1

2.

3.

4.

SOLUTION:

At expiration, the stock price is 50 and therefore both options are “out-of-the-money”; A and B are eliminated.

With a strike price of 45 and a minimum stock price of 46, option A is never in the money; D is eliminated.

With a strike price of 55, option B will be in the money at the time the stock price is 58; C is eliminated and E is the answer.

5.

6. Jeff deposits 10 into a fund today and 20 fifteen years later. Interest for the first 10 years is credited at a nominal discount rate of d compounded quarterly, and thereafter at a nominal interest rate of 6% compounded semiannually. The accumulated balance in the fund at the end of 30 years is 100.

Calculate d.

7. John borrows 10000 for 10 years and uses a sinking fund to repay the principal. The sinking fund deposits earn an annual effective interest rate of 5 percent. The total required payment for both the interest and the sinking fund deposit made at the end of each year is 1445.04.

Calculate the annual effective interest rate charged on the loan.

8. A 30-year 15% bond with semi-annual coupons is purchased for 110% of par to yield a nominal annual rate of 13.66% convertible semi-annually.

The redemption value is what percent of the par value?

9. Jim buys a 10-year bond with par value of 10000 and 8 percent semiannual coupons. The redemption value of the bond at the end of 10 years is 10500.

Calculate the purchase price to yield 6 percent convertible quarterly.

SOLUTION :

Note: The coupons are paid out semiannually, interest is convertible quarterly, hence we need to translate it into semiannual interest.

10. Travis purchased a soccer team and financed the purchase with a 15 year loan.

Interest was charged at 6.00% per annum and payments were made on an annual basis

with the first payment made one year after the loan was originated.

Travis's principal payment in the 14th year was $73,309.19.

How much interest was paid with the payment in the 4th year?

SOLUTION:

11. Determine which of the following situations is the LEAST likely to exemplify the use of derivatives as a risk management tool by an organization in the United States.

a) A commercial airline enters into long future fuel contracts for60% of its fuel needs.b) An oil firm that will deliver 2 million barrels enters into short forward oil contracts over the following 18 months.c) An investment bank enters into long future S&P index contracts given its view that the index will increase over the next 30 days.d) A computer manufacturer will make a payment to its German supplier, and enters into a long future Euro contract.e)An insurance company investing in floating-rate instruments swaps floating interest rates for fixed interest rates.

SOLUTION: All but (C) reduce risk by locking in a given result. Answer (C) involves taking on additional risk.

12.

Additional info :

i) The total profit from a bear spread created by selling a 40 strike call and buying a 45 strike call

ii) The total profit from a bull spread created by buying a 40 strike put and selling a 45 strike put

iii) The total profit from a straddle created by selling a 40 strike call and selling a 40 strike put

iv) The total profit from a strangle created by buying a 40 strike put and buying a 45 strike call

13. Fixed rates for interest rate swaps are as follows:

4.6% (1-year) 5.3% (2-year) 5.4% (3-year)

Compute the price of a two-year zero-coupon bond per $1 of maturity payment.

SOLUTION:

14.

SOLUTION:

15. Professor JT receives a perpetuity for his retirement that pays $300 at the end of year 6, $600 at the end of year 10,

$900 at the end of year 14, with payments continuing to be made every four years thereafter at an amount equal to $300 more than the immediately preceding payment.

The present value of the third payment is $535.35.

Calculate the present value of this perpetuity.

SOLUTION:

You should recognize that you have an arithmetic increasing perpetuity with payments every 4 years that starts with a payment of $300 in year 6, and each payment increases by $300.

So, to find the value of the perpetuity, we see that

P = 300, Q = 300 and we have to solve for the 4 year effective rate, i.

We know the present value of the 3rd payment is $535.35.

The 3rd payment is $900, payable at time 14.

So, the present value of that is $900 discounted back for 3.5 four-year periods.

i equals 16%.

Now, if we use the formula for a perpetuity immediate the present value at the start of the perpetuity is

That is the value at the start of the perpetuity- that is at time 2 because it is the value of a perpetuity immediate!

We must discount that back to time zero to get the present value.

That is discount for 2 years, or one-half of a 4 year period.

16.

The current price of a medical company’s stock is 75. The expected value of the stock price in three years is 90 per share. The stock pays no dividends.

You are also given:

I. The risk-free interest rate is positive.II. There are no transaction costs.

III. Investors require compensation for risk.

The price of a three-year forward on a share of this stock is , and at this price an investor is willing to enter into the forward.

Determine what can be concluded about X

SOLUTION:

For stocks without dividends and in the absence of transaction costs, the stock’s forward price is the future value of its spot price based on the risk-free interest rate; otherwise there would be an arbitrage opportunity. Because the risk-free interest rate is positive, the forward price must be greater than the spot price of 75.

Because these investors are risk-averse (i.e. they prefer not to take risks if the average rate of return is the same) they need to receive on the average a greater return than the risk-free interest rate on the shares they invest in this stock. In other words, they need to receive a risk premium (incentive) for taking on risk.

The forward price only includes the risk-free interest rate and not the risk premium, so the forward price is less than the expected value of the future stock price, namely 90.

17. Gertrude deposits 10,000 in a bank. During the first year, the bank credits an annual effective rate of interest i. During the second year, the bank credits an annual effective rate of interest (i – 5 percent). At the end of two years, she has 12,093.75 in the bank.

What would Gertrude have in the bank at the end of three years, if the annual effective rate of interest were (i + 9%) for each of the three years?

SOLUTION:

18. Company ABC is required to pay their customers $20,000 after 3 years.

Based on an annual effective interest rate of 4%, Andy, the company’s actuary, uses full immunization strategy to construct a portfolio of assets using a 2-year zero-coupon bond and a 4-year zero-coupon bond.

Calculate the par amount for the 2-year zero-coupon bond assuming full immunization is met.

For full immunization, the following conditions must hold:

I. PV(assets) = PV(liabilities)II. MacD(assets) = MacD(liabilities) or P'assets = P'liabilities

III. There is one asset cash inflow before the liability cash outflow, and one asset cash inflow after the liability cash outflow.

19. For a position in a derivative, the maximum loss is unlimited whereas the maximum gain is the future value of the derivative’s premium.

Which of the following best describes the situation above?

SOLUTION:

20. A 20 year bond has an annual effective yield rate of 6.00%.

Coupons are paid semi-annually at 5.75%.

The bond is redeemed at par value of 10,000 at maturity.

How much would the price increase if the yield rate changes to 6.25% convertible semi-annually?

SOLUTION:

Using your calculator

For Bond A:

N = 40

I/Y = 2.9563 (6% annual effective converted to semi-annual effective)

PMT = 287.50

FV = 10,000

CPT PV = 9810.74

For Bond B, only change needed is the interest rate

I/Y = 3.125

CPT PV = 9433.63

Difference is 9433.63 – 9810.74 = –377.11

21. Liek enters into a long forward contract. If the spot price at expiration were S, his payoff would be –20.

If the spot price at expiration were 1.2S, his payoff would be X.

Xin enters into a short forward contract. If the spot price at expiration were 0.8S, her payoff would be 40.

If the spot price at expiration were 1.1S, her payoff would be Y.

The forward price for both Liek's and Xin's contract is the same.

Calculate X + Y.

SOLUTION:

22. A 10,000 par value 10-year bond with 8% annual coupons is bought at a premium to yield an annual effective rate of 6%.

Calculate the interest portion of the 7th coupon.

23. The President of SALT Solutions would like to reward his staff by paying each employee a bonus. The President has informed his staff that the bonuses totaling 25,000 will be paid on “Bonus Day” but the exact date is not given.

In order to fund this bonus payment, the President invests in a zero coupon bond with a face amount of 20,016 that matures 1 year before “Bonus Day”. He also invests in a zero coupon bond with a face amount of B that matures 5 years after “Bonus Day”.

Assuming a force of interest of 4%, determine the minimum value for B so that the investments will be sufficient to pay the bonus on “Bonus Day” regardless of the size of interest rate changes.

SOLUTION:

3 criteria must be met:

1. PA = PL

2. P'A = P'L

3. The portfolio consists of at least one asset that has a duration shorter AND longer than the duration for the liability. This condition is met by the problem, assuming t is positive.

24. Angus wants to create a 40-48-50 asymmetric butterfly spread using combination of $40-strike call options, $48-strike call options and $50-strike call options.

What combination of options should Angus use to create the desired spread?

SOLUTION:

Therefore, for every K2-strike call we write, we buy 0.2 units of K1-strike call and 0.8 units of K3-strike call.

In particular, for every 48-strike call that we write, we buy 0.2 units of 40-strike calls and 0.8 units of 50-strike calls.

Hence, to create an asymmetric butterfly spread, if Angus writes 10 units of 48-strike calls, he has to:

Buy 10(0.2) = 2 units of 40-strike calls, and Buy 10(0.8) = 8 units of 50-strike calls.

25. An insurance company has a known liability of 1,000,000 that is due 8 years from now. The technique of full immunization is to be employed. Asset I will provide a cash flow of 300,000 exactly 6 years from now. Asset II will provide a cash flow of X, exactly y years from now, where y>8.

The annual effective interest rate is 4%. Calculate X.

26.

A three year annual coupon $1000 par bond has a coupon rate of 4%. Use the yield curve above

to find the price P and then use this price to find the yield to maturity.

Using your calculator

N = 3

PV = –999.28

PMT = 40

FV = 1000

CPT I/Y = 4.03%

27.

SOLUTION:

28. All of the following are reasons for a corporation not to engage in hedging, except:

SOLUTION:

C. Managerial risk aversion is a reason to hedge

29. An insurance company wants to match liabilities of 25,000 payable in one year and 20,000

payable in two years with specific assets. The following assets are currently available:

Calculate the smallest amount the company needs to disburse today to purchase assets that will

exactly match these liabilities.

SOLUTION:

The strategy is to use the two highest yielding assets: the one-year coupon bond and the two-year zero coupon bond.

The cost of these bonds is 

30. A perpetuity of $1 each year, with the first payment due immediately, has a present value of

$25 at an annual effective rate of i%. The owner exchanges it for another perpetuity with the

first payment due immediately and subsequent payments due at two year intervals. What

should the payment of the second perpetuity be, in order to keep the same interest rate, i%, and

the same present value?

SOLUTION:

31. Larry is repaying a loan with payments of $2,500 at the end of every two years. If the amount of interest in the fourth installment is $2,458, find the amount of principal in the seventh installment.

Assume an annual effective interest rate of 13%.

SOLUTION:

32. Calculate the nominal rate of interest convertible once every three years that is equivalent

to a nominal rate of discount convertible monthly.

SOLUTION:

33. Determine which of the following statements is false with respect to Redington

immunization.

a) Modified duration may change at different rates for each of the assets and liabilities as time goes by.b) Redington immunization requires infrequent rebalancing to keep modified duration of assets equal to modified duration of liabilities.c) This technique is designed to work only for small changes in the interest rate.d) The yield curve is assumed to be flat.e) The yield curve shifts in parallel when the interest rate changes.

ANSWER:

All are true except B. Immunization requires frequent rebalancing.

34. Sally lends 10,000 to Tim. Tim agrees to pay back the loan over 5 years with monthly payments payable at the end of each month.

Sally can reinvest the monthly payments from Tim in a savings account paying interest at 6%, compounded monthly. The yield rate earned on Sally’s investment over the five-year period turned out to be 7.45%, compounded semi-annually.

What nominal rate of interest, compounded monthly, did Sally charge Tim on the loan?

SOLUTION:

35. On December 31, 1984, Smith borrowed $5,000 to be repaid in four years with level

payments made at the end of every quarter. The first payment was made on March 31, 1985.

The effective annual interest rate was 4%. What was the amount of interest paid in 1986?

SOLUTION: