Fight Finance

Question 42  interest only loan

You just signed up for a 30 year interest-only mortgage with monthly payments of $3,000 per month. The interest rate is 6% pa which is not expected to change.

How much did you borrow? After 15 years, just after the 180th payment at that time, how much will be owing on the mortgage? The interest rate is still 6% and is not expected to change. Remember that the mortgage is interest-only and that mortgage payments are paid in arrears (at the end of the month).

(a) $495,533.92, $349,640.96

(b) $500,374.84, $355,510.54

(c) $500,374.84, $250,187.42

(d) $600,000.00, $600,000.00

(e) $600,000.00, $300,000.00

Question 76  CAPM, SML

Government bonds currently have a return of 5%. A stock has a beta of 2 and the market return is 7%. What is the expected return of the stock?

(a) 5%

(b) 7%

(c) 9%

(d) 12%

(e) 19%

Question 517  DDM

A stock is expected to pay its next dividend of $1 in one year. Future annual dividends are expected to grow by 2% pa. So the first dividend of $1 will be in one year, the year after that $1.02 (=1*(1+0.02)^1), and a year later $1.0404 (=1*(1+0.02)^2) and so on forever.

Its required total return is 10% pa. The total required return and growth rate of dividends are given as effective annual rates.

Calculate the current stock price.

(a) $10

(b) $12.254902

(c) $12.5

(d) $12.75

(e) $13.75

Question 554  inflation, real and nominal returns and cash flows

On his 20th birthday, a man makes a resolution. He will put $30 cash under his bed at the end of every month starting from today. His birthday today is the first day of the month. So the first addition to his cash stash will be in one month. He will write in his will that when he dies the cash under the bed should be given to charity.

If the man lives for another 60 years, how much money will be under his bed if he dies just after making his last (720th) addition?

Also, what will be the real value of that cash in today's prices if inflation is expected to 2.5% pa? Assume that the inflation rate is an effective annual rate and is not expected to change.

The answers are given in the same order, the amount of money under his bed in 60 years, and the real value of that money in today's prices.

(a) $21,600,     $95,035.46

(b) $21,600,     $49,515.44

(c) $21,600,     $4,909.33

(d) $21,600,     $2,557.86

(e) $11,254.05,     $2,557.86

Question 592  future, margin call

A trader buys one December futures contract on orange juice. Each contract is for the delivery of 10,000 pounds. The current futures price is $1.20 per pound. The initial margin is $5,000 per contract, and the maintenance margin is $4,000 per contract.

What is the smallest price change would that would lead to a margin call for the buyer?

(a) A price fall of $0.76 per pound.

(b) A price fall of $0.10 per pound.

(c) A price fall of $0.04 per pound.

(d) A price rise of $0.04 per pound.

(e) A price rise of $0.10 per pound.

Question 593  future, arbitrage table

The price of gold is currently $700 per ounce. The forward price for delivery in 1 year is $800. An arbitrageur can borrow money at 10% per annum given as an effective discrete annual rate. Assume that gold is fairly priced and the cost of storing gold is zero.

What is the best way to conduct an arbitrage in this situation? The best arbitrage strategy requires zero capital, has zero risk and makes money straight away. An arbitrageur should sell 1 forward on gold and:

(a) Borrow $636.3636 and use it to buy 0.9091 ounces of gold right now (t=0). Then pay back the loan with $700 at the end (t=1).

(b) Borrow $700 and use it to buy 1 ounce of gold right now (t=0). Then pay back the loan with $770 at the end (t=1).

(c) Borrow $727.2727 and use it to buy 1 ounce of gold right now (t=0). Then pay back the loan with $800 at the end (t=1).

(d) Borrow $800 and use it to buy 1.1039 ounces of gold right now (t=0). Then pay back the loan with $880 at the end (t=1).

(e) Borrow $880 and use it to buy 1 ounce of gold right now (t=0). Then pay back the loan with $800 at the end (t=1).

Question 636  option, option payoff at maturity, no explanation

Which of the below formulas gives the payoff ##(f)## at maturity ##(T)## from being long a call option? Let the underlying asset price at maturity be ##S_T## and the exercise price be ##X_T##.

(a) ##f_{LC,T}=max⁡(S_T-X_T,0)##

(b) ##f_{LC,T}=max⁡(X_T-S_T,0)##

(c) ##f_{LC,T}=-max⁡(S_T-X_T,0)##

(d) ##f_{LC,T}=-max⁡(X_T-S_T,0)##

(e) ##f_{LC,T}=min⁡(X_T-S_T,0)##

Question 648  margin call, future

A trader buys a one year futures contract on crude oil. The contract is for the delivery of 1,000 barrels. The current futures price is $38.94 per barrel. The initial margin is $3,410 per contract, and the maintenance margin is $3,100 per contract.

What is the smallest price change that would lead to a margin call for the buyer?

(a) A price fall of $0.087571 per barrel.

(b) A price fall of $0.31 per barrel.

(c) A price fall of $3.41 per barrel.

(d) A price fall of $3.54 per barrel.

(e) A price fall of $3.894 per barrel.

Question 679  option, no explanation

A trader sells one crude oil European style call 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) Obligation to sell the underlying oil at $44 per barrel.

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

(d) Obligation to buy the underlying oil $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 721  mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

Fred owns some Commonwealth Bank (CBA) shares. He has calculated CBA’s monthly returns for each month in the past 20 years using this formula:

###r_\text{t monthly}=\ln⁡ \left( \dfrac{P_t}{P_{t-1}} \right)###

He then took the arithmetic average and found it to be 1% per month using this formula:

###\bar{r}_\text{monthly}= \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( r_\text{t monthly} \right)} }{T} =0.01=1\% \text{ per month}###

He also found the standard deviation of these monthly returns which was 5% per month:

###\sigma_\text{monthly} = \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( \left( r_\text{t monthly} - \bar{r}_\text{monthly} \right)^2 \right)} }{T} =0.05=5\%\text{ per month}###

Which of the below statements about Fred’s CBA shares is NOT correct? Assume that the past historical average return is the true population average of future expected returns.

(a) The returns ##r_\text{t monthly}## are continuously compounded monthly returns and are likely to be normally distributed, so the mean, median and mode of these continuously compounded returns are all equal to 1% per month.

(b) The annualised average continuously compounded return is ##\bar{r}_\text{cc annual}=12×0.01=0.1=12\%\text{ pa}##. The annualised standard deviation is ##\sigma_\text{annual} = \sqrt{12}×0.05=0.173205081=17.32\%\text{ pa}##.

(c) Over the next 10 years the mean, median and mode continuously compounded 10 year returns will all equal ##0.01 \times 12 \times 10 = 120\%##.

(d) Over the next 10 years the expected mean gross discrete 10 year return is ##e^{(0.01 - 0.05^2/2)×12×10} = 2.857651118## and the median gross discrete 10 year return is ##e^{(0.01 + 0.05^2/2)×12×10}=3.857425531##.

(e) If the current price of the CBA shares is $75, then in 10 years they’re expected to have a mean value of ##75×e^{(0.01 + 0.05^2/2)×12×10} = 289.3069148## and a median value of ##75×e^{0.01×12×10}=249.0087692##.