exam fm practice exam 2

8/13/2019 Exam FM Practice Exam 2

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Exam FM/2Practice Exam 2

Copyright c2013 Actuarial Investment.

1. $500 is deposited into an account earning interest at a force of interest of 11+t

. How much

interest is earned in the fourth year?

(A) 450

(B) 500

(C) 2000

(D) 2500

(E) 3125

2. With all else held constant, which of the following are true regarding convexity?

(I) Convexity of a portfolio with larger cashflows is lower than convexity of a portfolio withsmaller cashflows.

(II) Convexity calculated at a high interest rate is lower than convexity calculated at a lower

interest rate.

(III) Convexity of a single cashflow later into the future is higher than convexity of a single

cashflow sooner.

(IV) Convexity of a portfolio with higher modified duration is higher than convexity of a

portfolio with lower modified duration.

(A) (III) only

(B) (II) and (IV)

(C) (I), (II), and (III)

(D) (II), (III), and (IV)

(E) The answer is not given by any of (A), (B), (C), or (D).

3. Two bonds with annual coupons have the same yield ratej . The first bond is a 10-year bond

with face amount 1000 and a coupon rateqthat is 2 percentage points higher than the bonds

yield ratej . The second bond is a 10-year bond with face amount 1000 and a coupon rater

that is 3 percentage points lower than the bonds yield rate j .

The first bond is worth 350 more than the second bond. Calculate the price of the first bond.

(A) 870

(B) 981

(C) 1046

(D) 1140

(E) 1174

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4. Chris buys a call option with maturity inn months, a strike price of 23, and a premium of 3.

His profit at maturity is 1.25.

At the time he buys the call option, the price of the underlying asset is 25. After he buys the

call option, the value of the underlying asset increases by 1% per month forever.

The annual effective rate of interest is 4%. Calculate n.

(A) 5

(B) 6

(C) 7

(D) 8

(E) 9

5. A loan makes level monthly payments ofP at the end of each month for 36 months. The

interest paid in the6th month is 13.

The annual effective interest rate is 2%. Calculate P.

(A) 240

(B) 261

(C) 269

(D) 275

(E) 283

6. The price of a two-year zero-coupon bond with face amount 1000 is 905. Six-month forward

rates are given in the table below.

T (years) i(T .5, T).5 2.61 2.51.5 X2 2.6

The price of a two-year bond with face amount 1000 and coupons at a rate ofr% convertible

semiannually is 1030. Calculater.

(A) 3.3

(B) 5.1

(C) 6.7

(D) 7.8

(E) 8.8

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7. An investor believes that a stock is very volitile and wants a position to capitalize on this

belief. In which of the following positions is he most likely to invest?

(A) Long position in a bear spread

(B) Long position in a butterfly spread

(C) Long position in a straddle

(D) Short position in a put ratio spread

(E) Short position in a strangle

8. A company has a liability of 1000 in 4 years. The company wants to provide Redington im-

munization for the liability by purchasing two zero-coupon bonds are available for purchase

at any face amount. Bond Xmatures in 2 years and bondYmatures in 5 years. The annual

effective rate of interest is 5%. What amount of bond Y should be purchased to provide

Redington immunization for this liability?

(A) 400

(B) 500

(C) 600

(D) 700

(E) 800

9. Two 12-year loans with the same interest rate have annual payments at the end of each year.

The combined interest paid in the 5th payments of the loans is 200. The first loan is worth1000 and has payments of 140. The other loan is worthX. CalculateX.

(A) 1817

(B) 1857

(C) 1876

(D) 1906

(E) 1939

10. An annuity immediate with 30 annual payments is worth 392. In years that are divisible by

n, the payment is 27. In all other years, the payment is 19. The annual effective rate of

interest is 3%. Calculate n.

(A) 5

(B) 6

(C) 7

(D) 8

(E) 9

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15. An investor purchases a portfolio that produces cashflows of 200 at time 4,Xat time 5, and

320 at time 8. It is known that the cashflow ofXat time 5 makes up 20% of the value of the

portfolio and that the rate of interest per time period is 5%.

Calculate the Macaulay duration of the portfolio.

(A) 5.1

(B) 5.5

(C) 6.0

(D) 6.9

(E) 7.3

16. An investor believes that over the next several years, the value of an asset will have a large

overall decrease in value, but that the value will experience significant fluctuation while it

declines. Into which of the following contracts is the investor most likely to enter?

(A) Long position in an American put option

(B) Long position in a European call option

(C) Short position in an American call option

(D) Short position in a European call option

(E) Short position in a European put option

17. The annual effective rate of interest is i. The present value of an annuity immediate with

n annual payments of 1 is X. The present value of an annuity immediate with2n annualpayments of 1 is1.5X. Find the accumulated value of 1 inn years.

(A) 0.50

(B) 1.50

(C) 1.67

(D) 1.75

(E) 2.00

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18. BondXis a 10-year bond with annual coupons of 10%. For the forseeable future, it is avail-

able to purchase at par in any face amount. Molly buys $10,000 of bondX. As she recieves

coupons from her initial purchase, she reinvests them by buying more of bond X. She then

reinvests those coupon payments (all coupon payments not from the initial purchase) into an

account paying annual interest at a rate of 6%.

How much money (excluding the value of bonds not yet redeemed) does Molly have aftershe receives the face amount of the original $10,000 bond at the end of 10 years?

(A) 15301

(B) 16619

(C) 18793

(D) 20210

(E) 23301

19. A stock is selling today for 25.00, and the three-month forward price for the stock is 25.50.The stock does not pay dividends. The annual effective rate of interest is 7.4%. An investor

borrows 100,000 to exploit this arbitrage opportunity. What is the investors gain at the end

of three months?

(A) 200

(B) 400

(C) 500

(D) 700

(E) 900

20. An investor buys two puts for the same underlying asset that each mature in six months. Put

Xhas a strike price of 48 and a premium of 3. PutY has a strike price of 51 and a premium

of 4. At maturity, the investor exercises both options and makes a net profit of 0. The annual

effective interest rate is 5%. What is the underlying assets price at maturity?

(A) 45.91

(B) 46.22

(C) 47.60

(D) 52.17(E) 53.09

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21. A perpetuity immediate makes annual payments. The first payment is 1000. Subsequent

payments increase by 100 until they reach 2000. All remaining payments are 2000.

The annual effective rate of interest is 13%. Calculate the present value of the perpetuity.

(A) 11866

(B) 12993

(C) 15385

(D) 16932

(E) 18903

22. A 12-year bond has an annual effective yield rate of 4% and makes semiannual coupons of

X. It has a face amount of 1000 and a price of 1145.89.

A 5-year bond has an annual effective yield rate of 4% and makes semiannual coupons of

X 15. It has a face amount of 1000 and a price ofP. CalculateP.

(A) 822.67

(B) 861.55

(C) 901.83

(D) 934.32

(E) 1002.43

23. Which of the following are true regarding swaps?

(I) An interest rate swap can be used to borrow at a lower interest rate than would otherwise

be possible

(II) An interest rate swap can be used to reduce uncertainty caused by changes in interest

rates

(III) In a swap, the present value of the remaining payments of each of the two sets of

payments to be exchanged must remain equal for the term of the swap

(A) (I) only

(B) (II) only

(C) (I) and (II)

(D) (II) and (III)

(E) The answer is not given by any of (A), (B), (C), or (D)

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24. On January 1, a fund has 900. At some time during the year, a deposit is made ofX. On

December 31, the funds balance is 1500.

The dollar-weighted rate of return of the fund is 17

, but if the deposit had been made one

month later, the dollar-weighted rate of return would have been 427

.

CalculateX.

(A) 367

(B) 400

(C) 417

(D) 450

(E) 480

25. It is known thatK1 < K2 < K3 < K4 < K5. An investor purchases a portfolio that consists

of long positions in a K1-K2-K3 butterfly spread and a K4-K5 2:1 call ratio spread. Over

what interval(s) is the investors payoff positive?

(A) (0, K1), (K3, K5)

(B) (K1, K3), (K4, K5)

(C) (K1, K3), (K4, 2K5 K4)

(D) (K1, K3 K2), (K4, K5)

(E) The answer is not given by any of (A), (B), (C), or (D).

26. A 12-year bond has annual coupons of 5%. The amount for accumulation of discount in the

8th

year is twice the amount for accumulation of discount in the 4th

year. The price of thebond is equal to its face amount. Calculate the yield rate.

(A) 4.2%

(B) 5.0%

(C) 5.4%

(D) 5.9%

(E) 6.3%

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27. A 10-year loan makes 9 annual payments of 300 at the end of each year followed by a balloon

payment of 700 at the end of year 10. After 3 years, the outstanding balance is 2000. The

loan amount isX. CalculateX.

(A) 2238

(B) 2382

(C) 2467

(D) 2529

(E) 2709

28. The annual effective rate of interest is 2.8%. The future value of a 24-year annuity due with

annual payments ofP isX. The present value of a 24-year annuity immediate with annual

payments ofP2 isX.

CalculateX.

(A) 57

(B) 61

(C) 65

(D) 69

(E) 73

29. An investor purchases a futures contract to buy 10,000 shares ofProfitable, Inc.in 3 months

at a price ofXper share. There is a 4% commission on the futures contract. In 3 months,

the price of one share ofProfitable, Inc. is 35.50. The investors net profit is 580. Calculate

X.

(A) 34.02

(B) 34.08

(C) 34.19

(D) 36.92

(E) 37.80

30. The first payment of an annuity immediate with annual payments is 100 and subsequent

payments increase by 2%. The final payment is 200. If the annual effective rate of interest

is 5%, what is the present value of the annuity?

(A) 1997

(B) 2125

(C) 2159

(D) 3079

(E) 3187

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31. Fund A, Fund B, Fund C, and Fund D each have a beginning balance of 1000 on January

1 and an ending balance of 1000 on December 31. Deposits and withdrawals are made ac-

cording to the following schedule, with positive numbers representing deposits and negative

numbers representing withdrawals.

Date Fund A Fund B Fund C Fund DJanuary 1

February 1 50 200March 1 100 75 200April 1 50May 1 100 75June 1 50 75 200July 1 100August 1 50 200September 1 100 200 75October 1 50

November 1 100 75December 1 200 75

Which of the funds has the highest dollar-weighted rate of return?

(A) Fund A

(B) Fund B

(C) Fund C

(D) Fund D

(E) Two or more of the funds have the same dollar-weighted rate of return

32. All of the following options have the same maturity date and are for the same underlying

asset. Given the right conditions, which of the following positions could offer an opportunity

for arbitrage?

(I) A long position in the asset, a sale of a zero-coupon bond, and a short position in a

forward contract

(II) A short position in a call option and a long position in a put option

(III) A short position in a forward contract, a sale of a zero-coupon bond, and a long position

in a convertible bond

(A) (I) only

(B) (I) and (II)

(C) (II) and (III)

(D) (I), (II), and (III)

(E) The answer is not given by any of (A), (B), (C), or (D)

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33. An investor writes a 4:1 put ratio with a net premium of 24. The maximum amount the

investor could lose is 15, which occurs if the price of the underlying asset at expiration is 35.

What is the maximum amount the investor could gain?

(A) 24

(B) 90

(C) 125

(D) The investors maximum gain is unlimited.

(E) There is not enough information given to determine the investors maximum gain.

34. An investor purchases a 20-year bond with annual coupons of 5%. The bond is callable

immediately after any coupon payment in the12th year or later. It has a face value of 1000and a price of 927. The investor will earn an annual effective yield of at least j %. Calculate

j.

(A) 5.00

(B) 5.26

(C) 5.62

(D) 5.71

(E) 5.86

35. A loan is repaid withnlevel annual payments starting 1 year after the loan is taken out. The

outstanding balance after payment n2

is two-thirds of the loan amount. The annual effective

rate of interest is 8%. Calculate n.

(A) 16

(B) 18

(C) 20

(D) 22

(E) 24

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exam fm practice exam 2

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