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Unformatted text preview: Family name, comma, personal name:
Your student ID: UNIVERSITY OF TORONTO
Faculty of Arts and Science ACT245HIS 2008
Duration — 2 Hours Aids: All calculators allowed. Scrap paper OK. Instructor: Keith Sharp PhD FSA CFA NOTES: Any scrap is to be handed in with this book. It’s OK to write on book. This is a closed book exam. Multiple choice: only your letter answer mark sense sheet will be graded. Each of the 24 questions: 10 points correct, two if blank, zero points if wrong So expectation if you guess is the same as leaving a blank. Make sure you’ve indicated your letter answers on the mark sense sheet before time’s up Please stay in your seats and don’t talk till all question papers and mark sense sheets have
been collected. Photo ID on desk during exam please. Name and student ID on this question paper, on mark sense sheet and on scrap please. 10. Please identify your Privacy ID in the page footer (A, B, C or D) and code it as the answer for question 25.
l 1. Good luck! SQVPP’NT‘ 5°.“ ACT245H] 808 Final Privacy ID A v03 Page I out of 15 UNIVERSITY OF TORONTO: ACT245HIS 2008 FINAL 1.In a country where bond coupons are paid annually, a 7% twoyear bond is priced at 96 and
an 8% oneyear bond is priced at 102. Prices are quoted per 100 face and they mature at 100.
Calculate the forward rate for the second year, in (A) Less than 5.000%
(B) 5.000% but less than 6.000%
(C) 6.000% but less than 7.000%
(D) 7.000% but less than 8.000%
(E) 8.000% or more 2. You are given the following term structure: 51:0.15
52:0.10
S3=0.50 These are effective rates of interest for zerocoupon bonds of l , 2 and 3 years maturity,
respectively. A newly issued 3year bond with face amount 100 has annual coupon rate 13%,
with coupons paid once per year starting one year from now. Find the price of the bond to the
nearest $5. (A) $45
(B) $50
(C) $55
(D) $60
(E) The correct answer is not given by (A), (B), (C) or (D) ACT245lll 508 Final Privacy D A v03 Page 2 oulof15 UNIVERSITY OF TORONTO: ACT245H1S 2008 FINAL 3. The term structure of effective annual yield rates for zerocoupon bonds is given as
follows: 1 and 2year maturity, 10%
3 and 4year maturity, 12% You are given the price of a 5year bond with face amount 100, and annual coupons at rate 5%
is 72.68. Find the 4year forward effective annual interest rate (in effect for the 5th year). (A) Less than 14.000% (B) l4.000% but less than 15.000%
(C) 15.000% but less than 16.000%
(D) l6.000% but less than 17.000%
(E) 17.000% or more 4. You are given the following term structure of spot interest rates: Term (in years) Spot interest rate 4.50% 5.75% 6.25% 6.50%
A threeyear annuityimmediate will be issued a year from now with annual payments of
5000. Using the forward rates, calculate the present value of this annuity a year from now. (A) Less than $13,080.00 (B) $13,080.00 but less than $13,100.00
(C) $13,100.00 but less than $13,120.00
(D) $13,120.00 but less than $13,140.00
(E) $13,140.00 or more ACT245H1 808 Final Privacy 1D A v03 Page 3 out of IS UNIVERSITY OF TORONTO: ACT245HIS 2008 FINAL 5. You are given: S1=io,1=0.083
S2=ioy2=0.090
i2,4=0.1 1 1 Calculate S4 (A) Less than 0.10000 (B) 0.10000 but less than 0.10050
(C) 0.10050 but less than 0.10100
(D) 0.10100 but less than 0.10150
(E) 0.10150 or more ACTZ45H1 508 Final PriVacy ID A v03 Page 4 out of 15 UNIVERSITY OF TORONTO: ACT245HlS 2008 FINAL 6. A couple will be receiving two pensions from Toronto Durable insurance company, both in
the form of an immediate annuity certain: Pension Annual amount Term certain At an interest rate of 5% per annum effective calculate the modiﬁed duration of this liability. (A) Less than 7.600 (B) 7.600 but less than 7.700
(C) 7.700 but less than 7.800
(D) 7.800 but less than 7.900
(E) 7.900 or more 7. A liability of 200 is due at time 10. An attempt is made to immunize this liability at i0:
0.08 by means of two zerocoupon bonds of amounts A5 and A 15 due at times 5 and 15,
respectively. Calculate A 15, . (A) Less than 145.500 (B) 145.500 but less than 146.500
(C) 146.500 but less than 147.500
(D) 147.500 but less than 148.500
(E) 148.500 or more ACT245HI 508 Final Privacy ID A v03 Page 5 out of 15 UNIVERSITY OF TORONTO:ACT245H1S 2008 FINAL 8. Jose and Chris each sell a different stock short for the same price. For each investor, the
margin requirement is 50% and interest on the margin debt is paid at an effective annual rate
of 6%. Each investor buys back his stock one year later at a price of 760. Jose’s stock paid a
dividend of 19 at the end of the year while Chris’s stock paid no dividends. During the one
year period, Chris’s return on the stock is i effective, which is twice the return earned by Jose.
Calculate i. (A) Less than 8.000% (B) 8.000% but less than 9.000%
(C) 9.000% but less than 10.000%
(D) 10.000% but less than 11.000%
(E) 1 1.000% or more 9. Time is measured in years. At time 0 you take the long side of a forward agreement to pay
a delivery price of $95.00 per kilo for zirconiumore at time 3. The ore has an annual storage
cost of 1% of value, payable continuously. Interest rates are 3% per annum continuous, and
don’t change. By time 1, the spot price of ore has increased 13% from its time zero spot price.
Calulate per kilo the value of your forward contract (the value of ‘the piece of paper’) at time
1. (A) Less than $7.500 (B) $7.500 but less than $7.750
(C) $7.750 but less than $8.000
(D) $8.000 but less than $8.250
(E) $8.250 or more ACT245H1 808 Final Privacy 1D A ‘03 Page 6 out of 15 UNIVERSITY OF TORONTO: ACT245HIS 2008 FINAL 10. A cap arranged at time 0 on XYZ stock consists of a short position in one share of the
stock, then priced at $20.00, along with a call option purchased at $1.89 with strike price 25
and expiring at time 1. Assume that the difference between the price of the shorted stock and
the call is invested at time 0 at the same rate, 5% per annum effective, as the riskfree rate used to calculate proﬁt. Calculate as at time 1 the proﬁt if at time 1 the spot price of XYZ
stock equals 10. (A) Less than $8.900 (B) $8.900 but less than $9.000
(C) $9.000 but less than $9.100
(D) $9.100 but less than $9.200
(E) $9.200 or more 11.A stock index that pays no dividends is currently priced at 1000. Assume that you can
borrow at 7% and lend at 6% (continuously compounded). You are considering cashand
carry and reverse cashandcan'y arbitrage opportunities for a one year forward contract in the
index, where there would be zero net cash ﬂow at time 0. Suppose that there is a $5 cost for
going either long or short on a forward contract on the index and there is a 1% cost to go short
or long on the index at time 0, but the forward contract is settled by delivery of the index at
time 1 with no cost. Find the modulus (absolute value) of the difference between the upper
and lower noarbitrage bounds on the delivery price of the forward (A) Less than $40000 (B) $40.000 but less than $41,000
(C) $41000 but less than $42000
(D) $42000 but less than $43000
(E) $43,000 or more ACT245H] 508 Final Privacy 1D A v03 Page 7 out of 15 UNIVERSITY OF TORONTO: ACT 2451118 2008 FINAL 12.Eurodollar futures prices with maturities of 3, 6, and 9 months are 89.50, 88.75, and 88.40,
respectively. What is the swap rate R (per year, compounded quarterly) on 9month
securities? (A) Less than 11.100% (B) 11.100% but less than 11.300%
(C) 11.300% but less than 11.500%
(D) I 1.500% but less than 11.700%
(E) 11.700% or more 13. Smith sells short 1000 shares of stock at a current price of $2 per share. The stock pays a
dividend of $.20 per share per year. Smith is required to put up 40% margin on the short sale,
the margin account earns 5% interest for one year. What is the upper bound on the stock price
per share at the end of one year that will allow Smith to cover the short sale and still at least
break even? Give the answer to the nearest cent. (A) $1.84
(B) $1.88
(C) $1.92
(D) $1.96
(E) The correct answer is not given by (A), (B), (C) or (D) ACT245H1 508 Final Privacy ID A V0} Page 8 out of 15 UNIVERSITY OF TORONTO: ACT245HlS 2008 FINAL l4.Yesterday your institution went short an exercise 30 straddle on Lehman stock which was
then trading at $41. The exercise 30 put was trading at $2. The exercise 30 put and the
exercise 30 call both expire today. Neglect the interest for a day when using putcall parity
and for other calculations. Today Lehman stock is trading at $24. Calculate your institution’s
proﬁt on the straddle to the nearest dollar. (A) Minus $9
(B) $0 (C) $9 (D) $18 (E) The correct answer is not given by (A), (B), (C) or (D) ACT245Hl 308 Final Privacy ID A v03 Page 9 out of 15 UNIVERSITY OF TORONTO; ACT245H1S 2008 FINAL 15. Today is time t=0, measured in years. Stock in Schizo Inc paid a dividend yesterday and
is today trading at So= $32. It is know that at time t=1 it will pay a dividend of $5 per share
and that at time t=2 it will pay a dividend equal to 2 percent of the time F2 stock price 82.
The riskfree rate r equals 6% per annum effective. Calculate the delivery price F 0, 2 of a
forward on the stock arranged at time t=0, with delivery date just after the time t=2 dividend. (A) Less than $29900
(B) $29,900 but less than $30.000
(C) $30.000 but less than $30.100
(D) $30.100 but less than $30,200
(B) More than $30200 ACT245HI 508 Final Privacy ID A \‘03 Page 10 out of15 UNIVERSITY OF TORONTO: ACT245HlS 2008 FINAL 16.KidCo Cereal Company sells “Sugar Corns” for $2.50 per box. The company will need to
buy 20,000 bushels of corn in 6 months to produce 40,000 boxes of cereal. Noncom costs
total $60,000. What is the company’s proﬁt (in excess of that in for an investment at the risk
free rate) if they purchase call options at $0.12 per bushel with a strike price of $1 .60? Take
account of all transactions: sales, all costs and option costs and interest. Interest rates are
8.0% per annum compounded semiannually. The spot price in 6 months is $1.65 per bushel.
Give the answer to the nearest dollar. (A) $5,504 proﬁt
(B) $8,005 loss
(C) $12,064 proﬁt (D) $11,293 loss (E) The correct answer is not given by (A), (B), (C) or (D) 17.At time 0, the share price of ABC stock was $95.25. At that time, a put option on a share of
ABC stock with a strike price of $120 expiring one year later had a premium of $40.40. Risk
free interest rate is 5% annual effective. Determine the proﬁt on the written put option on the
expiry date if the time 1 stock value is 108. ’ (A)Less than $30000
(B) $30000 but less than $31000
(C) $31000 but less than $32000
(D) $32000 but less than $33000
(E) $33000 or more ACT245HI 508 Final Privacy ID A \‘03 Page 11 out of15 UNIVERSITY OF TORONTO: ACT245HIS 2008 FINAL 18. The Sidney Smith lobby TV, tuned to the news channel, indicates the following: S&P500 spot price: 1438.32 S&P500 futures price: 1440.12 Dividend yield on S&P500: 1.95% per annum continuous
Yield on 10—year Treasury bond: 5.13% (bondequivalent) “Bond equivalent” means “per annum compounded semiannually” Use a 360 day year. Calculate the number of days 11 to maturity of the future. (A) Less than 13.000 days (B) 13.000 days but less than14.000 days
(C) 14.000 days but less than 15.000 days
(D) 15.000 days but less than 16.000 days
(E) 16.000 days or more l9.Use the following information. Price of XYZ stock at time 0 is 20. Annual effective
interest is at rate 5%. Call and put option (European) values for various strike prices are: Strike Price Call Price
1 .35 2.64
3.17
4.36 I_— It is assumed that XYZ stock pays no dividends.A ﬂoor position has a minimum proﬁt at time
1 of 5.41. Determine the strike price of the put that is part of the ﬂoor. As usual with this type
of question, please give the nearest answer.
(A) 15 (B) 17 (C) 19 (D) 20 (E) 21 ACT245Hl 508 Final Privacy 1D A \'03 Page 12 out of 15 UNIVERSITY OF TORONTO: ACT245HlS 2008 FINAL 20.Subprime mortgage lender Shady Sid Loans Urgent Money Inc needs to borrow money,
and decides to issue $6 billion par amount of 15year bonds. The coupon rate on SSLUM
bonds is to be 7% per year, with coupons paid at the end of every halfyear. Wall Street
investment bank Scare Turns has agreed to underwrite the bond at issue. ST has guaranteed to
buy at a price of $98 per $100 par any bonds for which it cannot ﬁnd purchasers. You work
for ST and are concerned that house price worries might impact the market for these SSLUM
bonds. To evaluate the risk exposure at the market interest rate level at which the $98
guarantee is activated, calculate ST,’s potential loss on the whole issue for a one basis point
(0.01% per annum compounded semiannually) rise in market interest rates. Make the
calculation at an initial interest rate equal to that at which the guarantee kicks in. (A) Less than $5,300,000
(B) $5,300,000 but less than $5,400,000
(C) $5,400,000 but less than $5,500,000
(D) $5,500,000 but less than $5,600,000
(E) $5,600,000 or more
21. Suppose that ﬁrms face a 30% income tax rate on all proﬁts. In particular, losses receive
full credit. F irrn A has a 50% probability of a $2,000 proﬁt and a 50% probability of a $600
loss each year. Calculate the expected aftertax proﬁt next year for Firm A. (A) Less than $100000
(B) $100000 but less than $200000
(C) $200000 but less than $300000
(D) $300000 but less than $400000
(E) More than $400000 ACT245H1 808 Final Privacy ID A v03 Page 13 out of 15 UNIVERSITY OF TORONTO: ACT245HlS 2008 FINAL 22. Mercury (quicksilver) has storage costs of $2 per annum per kilo, paid annually in
advance, in your ﬁ'iend’s garage, but the market is assuming that storage costs are 1.5%
continuous per annum. The yield curve is ﬂat, and all interest rates are 5% per annum (force
of interest) and remain at that level. The current spot price of mercury is $100 per kilo. You
have two methods to ensure that you have a kilo of mercury three years ﬁ'om now. Method 1: buy it now, spot, and pay'storage in the garage for three years
Method II: go long a three—year forward mercury contract, buying new a threeyear zero
coupon bond to fund your payment under the contract. Calculate how much wealthier you are after three years if you use Method 11 than if you use
Method 1. Hint: storage costs are equivalent to a negative dividend. (A) Less than $0.17000
(B) $017000 but less than $018000
(C) $0.18000 but less than $0.19000 '
(D) $019000 but less than $020000
(E) $020000 or more 23. You use 7,500 cubic meters of gas on January 1 every year. On January 2, 2009 you sign
a ﬁve—year contract with Ontario Entropy Savings at a ﬁxed price of 39.7 cents per cubic
meter for the deliveries on January 1 of 2010 through 2014 inclusive. Payments are made at the time of delivery.
I Zerocoupon bond yield effective
er year, maturity at t
4.100 Jan 1, 2010
Jan 1, 2011 4.060 
4.000 Jan 1, 2012
3.950
3.920 Jan 1, 2013
Calculate the value at January 2, 2009 to CBS of having persuaded you to sign this contract. Forward gas price at Jan
2, 2009, delivery at t 31.4844 cents/cub metre Jan 1,2014 (A) Less than $1 ,850000
(B) $1 ,850000 but less than $1 ,950.000
(C) $1 ,950000 but less than $2,050.000
(D) $2,050,000 but less than $2,150.000
(E) $2,150.000 or more ACTZ45HI 808 Final Privacy 1D A \‘03 Page 14 out of 15 UNIVERSITY OF TORONTO: ACT245HlS 2008 FINAL 24.From the data below, calculate the electricity rate appropriate to a 3—year ﬁxed rate
contract with deliveries at yearend. Forward electricity price at Zerocoupon bond yield ejféctive
delive at t (cents/kWh) :er year, maturity at t (%) (A) Less than 10.600 (B) 10.600 but less than 10.800
(C) 10.800 but less than 1 1.000
(D) 11.000 but less than 1 1.200
(E) 11.200 or more 25.If not already done, please identifying your Privacy ID in the page footer (A, B, C or D) and
code it as the answer for question 25. Total marks: 240 (24 questions) ACT245H1 508 Final Privacy ID A \‘03 Page 15 out of 15 ...
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