYZ Corp. that expires in six months. The market price of an at-the-money Europeancall option expiring in six months is $2.35. The market price of a European call witha strike price of $27.50 expiring in six months is $1.35.
(1) [3 points] Draw a chart showing the total profit at the end of six months fromholding one share of XYZ Corporation and writing one at-the-money European calloption expiring in six months as a function of the XYZ Corporation share price in sixmonths time. (Your chart should provide numerical values identifying the key partsof the chart as was done in class.)
(2) [4 points] Draw a chart showing the total profit at the end of six months fromholding one share of XYZ Corporation and writing one European call with a strikeprice of $27.50 expiring in six months as a function of the XYZ Corporation shareprice in six months time. (Your chart should provide numerical values identifying thekey parts of the chart as was done in class.)
(3) [3 points] What is the greatest possible total return at the end of six months fromholding one share of XYZ Corporation and writing one European call with a strikeprice of $27.50 expiring in six months?
Question 4. Assume that you open a 100 share short position in Jiffy Inc. commonstock at the bid-ask price of $32.00 - $32.50. When you close your position the bid-askprices are $32.50 - $33.00. If you pay a commission rate of 0.5%, calculate your profitor loss on the short investment?
Question 5. The Federated Bank of Canada is offering a structured product thatguarantees the return of 85% of the investor's capital at the end of 5 years. Thecontinuously compounded interest rate is r = 0.05. The index underlying the structured product is currently at 1200 (i. e. So = 1200). The current market price of oneat-the-money European call on the underlying index expiring in 5 years is $350.
(1) [5 points] Assuming that the Federated Bank of Canada charges the investornothing for this contract (i.e. the haircut is zero), compute the participation rate forthe structured product.
(2) [5 points] Assume that the Federated Bank of Canada tells the investor that aftertheir fee is applied the investor's total return for the five year investment horizon hasthe profile
R = -0.15 + 0.9875· (R1NDEJ+.
As in class, RINDEX denotes the total return on the underlying index for the five-yearperiod. What has the investor been charged for this product as a percentage of theirinitial investment?
ACT 2020 - MIDTERM # 1 3
Question 6. The continuously compounded interest rate is r = 0.08. The market price of a European put option on a market index that expires in 4 months is$93.39348. The current level of the market index is 1100 and the strike level on theput option is 1200. What is the price of a European call option on a market indexthat expires in 4 months with a strike level of 1200?
Suppose the 6-month $1,200-strike S&R index put option trades at a bid of $72.97 and at an ask of$74.44. Suppose you can enter into an S&R index forward contract for $1,260. The 6-montheffective interest rate is 5%.
Draw, in the same diagram, the profit for a short put and a long forward position.
At what price is the profit of the put option the same as the profit of the forward contract? If theindex level is higher than the threshold you calculated, which instrument (put or forward) makesmore money? .
2. Jr J.
Suppose the stock price is $40 and the effective annual interest rate is 8%. Drawpayoff and profit diagrams for the following options:
a. 35-strike put with a premium of $1.53.
b. 40-strike put with a premium of $3.26.
c. 45-strike put with a premium of $5.75.
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(a)Prolit diagram of a long forward, short P<.t
300
200
100
-3001000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500
Index price
(b) We need to solve (remember that we rece~ve the proceeds from the sale of the put option, andcan earn interest on them):
$72.97 x (l + 0.05) = Sr - $1,260
~ Sr = $1,336.62
Our profit from the sold put option is capped at the initial premium, plus interest, that wereceive. Therefore, to the right of the threshold, we earn more profit with the long forwardcontract.
In order to be able to draw profit diagrams, we need to find the future values of the put premia.
They are:
a) 35-strike put: $1.53 x (\ + 0.08) = $1.6524
b) 40-strike put: $3.26 x (I + 0.08) = $3.5208
c) 45-strike pur: $5.75 x (I + 0.08) = $6.2\
We get the following payoff diagrams: ,45 ,, Payoff diagram of the different long p<.t opllons
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We get the profit diagram by deducting the option premia from the payoff graphs. The profit diagramlooks as follows:
Profit diagram of the dofferent long put options40 r----,----.- ,
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Intuitively, whenever the 35-strike put option pays off (i.e., has a payoff bigger than zero), the
40-strike and the 35-strike options also payoff. However, there are some instances in which the
40-strike option pays off and the 35-strike options does not. Similarly, there are some instances in
which the 45-strike option pays off, and neither the 40-strike nor the 35-strike payoff. Therefore, the45-strike offers more potential than the 40- and 35-strike, and the 40-strike offers more potential
than the 35-strike. We pay for these additional payoff possibilities by initially paying a higher
premium. It makes sense that the premium is increasing in the strike price.