Fight Finance

Question 146  APR, effective rate

A three year corporate bond yields 12% pa with a coupon rate of 10% pa, paid semi-annually.

Find the effective six month yield, effective annual yield and the effective daily yield. Assume that each month has 30 days and that there are 360 days in a year.

All answers are given in the same order:

##r_\text{eff semi-annual}##, ##r_\text{eff yearly}##, ##r_\text{eff daily}##.

(a) 0.06, 0.1236, 0.000324.

(b) 0.058301, 0.12, 0.000315.

(c) 0.05, 0.1025, 0.000271.

(d) 0.05, 0.1, 0.000278.

(e) 0.048809, 0.1, 0.000265.

Question 249  equivalent annual cash flow, effective rate conversion

Details of two different types of desserts or edible treats are given below:

• High-sugar treats like candy, chocolate and ice cream make a person very happy. High sugar treats are cheap at only $2 per day.
• Low-sugar treats like nuts, cheese and fruit make a person equally happy if these foods are of high quality. Low sugar treats are more expensive at $4 per day.

The advantage of low-sugar treats is that a person only needs to pay the dentist $2,000 for fillings and root canal therapy once every 15 years. Whereas with high-sugar treats, that treatment needs to be done every 5 years.

The real discount rate is 10%, given as an effective annual rate. Assume that there are 365 days in every year and that all cash flows are real. The inflation rate is 3% given as an effective annual rate.

Find the equivalent annual cash flow (EAC) of the high-sugar treats and low-sugar treats, including dental costs. The below choices are listed in that order.

Ignore the pain of dental therapy, personal preferences and other factors.

(a) -$332.8709, -$68.2065

(b) -$327.595, -$62.9476

(c) -$828.9808, -$808.5709

(d) -$829.6304, -$810.2613

(e) -$1,093.4153, -$1,594.5881

Question 334  option

Which option position has the possibility of unlimited potential losses?

(a) Long call options.

(b) Short call options.

(c) Long put options.

(d) Short put options.

(e) No option positions have the possibility of unlimited potential losses.

Question 453  DDM, income and capital returns

The perpetuity with growth equation is:

###P_0=\dfrac{C_1}{r-g}###

Which of the following is NOT equal to the expected capital return as an effective annual rate?

(a) ##g##

(b) ##r+\dfrac{C_1}{P_0}##

(c) ##\dfrac{C_2}{C_1} -1##

(d) ##\dfrac{C_3-C_2}{C_2} ##

(e) ##\left( \dfrac{P_5}{P_3} \right)^{1/2}-1##

Question 572  bond pricing, zero coupon bond, term structure of interest rates, expectations hypothesis, forward interest rate, yield curve

In the below term structure of interest rates equation, all rates are effective annual yields and the numbers in subscript represent the years that the yields are measured over:

###(1+r_{0-3})^3 = (1+r_{0-1})(1+r_{1-2})(1+r_{2-3}) ###

Which of the following statements is NOT correct?

(a) ##r_{0-3}## is the three year spot rate, given as an effective annual rate.

(b) ##r_{0-1}## is the one year forward rate, given as an effective annual rate.

(c) ##r_{1-2}## is the one year forward rate one year ahead, given as an effective annual rate.

(d) ##r_{2-3}## is the one year forward rate two years ahead, given as an effective annual rate.

(e) ##r_{1-3} = \left((1+r_{1-2})(1+r_{2-3})\right)^{1/2}-1## is the two year forward rate, one year ahead, given as an effective annual rate.

Question 616  idiom, debt terminology, bond pricing

"Buy low, sell high" is a phrase commonly heard in financial markets. It states that traders should try to buy assets at low prices and sell at high prices.

Traders in the fixed-coupon bond markets often quote promised bond yields rather than prices. Fixed-coupon bond traders should try to:

(a) Buy at low yields, sell at high yields.

(b) Buy at high yields, sell at low yields.

(c) Buy at high yields, sell at high yields.

(d) Buy at low yields, sell at low yields.

(e) There is no preferable yield to buy or sell fixed-coupon debt.

Question 659  APR, effective rate, effective rate conversion, no explanation

A home loan company advertises an interest rate of 9% pa, payable monthly. Which of the following statements about the interest rate is NOT correct? All rates are given with an accuracy of 4 decimal places.

(a) The APR compounding monthly is 9.000% pa.

(b) The effective monthly rate is 0.7500% pa.

(c) The effective annual rate is 9.3807% pa.

(d) The effective 6 month rate is 4.5000% pa.

(e) The APR compounding semi-annually is 9.1704% pa.

Question 666  rights issue, capital raising

A company conducts a 2 for 3 rights issue at a subscription price of $8 when the pre-announcement stock price was $9. Assume that all investors use their rights to buy those extra shares.

What is the percentage increase in the stock price and the number of shares outstanding? The answers are given in the same order.

(a) -60%,   150%

(b) -42.22%,   150%

(c) -40%,   66.67%

(d) -22.22%,   66.67%

(e) -4.44%,   66.67%

Question 724  return distribution, mean and median returns

If a stock's future expected continuously compounded annual returns are normally distributed, what will be bigger, the stock's or continuously compounded annual return? Or would you expect them to be ?

Question 794  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 call option?

(a) ##N[d_1]##

(b) ##N[d_2]##

(c) ##−N[−d_1]##

(d) ##−N[−d_2]##

(e) ##N[−d_2]##

Where:

###d_1=\dfrac{\ln⁡[S_0/K]+(r+\sigma^2/2).T)}{\sigma.\sqrt{T}}### ###d_2=d_1-\sigma.\sqrt{T}=\dfrac{\ln⁡[S_0/K]+(r-\sigma^2/2).T)}{\sigma.\sqrt{T}}###