N14B47
N14B47
The University of Nottingham
BUSINESSSCHOOL
A LEVEL 4 MODULE, SPRING SEMESTER 2010-2011
N14B47 FINANCE AND FINANCIAL MARKETS
Time allowed THREE hours
______
Candidates may complete the front cover of their answer book and sign their desk card but must NOT write anything else until the start of the examination period is announced.
Answer FOUR Questions
All Questions carry equal marks
Only silent, self contained calculators with a Single-Line Display or Dual-Line Display
are permitted in this examination.
Dictionaries are not allowed with one exception. Those whose first language is not English may use a standard translation dictionary to translate between that language and English provided that neither language is the subject of this examination. Subject specific translation dictionaries are not permitted.
No electronic devices capable of storing and retrieving text, including electronic dictionaries, may be used.
DO NOT turn examination paper over until instructed to do so
ADDITIONAL MATERIAL: None
N14B47TURN OVER
N14B47
QUESTION 1
(a)PicardEnterprises expects to make cash payments in the future (a “liability”). Picard owns a bond which from which it expects to receive coupon payments and a final payment of principal (face value). The cash flows (in millions of pounds) are as follows:
YEAR: / 1 / 2 / 3 / 4Liability (millions) / 0.00 / -113.00 / -44.30 / -3.43
Bond (millions) / 20.00 / 20.00 / 20.00 / 120.00
Using a discount rate of 0.125 (12.5%) p.a., calculate the duration of the liability and the duration of the bond’s cash payments.
Suppose Picard can buy or sell other bonds also. How could it match the duration of the liability?
[30%]
(b) You own three Bonds. Each has principal $1,000 and pays coupons annually at 10%. Coupon payments for each bond fell due yesterday. The bonds will mature in 4 years, 9 years and 12 years respectively. Suppose that today the market prices for the bonds are all $1,000. What is the yield to maturity (“discount rate”) for each bond? [In order to gain full marks, you must explain, in words and arithmetic. Hint: consider $100 today, then push it out one year, then two years, etc.].
Suppose, also, that you believe discount rates will fall. Which bond would you then expect to become most valuable? [In order to gain full marks, you must sketch bond value versus discount rate for all three bonds, on the same diagram, and explain].
[40%]
(c)You have the following market values for government zero-coupon bonds (they pay $1,000 on maturity but no coupons), which mature in 1, 2 and 3 years:
1 year2 years3 years
$975.61 $933.51 $881.35
Use these data to value another government bond which pays both principaland interest asfollows: Principal $1,000 due 3 years from now. Coupons 9% p.a. due 1, 2 and 3 years from now.
[30%]
QUESTION 2
(a) You may consider shares and options to be divisible (e.g. you could own one hundredth of an option). The price of a share of a particular stock is £10. Consider a portfolio consisting of a long position in Δ shares of stockand a short position in one call option, exercise price £11. Suppose we are in a world in which is known that after one time step there are only two possible values for the stock, £13 and £7. Calculate the value of Δ, explaining your method. [30%]
(b) What is a one-dimensional random walk? What is the link between this, stock prices and option pricing models? [30%]
(c) Copy the following table and add the missing comments (two have been given to you, as examples)
Increase in this factorCall Value Put Value
Stock priceIncreases Decreases
Exercise Price
Variance of stock price
Time to maturity of option
Interest rate
Dividends paid before maturity
[20%]
(d) Express the put-call parity relationship in terms of combinations of payoff diagrams. What is the resulting payoff diagram, given a portfolio consisting of a long call option of a stock, exercise price X, and a short put option on the same stock and with the same exercise price? [20%]
QUESTION 3
(a) A bank, acting on behalf of an oil company, has put on the market an unusual bond with the following features:
The bond will pay no coupons. It will pay the principal (= face value) of $1,000, for each bond certificate held, 5 years from now. In addition, if the price of Brent crude oil at that time is below $80 per barrel then bondholders will receive an extra payment rising linearly from zero at oil price $30/barrel to a maximum at oil price $50/barrel, remaining at that level for all lower oil prices.
Sketch the payoff diagram for this bond.
Is this a sensible offering for an oil company to make, and why?
What changes would you recommend to the instrument in order to improve it as a hedging instrument for the oil company?
Which banks or investors might find this instrument attractive (or unattractive)?
Oil prices do not follow a simple random walk -how do you thinkthat might affect the valuation? [70%]
Continued on next page
(b) The following strange financial instrument has been issued by a bank. You have been asked how the bank might have created this instrument, in three different ways. You may use some or all of: forward contracts, bonds, calls, puts; any of which may be long or short. [Hint: this can be done in more than three ways, but you should provide three only]
[30%]
QUESTION 4
(a)An investment bank has issued a bond on behalf of PaxsonInternational, a company with a low credit rating. Each bond has face value (principal) of£1,000 and pays no coupons. If the bond is not called, converted or redeemed (i.e. put to the issuer) prior to maturity, the investor will receive $1,000 perbond. At any time prior to maturity, or on the maturity date, the investor can convert the bond into a fixed number of shares of Paxson International stock. Every year, on the last trading day of August, the investor will have the optionto put the bond back to Paxson International, for cash, according to a predetermined list of increasing exercise prices. On the same days, PaxsonInternational will also have the option to call the bond, for cash, according to a separate predetermined list of increasing exercise prices.
Discuss the features of the bond, explaining which of the features (conversion,call, put) increase the market value of the bond (i.e. the price which an investor might be willing to pay for it) and which decrease it.
[40%]
(b)Describe and discuss an application of Real Options in Real Estate (land and buildings).
[40%]
Continued on next page
(c)What is the “comparative advantage argument” for interest rate swaps? If a bank acts as an intermediary between two companies, swapping rates for them in order to give them better than they could have achieved directly in the market, and earn the bank a profit, is that profit risk-free (why)?
[20%]
QUESTION 5
Using material from the course, discuss the ways in which investment banks have made money through arbitrage, tax arbitrage and regulatory arbitrage; via special purpose vehicles; by persuading ratings agencies to give favourable ratings.
[100%]
QUESTION 6
(a)Discuss the options embedded in a fixed-rate UK mortgage and how these might be valued (hint: what are the two underlying stochastic variables?). [30%]
(b)Shares in a company are currently priced at $33 per shareof stock. The stock’s expected volatility (standard deviation) is 0.4 p.a. (40% p.a.). The risk-free rate is 0.02 p.a. (2% p.a.).
You are required to value a put option on a share of company stock using a two-step binomial tree with continuous discounting. The option is European. The put option’s exercise price is $17 and its time to maturity is 3 years. Stock prices in the binomial tree rise by a multiple “u” or fall by a multiple “d” where u = 1/d. The probability of a rise in stock price, in a risk-neutral world, is “p”. The value of u, d and p have been calculated for you:
u = 1.6321496
d = 0.6126889= 1/u
p = 0.4098
Draw the tree and use it to calculate the European put option’s current value, using continuous discounting. (No marks will be received for valuing a call option. You must use continuous discounting; no marks will be received for calculations which do not use continuous discounting )
Next, consider an American put option identical to the European option in every way except that it can be exercised early. Draw a
Continued on next page
new tree and use it to calculate the American put option’s current value, using continuous discounting. (As before, no marks will be received for valuing a call option.
You must use continuous discounting; no marks will be received for
calculations which do not use continuous discounting )
[70%]
QUESTION 7
(a)You have been offered perpetuities, of differing risk, as follows. Value the perpetuities.
(i) £25 per monthbut you have been given the discount rate as 26.82% per annum. [10%]
(ii) £228 p.a., starting four years from now and growing subsequently at 5% p.a. The discount rate is 14% p.a. over all time periods. [10%]
(iii)You receive an e-mail pointing you to a website offering bonds to investors. Transactions are completed online. One bond catches your eye. It is listed as being issued by the Bank of England, with the website acting as agent and taking an immediate fee from you of only £125 for each bond in addition to the bond price (your valuation for this question). A bond has coupons of £10,000 per annum in perpetuity, growing at 10% per annum. The appropriate rate for government bonds is 0.5% p.a. What is the value of the bond, in your view? Explain your answer. [20%]
(b)£2,400 will be deposited in a bank account four years from now. Interest will then accumulate at a rate of 9% p.a., compounded continuously.
(i) After a further eight years (i.e. twelve years from now), how much will be in the bank account?
(ii) What would be the present values of that amount, if discounted continuously at 9% p.a.?
(iii) What would be the present values of that amount, if discounted discretely at 9% p.a.(NOTcontinuously)?
(iv) What are the monthly equivalent rates of 9% continuously and discretely?
[40%]
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(c)Suppose it is possible for an unscrupulous trader to move a spot market price up or down by a small amount for a short time (say one day). How dramatically could the following option types be affected and why?
(i)Ordinary call or put option (“plain vanilla”)
(ii)Asian - an average of underlying prices at certain sampling times is used
(iii)Binary (digital)
(iv)Barrier
(v)Parisian - asset price must stay past the barrier for a pre-set period of time
[20%]
END
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