Fight Finance

Question 26  APR, effective rate

A European bond paying annual coupons of 6% offers a yield of 10% pa.

Convert the yield into an effective monthly rate, an effective annual rate and an effective daily rate. Assume that there are 365 days in a year.

All answers are given in the same order:

### r_\text{eff, monthly} , r_\text{eff, yearly} , r_\text{eff, daily} ###

(a) 0.0041, 0.05, 0.0001.

(b) 0.0080, 0.1, 0.0003.

(c) 0.0083, 0.1, 0.0003.

(d) 0.0083, 2.1384, 0.0031.

(e) 0.0083, 0.1047, 0.0033.

Question 48  IRR, NPV, bond pricing, premium par and discount bonds, market efficiency

The theory of fixed interest bond pricing is an application of the theory of Net Present Value (NPV). Also, a 'fairly priced' asset is not over- or under-priced. Buying or selling a fairly priced asset has an NPV of zero.

Considering this, which of the following statements is NOT correct?

(a) The internal rate of return (IRR) of buying a fairly priced bond is equal to the bond's yield.

(b) The Present Value of a fairly priced bond's coupons and face value is equal to its price.

(c) If a fairly priced bond's required return rises, its price will fall.

(d) Fairly priced premium bonds' yields are less than their coupon rates, prices are more than their face values, and the NPV of buying them is therefore positive.

(e) The NPV of buying a fairly priced bond is zero.

Question 160  interest only loan

You want to buy an apartment priced at $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as an interest only loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?

(a) $ 1,250.00

(b) $ 2,250.00

(c) $ 2,652.17

(d) $ 2,697.98

(e) $ 32,692.01

Question 377  leverage, capital structure

Issuing debt doesn't give away control of the firm because debt holders can't cast votes to determine the company's affairs, such as at the annual general meeting (AGM), and can't appoint directors to the board. or ?

Question 694  utility

Which of the below statements about utility is NOT generally accepted by economists? Most people are thought to:

(a) Prefer more to less, meaning that they will always like to have more wealth.

(b) Be risk averse, meaning that they dislike risk as measured by the standard deviation of wealth.

(c) Have a positively sloped utility function, so the gradient or first derivative of the utility function is always positive.

(d) Have a utility function that increases at a diminishing rate. So the shape is concave down like a frown, or the second derivative is always negative.

(e) Have a utility function that rises until it reaches the satiation point, then it falls because too much wealth causes problems.

Question 708  continuously compounding rate, continuously compounding rate conversion

Convert a 10% continuously compounded annual rate ##(r_\text{cc annual})## into an effective annual rate ##(r_\text{eff annual})##. The equivalent effective annual rate is:

(a) 230.258509% pa

(b) 10.536052% pa

(c) 10.517092% pa

(d) 10.468982% pa

(e) 9.531018% pa

Question 709  continuously compounding rate, APR

Which of the following interest rate quotes is NOT equivalent to a 10% effective annual rate of return? Assume that each year has 12 months, each month has 30 days, each day has 24 hours, each hour has 60 minutes and each minute has 60 seconds. APR stands for Annualised Percentage Rate.

(a) 9.7617696% is the APR compounding semi-annually ##(r_\text{apr comp 6mth})##

(b) 9.5689685% is the APR compounding monthly ##(r_\text{apr comp monthly})##

(c) 9.6454756% is the APR compounding daily ##(r_\text{apr comp daily})##

(d) 9.5310182% is the APR compounding per second ##(r_\text{apr comp per second})##

(e) 9.5310180% is the continuously compounded rate per annum ##(r_\text{cc annual})##

Question 807  market efficiency, expected and historical returns, CAPM, beta, systematic risk, no explanation

You work in Asia and just woke up. It looked like a nice day but then you read the news and found out that last night the American share market fell by 10% while you were asleep due to surprisingly poor macro-economic world news. You own a portfolio of liquid stocks listed in Asia with a beta of 1.6. When the Asian equity markets open, what do you expect to happen to your share portfolio? Assume that the capital asset pricing model (CAPM) is correct and that the market portfolio contains all shares in the world, of which American shares are a big part. Your portfolio beta is measured against this world market portfolio.

When the Asian equity market opens for trade, you would expect your portfolio value to:

(a) Remain unchanged.

(b) Instantaneously fall by 10%.

(c) Slowly fall by 10% over the day.

(d) Instantaneously fall by 16%.

(e) Slowly fall by 16% over the day.

Question 908  effective rate, return types, gross discrete return, return distribution, price gains and returns over time

For an asset's price to double from say $1 to $2 in one year, what must its gross discrete return (GDR) be? If the price now is ##P_0## and the price in one year is ##P_1## then the gross discrete return over the next year is:

###\text{GDR}_\text{annual} = \dfrac{P_1}{P_0}###

(a) 0%

(b) 30.102999566%

(c) 69.314718056%

(d) 100%

(e) 200%

Question 925  mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate, no explanation

The arithmetic average and standard deviation of returns on the ASX200 accumulation index over the 24 years from 31 Dec 1992 to 31 Dec 2016 were calculated as follows:

###\bar{r}_\text{yearly} = \dfrac{ \displaystyle\sum\limits_{t=1992}^{24}{\left( \ln⁡ \left( \dfrac{P_{t+1}}{P_t} \right) \right)} }{T} = \text{AALGDR} =0.0949=9.49\% \text{ pa}###

###\sigma_\text{yearly} = \dfrac{ \displaystyle\sum\limits_{t=1992}^{24}{\left( \left( \ln⁡ \left( \dfrac{P_{t+1}}{P_t} \right) - \bar{r}_\text{yearly} \right)^2 \right)} }{T} = \text{SDLGDR} = 0.1692=16.92\text{ pp pa}###

Assume that the log gross discrete returns are normally distributed and that the above estimates are true population statistics, not sample statistics, so there is no standard error in the sample mean or standard deviation estimates. Also assume that the standardised normal Z-statistic corresponding to a one-tail probability of 2.5% is exactly -1.96.

Which of the following statements is NOT correct? If you invested $1m today in the ASX200, then over the next 4 years:

(a) Continuously compounded mean and median returns are both 37.96% over the 4 year period.

(b) 95% confidence interval of the continuously compounded returns is between -28.3664% and 104.2864% over the 4 year period.

(c) Mean dollar value is $1.547835m while its median dollar value is $1.4617m in 4 years.

(d) 95% confidence interval of the dollar value is between $0.75302m and $2.17038m in 4 years.

(e) 95% confidence interval of the effective annual return is between -24.698% and 183.7332% over the 4 year period.