Fight Finance

Question 27  bill pricing, simple interest rate

A 180-day Bank Accepted Bill has a face value of $1,000,000. The interest rate is 8% pa and there are 365 days in the year. What is its price now?

(a) $15,400,000.00

(b) $8,371,559.63

(c) $962,757.81

(d) $962,045.33

(e) $64,935.06

Question 41  DDM, income and capital returns

The following is the Dividend Discount Model (DDM) used to price stocks:

### P_0 = \frac{d_1}{r-g} ###

Assume that the assumptions of the DDM hold and that the time period is measured in years.

Which of the following is equal to the expected dividend in 3 years, ## d_3 ##?

(a) ## d_1(1+g)^3 ##

(b) ## P_3(r-g) ##

(c) ## d_2(1+g)^2 ##

(d) ## P_0(1+g)^3(r-g) ##

(e) ## P_0(1+g)^2(r-g) ##

Question 382  Merton model of corporate debt, real option, option

In the Merton model of corporate debt, buying a levered company's shares is equivalent to:

(a) Buying the company's assets.

(b) Buying a call option on the company's assets.

(c) Buying a put option on the company's assets.

(d) Buying the company's assets and buying a call option on those assets.

(e) Buying the company's assets and buying a put option on those assets.

Question 387  real option, option

One of the reasons why firms may not begin projects with relatively small positive net present values (NPV's) is because they wish to maximise the value of their:

(a) Expansion option.

(b) Abandonment option.

(c) Timing (or delaying) option.

(d) Production (or switching) option.

(e) Underlying asset.

Question 404  income and capital returns, real estate

One and a half years ago Frank bought a house for $600,000. Now it's worth only $500,000, based on recent similar sales in the area.

The expected total return on Frank's residential property is 7% pa.

He rents his house out for $1,600 per month, paid in advance. Every 12 months he plans to increase the rental payments.

The present value of 12 months of rental payments is $18,617.27.

The future value of 12 months of rental payments one year in the future is $19,920.48.

What is the expected annual rental yield of the property? Ignore the costs of renting such as maintenance, real estate agent fees and so on.

(a) 3.1029%

(b) 3.3201%

(c) 3.7235%

(d) 3.9841%

(e) 7%

Question 785  fixed for floating interest rate swap, non-intermediated swap

The below table summarises the borrowing costs confronting two companies A and B.

Bond Market Yields
	Fixed Yield to Maturity (%pa)	Floating Yield (%pa)
Firm A	3	L - 0.4
Firm B	5	L + 1

 

Firm A wishes to borrow at a floating rate and Firm B wishes to borrow at a fixed rate. Design a non-intermediated swap that benefits firm A only. What will be the swap rate?

(a) 2% pa.

(b) 2.6% pa.

(c) 3.4% pa.

(d) 4% pa.

(e) 4.6% pa.

Question 793  option, hedging, delta hedging, gamma hedging, gamma, Black-Scholes-Merton option pricing

A bank buys 1000 European put options on a $10 non-dividend paying stock at a strike of $12. The bank wishes to hedge this exposure. The bank can trade the underlying stocks and European call options with a strike price of 7 on the same stock with the same maturity. Details of the call and put options are given in the table below. Each call and put option is on a single stock.

European Options on a Non-dividend Paying Stock
Description	Symbol	Put Values	Call Values
Spot price ($)	##S_0##	10	10
Strike price ($)	##K_T##	12	7
Risk free cont. comp. rate (pa)	##r##	0.05	0.05
Standard deviation of the stock's cont. comp. returns (pa)	##\sigma##	0.4	0.4
Option maturity (years)	##T##	1	1
Option price ($)	##p_0## or ##c_0##	2.495350486	3.601466138
##N[d_1]##	##\partial c/\partial S##		0.888138405
##N[d_2]##	##N[d_2]##		0.792946442
##-N[-d_1]##	##\partial p/\partial S##	-0.552034778
##N[-d_2]##	##N[-d_2]##	0.207053558
Gamma	##\Gamma = \partial^2 c/\partial S^2## or ##\partial^2 p/\partial S^2##	0.098885989	0.047577422
Theta	##\Theta = \partial c/\partial T## or ##\partial p/\partial T##	0.348152078	0.672379961

 

Which of the following statements is NOT correct?

(a) If the underlying stock price suddenly rose by $0.01, the put option price would be expected to fall by less than $0.00552034777953178.

(b) If the underlying stock price suddenly fell by $0.01, the put option price would be expected to rise by more than $0.00552034777953178.

(c) If the underlying stock price suddenly rose by $0.01, the call option price would be expected to rise by more than $0.00888138404936379.

(d) To Delta hedge the 1000 long put options, long 552.0348 stocks.

(e) To Delta and Gamma hedge the 1000 long put options, long 2078.4226 call options and short 2397.9617 stocks.

Question 795  option, Black-Scholes-Merton option pricing, option delta, no explanation

Which of the following quantities from the Black-Scholes-Merton option pricing formula gives the Delta of a European put option?

(a) ##N[d_1]##

(b) ##N[d_2]##

(c) ##−N[−d_1]##

(d) ##−N[−d_2]##

(e) ##N[−d_2]##

Question 888  foreign exchange rate, speculation, no explanation

The current Australian exchange rate is 0.8 USD per AUD.

If you think that the AUD will depreciate against the USD, contrary to the rest of the market, how could you profit? Right now you should:

(a) Borrow 1m AUD and lend 0.8m USD.

(b) Borrow 1m USD and lend 1.25m AUD.

(c) Borrow 1m AUD and lend 1m AUD.

(d) Borrow 1m USD and lend 1m USD.

(e) Borrow 1m AUD and lend 1.25m AUD.

Question 956  option, Black-Scholes-Merton option pricing, delta hedging, hedging

A bank sells a European call option on a non-dividend paying stock and delta hedges on a daily basis. Below is the result of their hedging, with columns representing consecutive days. Assume that there are 365 days per year and interest is paid daily in arrears.

Delta Hedging a Short Call using Stocks and Debt
Description	Symbol	Days to maturity (T in days)
		60	59	58	57	56	55
Spot price ($)	S	10000	10125	9800	9675	10000	10000
Strike price ($)	K	10000	10000	10000	10000	10000	10000
Risk free cont. comp. rate (pa)	r	0.05	0.05	0.05	0.05	0.05	0.05
Standard deviation of the stock's cont. comp. returns (pa)	σ	0.4	0.4	0.4	0.4	0.4	0.4
Option maturity (years)	T	0.164384	0.161644	0.158904	0.156164	0.153425	0.150685
Delta	N[d1] = dc/dS	0.552416	0.582351	0.501138	0.467885	0.550649	0.550197
Probability that S > K at maturity in risk neutral world	N[d2]	0.487871	0.51878	0.437781	0.405685	0.488282	0.488387
Call option price ($)	c	685.391158	750.26411	567.990995	501.487157	660.982878	?
Stock investment value ($)	N[d1]*S	5524.164129	5896.301781	4911.152036	4526.788065	5506.488143	?
Borrowing which partly funds stock investment ($)	N[d2]*K/e^(r*T)	4838.772971	5146.037671	4343.161041	4025.300909	4845.505265	?
Interest expense from borrowing paid in arrears ($)	r*N[d2]*K/e^(r*T)		0.662891	0.704985	0.594994	0.551449	?
Gain on stock ($)	N[d1]*(SNew - SOld)		69.052052	-189.264008	-62.642245	152.062648	?
Gain on short call option ($)	-1*(cNew - cOld)		-64.872952	182.273114	66.503839	-159.495721	?
Net gain ($)	Gains - InterestExpense		3.516209	-7.695878	3.266599	-7.984522	?
Gamma	Γ = d^2c/dS^2	0.000244	0.00024	0.000255	0.00026	0.000253	0.000255
Theta	θ = dc/dT	2196.873429	2227.881353	2182.174706	2151.539751	2266.589184	2285.1895

 

In the last column when there are 55 days left to maturity there are missing values. Which of the following statements about those missing values is NOT correct?

(a) The call option price is expected to be $654.757851.

(b) The stock investment value used for hedging should be $5506.488143, partly funded by $4845.505265 in debt.

(c) The interest expense on the borrowing from the previous day will be $0.663813.

(d) The gain on the stock is zero and the gain on the short call option is $6.225027.

(e) The net gain is $5.561214.