Fight Finance

Question 57  interest only loan

You just borrowed $400,000 in the form of a 25 year interest-only mortgage with monthly payments of $3,000 per month. The interest rate is 9% pa which is not expected to change.

You actually plan to pay more than the required interest payment. You plan to pay $3,300 in mortgage payments every month, which your mortgage lender allows. These extra payments will reduce the principal and the minimum interest payment required each month.

At the maturity of the mortgage, what will be the principal? That is, after the last (300th) interest payment of $3,300 in 25 years, how much will be owing on the mortgage?

(a) $6,766.6469

(b) $35,748.4866

(c) $63,663.4188

(d) $90,000.0000

(e) Nothing, the mortgage will be fully paid off prior to maturity.

Question 83  portfolio risk, standard deviation

Portfolio Details
Stock	Expected return	Standard deviation	Correlation ##(\rho_{A,B})##	Dollars invested
A	0.1	0.4	0.5	60
B	0.2	0.6		140

What is the standard deviation (not variance) of returns of the above portfolio?

(a) 0.4368

(b) 0.4911

(c) 0.6331

(d) 0.6564

(e) 0.7348

Question 222  fully amortising loan, APR

You just agreed to a 30 year fully amortising mortgage loan with monthly payments of $2,500. The interest rate is 9% pa which is not expected to change.

How much did you borrow? After 10 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change. The below choices are given in the same order.

(a) $320,725.47,     $284,977.19

(b) $310,704.66,     $277,862.39

(c) $310,704.66,     $197,354.23

(d) $308,209.62,     $273,856.37

(e) $308,209.62,     $192,529.73

Question 248  CAPM, DDM, income and capital returns

The total return of any asset can be broken down in different ways. One possible way is to use the dividend discount model (or Gordon growth model):

###p_0 = \frac{c_1}{r_\text{total}-r_\text{capital}}###

Which, since ##c_1/p_0## is the income return (##r_\text{income}##), can be expressed as:

###r_\text{total}=r_\text{income}+r_\text{capital}###

So the total return of an asset is the income component plus the capital or price growth component.

Another way to break up total return is to use the Capital Asset Pricing Model:

###r_\text{total}=r_\text{f}+β(r_\text{m}- r_\text{f})###

###r_\text{total}=r_\text{time value}+r_\text{risk premium}###

So the risk free rate is the time value of money and the term ##β(r_\text{m}- r_\text{f})## is the compensation for taking on systematic risk.

Using the above theory and your general knowledge, which of the below equations, if any, are correct?

(I) ##r_\text{income}=r_\text{time value}##

(II) ##r_\text{income}=r_\text{risk premium}##

(III) ##r_\text{capital}=r_\text{time value}##

(IV) ##r_\text{capital}=r_\text{risk premium}##

(V) ##r_\text{income}+r_\text{capital}=r_\text{time value}+r_\text{risk premium}##

Which of the equations are correct?

(a) I, IV and V only.

(b) II, III and V only.

(c) V only.

(d) All are true.

(e) None are true.

Question 269  time calculation, APR

A student won $1m in a lottery. Currently the money is in a bank account which pays interest at 6% pa, given as an APR compounding per month.

She plans to spend $20,000 at the beginning of every month from now on (so the first withdrawal will be at t=0). After each withdrawal, she will check how much money is left in the account. When there is less than $500,000 left, she will donate that remaining amount to charity.

In how many months will she make her last withdrawal and donate the remainder to charity?

(a) In 31 months (t=31 months).

(b) In 30 months (t=30 months).

(c) In 28 months (t=28 months).

(d) In 27 months (t=27 months).

(e) In 26 months (t=26 months).

Question 557  portfolio weights, portfolio return

An investor wants to make a portfolio of two stocks A and B with a target expected portfolio return of 6% pa.

• Stock A has an expected return of 5% pa.
• Stock B has an expected return of 10% pa.

What portfolio weights should the investor have in stocks A and B respectively?

(a) 80%, 20%

(b) 60%, 40%

(c) 40%, 60%

(d) 20%, 80%

(e) 20%, 20%

Question 681  no explanation

A trader sells one crude oil European style put option contract on the CME expiring in one year with an exercise price of $44 per barrel for a price of $6.64. The crude oil spot price is $40.33. If the trader doesn’t close out her contract before maturity, then at maturity she will have the:

(a) Obligation to buy the underlying oil at $44 per barrel.

(b) Right to buy the underlying oil at $44 per barrel if she wants.

(c) Right to sell the underlying oil at $44 per barrel if she wants.

(d) Obligation to buy the underlying oil at $44 per barrel if the counterparty chooses to sell it.

(e) Obligation to sell the underlying oil at $44 per barrel if the counterparty chooses to buy it.

Question 831  option, American option, no explanation

Which of the following statements about American-style options is NOT correct? American-style:

(a) Options are always worth more than or equal to equivalent European-style options.

(b) Call options on dividend-paying stocks should sometimes be exercised just before the dividend.

(c) Put options on dividend-paying stocks should sometimes be exercised just after the dividend.

(d) Call options should be exercised now if the intrinsic option value ##(S-K)## is greater than the expected present value of the option’s future payoffs.

(e) Put options should be exercised now if the intrinsic option value ##(K-S)## is less than the expected present value of the option’s future payoffs.

Question 976  comparative advantage in trade, production possibilities curve, no explanation

Arthur and Bindi are the only people on a remote island. Their production possibility curves are shown in the graph.

Which of the following statements is NOT correct?

(a) Arthur has the absolute advantage at picking dates.

(b) Bindi has the absolute advantage at picking coconuts.

(c) Arthur has the comparative advantage at picking dates.

(d) Bindi has the comparative advantage at picking dates.

Question 1003  Black-Scholes-Merton option pricing, log-normal distribution, return distribution, hedge fund, risk, financial distress

A hedge fund issued zero coupon bonds with a combined $1 billion face value due to be paid in 3 years. The promised yield to maturity is currently 6% pa given as a continuously compounded return (or log gross discrete return, ##LGDR=\ln[P_T/P_0] \div T##).

The hedge fund owns stock assets worth $1.1 billion now which are expected to have a 10% pa arithmetic average log gross discrete return ##(\text{AALGDR} = \sum\limits_{t=1}^T{\left( \ln[P_t/P_{t-1}] \right)} \div T)## and 30pp pa standard deviation (SDLGDR) in the future.

Analyse the hedge fund using the Merton model of corporate equity as an option on the firm's assets.

The risk free government bond yield to maturity is currently 5% pa given as a continuously compounded return or LGDR.

Which of the below statements is NOT correct? All figures are rounded to the sixth decimal place.

(a) The zero coupon bond liabilities are currently priced at $0.835270 billion.

(b) If the hedge fund were to immediately liquidate all shares and repay all bond liabilities, it would have $0.264730 billion of assets now.

(c) The hedge fund's current market capitalisation of equity would be worth $0.341971 billion.

(d) The probability that the hedge fund's share assets are worth less than its liabilities when the bond matures is 58.406040% in a risk-neutral world where all assets earn the risk free rate.

(e) The probability that the hedge fund's share assets are worth less than its liabilities when the bond matures is 22.339580% in the risk-averse world where investors earn the higher returns on stocks for bearing risk.