Fight Finance

Question 47  implicit interest rate in wholesale credit

A wholesale horticulture nursery offers credit to its customers.

Customers are given 60 days to pay for their goods, but if they pay immediately they will get a 3% discount.

What is the effective interest rate implicit in the discount being offered? Assume 365 days in a year and that all customers pay either immediately or on the 60th day. All rates given below are effective annual rates.

(a) 0.44858472

(b) 0.203571651

(c) 0.1825

(d) 0.16913962

(e) 0.164576124

Question 131  APR, effective rate

Calculate the effective annual rates of the following three APR's:

• A credit card offering an interest rate of 18% pa, compounding monthly.
• A bond offering a yield of 6% pa, compounding semi-annually.
• An annual dividend-paying stock offering a return of 10% pa compounding annually.

All answers are given in the same order:

##r_\text{credit card, eff yrly}##, ##r_\text{bond, eff yrly}##, ##r_\text{stock, eff yrly}##

(a) 0.1956, 0.0609, 0.1.

(b) 0.015, 0.09, 0.1.

(c) 0.1881, 0.0609, 0.1025.

(d) 0.1956, 0.0617, 0.1047.

(e) 6.2876, 0.1236, 0.1.

Question 153  bond pricing, premium par and discount bonds

Bonds X and Y are issued by different companies, but they both pay a semi-annual coupon of 10% pa and they have the same face value ($100) and maturity (3 years).

The only difference is that bond X and Y's yields are 8 and 12% pa respectively. Which of the following statements is true?

(a) Bonds X and Y are premium bonds.

(b) Bonds X and Y are discount bonds.

(c) Bond X is a discount bond but bond Y is a premium bond.

(d) Bond X is a premium bond but bond Y is a discount bond.

(e) Bonds X and Y have the same price.

Question 298  interest only loan

A prospective home buyer can afford to pay $2,000 per month in mortgage loan repayments. The central bank recently lowered its policy rate by 0.25%, and residential home lenders cut their mortgage loan rates from 4.74% to 4.49%.

How much more can the prospective home buyer borrow now that interest rates are 4.49% rather than 4.74%? Give your answer as a proportional increase over the original amount he could borrow (##V_\text{before}##), so:

###\text{Proportional increase} = \frac{V_\text{after}-V_\text{before}}{V_\text{before}} ###

Assume that:

• Interest rates are expected to be constant over the life of the loan.

• Loans are interest-only and have a life of 30 years.

• Mortgage loan payments are made every month in arrears and all interest rates are given as annualised percentage rates compounding per month.

(a) 0.055679

(b) 0.029631

(c) 0.029547

(d) 0.006245

(e) 0.0025

Question 639  option, option payoff at maturity, no explanation

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

(a) ##f_{SP,T}=max⁡(S_T-X_T,0)##

(b) ##f_{SP,T}=max⁡(X_T-S_T,0)##

(c) ##f_{SP,T}=-max⁡(S_T-X_T,0)##

(d) ##f_{SP,T}=-max⁡(X_T-S_T,0)##

(e) ##f_{SP,T}=min⁡(X_T-S_T,0)##

Question 673  CAPM, beta, expected and historical returns

A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.

In the last 5 minutes, bad economic news was released showing a higher chance of recession. Over this time the share market fell by 1%. The risk free rate was unchanged.

What do you think was the stock's historical return over the last 5 minutes, given as an effective 5 minute rate?

(a) -12.5%

(b) -4%

(c) -1.5%

(d) -1%

(e) 12.5%

Question 821  option, option profit, option payoff at maturity, no explanation

You just paid $4 for a 3 month European style call option on a stock currently priced at $47 with a strike price of $50. The stock’s next dividend will be $1 in 4 months’ time. Note that the dividend is paid after the option matures. Which of the below statements is NOT correct?

(a) You have the right to buy the underlying stock in 3 months’ time for a price of $50 if you want.

(b) If the dividend in 4 months were unexpectedly cancelled because the firm decided to re-invest its cash rather than pay it out then the 3 month call option price would be unaffected.

(c) If the stock price is $49 in 3 months then you wouldn’t exercise the ‘out of the money’ option.

(d) If the stock price is $51 in 3 months then you wouldn’t exercise or else you’ll incur a loss of $3.

(e) If the stock price is $57 in 3 months then you would exercise. Your profit would be $3 and payoff at maturity $7.

Question 833  option, delta, theta, standard deviation, no explanation

Which of the following statements about an option (either a call or put) and its underlying stock is NOT correct?

(a) The option’s expected future continuously compounded returns are always more than or equal to the underlying stock’s expected future continuously compounded returns.

(b) The option’s standard deviation of dollar price changes is always less than or equal to the underlying stock’s standard deviation of dollar price changes.

(c) The option’s standard deviation of continuously compounded returns are always less than or equal to the underlying stock’s standard deviation of continuously compounded returns.

(d) As time elapses and the maturity date of an option approaches, its price will fall, all other things remaining equal.

(e) If the underlying stock’s price rises by $0.01, the call option’s price will rise by less than $0.01 and the put option’s price will fall by less than $0.01.

Question 894  balance of payments, current account, no explanation

Below are four graphs of Australia's external position, published in the RBA's chart pack.

Assume that all assets and liabilities are debt which makes interest income and equity which makes dividend income.

Which of the following statements is NOT correct? As at the end of 2017, Australia’s:

(a) Trade surplus was roughly zero, so Australians exported as much as they imported.

(b) Net Income was negative, so Australians paid more dividends and interest to foreigners than they received. This is probably because Australia has greater gross foreign liabilities than gross foreign assets.

(c) Current account deficit means Australians have to lend to foreigners by buying foreigners’ debt and equity which represent net capital outflows out of Australia.

(d) Net foreign equity liabilities were negative (less than zero) so Australians had positive net foreign equity assets which means that Australians owned more foreign shares than foreigners owned of Australian shares.

(e) Persistent current account deficit will make its net foreign liabilities greater and greater.

Question 981  margin loan, Basel accord, credit conversion factor

Margin loans secured by listed stock have a Basel III risk weight of 20%.

For margin loans that cannot be immediately cancelled by banks and asked to be repaid, the credit conversion factor (CCF) is 20%.

Suppose you have a stock portfolio worth $500,000, financed by:

• $300,000 of your own money; and
• $200,000 of the bank’s funds in the form of a margin loan which can only be cancelled by the bank after 5 days notice. The margin loan’s maximum LVR is 70%.

How much regulatory capital must the bank hold due to your margin loan? Assume that the bank wishes to pay dividends to its shareholders, so include the 2.5% capital conservation buffer in your calculations.

(a) $2100

(b) $4200

(c) $4800

(d) $5670

(e) $6300