Fight Finance

Question 101  payout policy, no explanation

An established mining firm announces that it expects large losses over the following year due to flooding which has temporarily stalled production at its mines. Which statement(s) are correct?

(i) If the firm adheres to a full dividend payout policy it will not pay any dividends over the following year.

(ii) If the firm wants to signal that the loss is temporary it will maintain the same level of dividends. It can do this so long as it has enough retained profits.

(iii) By law, the firm will be unable to pay a dividend over the following year because it cannot pay a dividend when it makes a loss.

Select the most correct response:

(a) Only (i) is true.

(b) Only (ii) is true.

(c) Only (iii) is true.

(d) Only (i) and (ii) is true.

(e) All statements (i), (ii) and (iii) are true.

Question 119  market efficiency, fundamental analysis, joint hypothesis problem

Your friend claims that by reading 'The Economist' magazine's economic news articles, she can identify shares that will have positive abnormal expected returns over the next 2 years. Assuming that her claim is true, which statement(s) are correct?

(i) Weak form market efficiency is broken.

(ii) Semi-strong form market efficiency is broken.

(iii) Strong form market efficiency is broken.

(iv) The asset pricing model used to measure the abnormal returns (such as the CAPM) is either wrong (mis-specification error) or is measured using the wrong inputs (data errors) so the returns may not be abnormal but rather fair for the level of risk.

Select the most correct response:

(a) Only (iii) is true.

(b) Only (ii) and (iii) are true.

(c) Only (i), (ii) and (iii) are true.

(d) Either (ii) and (iii) are true, or (iv) is true, or (ii), (iii) and (iv) are true.

(e) Either (i), (ii) and (iii) are true, or (iv) is true, or all are true.

Question 147  bill pricing, simple interest rate, no explanation

A 30-day Bank Accepted Bill has a face value of $1,000,000. The interest rate is 8% pa and there are 365 days in the year. What is its price now?

(a) $294,117.65

(b) $993,467.61

(c) $993,694.40

(d) $3,400,000.00

(e) $11,550,632.91

Question 288  Annuity

There are many ways to write the ordinary annuity formula.

Which of the following is NOT equal to the ordinary annuity formula?

(a) ##V_0 = \dfrac{C_1}{r} \left(1-\dfrac{1}{(1+r)^T} \right) ##

(b) ##V_0 = \dfrac{C_1 \left(1-\dfrac{1}{(1+r)^T} \right)}{r}##

(c) ##V_0 = C_1\dfrac{\left(1-(1+r)^{-T} \right)}{r}##

(d) ##V_0 = C_1 \left(1-(1+r)^{-T} \right) r^{-1}##

(e) ##V_0 = C_1 \left(r^{-1}-(1+r)^{-T-1} \right)##

Question 450  CAPM, risk, portfolio risk, no explanation

The accounting identity states that the book value of a company's assets (A) equals its liabilities (L) plus owners equity (OE), so A = L + OE.

The finance version states that the market value of a company's assets (V) equals the market value of its debt (D) plus equity (E), so V = D + E.

Therefore a business's assets can be seen as a portfolio of the debt and equity that fund the assets.

Let ##\sigma_\text{V total}^2## be the total variance of returns on assets, ##\sigma_\text{V syst}^2## be the systematic variance of returns on assets, and ##\sigma_\text{V idio}^2## be the idiosyncratic variance of returns on assets, and ##\rho_\text{D idio, E idio}## be the correlation between the idiosyncratic returns on debt and equity.

Which of the following equations is NOT correct?

(a) ##r_V = \dfrac{D}{V}.r_D + \dfrac{E}{V}.r_E##

(b) ##\beta_V = \dfrac{D}{V}.\beta_D + \dfrac{E}{V}.\beta_E##

(c) ##\sigma_\text{V syst}^2 = \left(\dfrac{D}{V}\right)^2.\sigma_\text{D syst}^2 + \left(\dfrac{E}{V}\right)^2.\sigma_\text{E syst}^2##

(d) ##\sigma_\text{V idio}^2 = \left(\dfrac{D}{V}\right)^2.\sigma_\text{D idio}^2 + \left(\dfrac{E}{V}\right)^2.\sigma_\text{E idio}^2 + 2.\dfrac{D}{V}.\dfrac{E}{V}.\rho_\text{D idio, E idio}.\sigma_\text{D idio}.\sigma_\text{E idio}##

(e) ##\sigma_\text{V total}^2 = \left(\dfrac{D}{V}\right)^2.\sigma_\text{D total}^2 + \left(\dfrac{E}{V}\right)^2.\sigma_\text{E total}^2##

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 707  continuously compounding rate, continuously compounding rate conversion

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

(a) 230.258509% pa

(b) 10.536052% pa

(c) 10.517092% pa

(d) 10.468982% pa

(e) 9.531018% pa

Question 712  effective rate conversion

An effective monthly return of 1% ##(r_\text{eff monthly})## is equivalent to an effective annual return ##(r_\text{eff annual})## of:

(a) 12.682503% pa

(b) 12.060201% pa

(c) 12% pa

(d) 11.940397% pa

(e) 3.464102% pa

Question 732  real and nominal returns and cash flows, inflation, income and capital returns

An investor bought a bond for $100 (at t=0) and one year later it paid its annual coupon of $1 (at t=1). Just after the coupon was paid, the bond price was $100.50 (at t=1). Inflation over the past year (from t=0 to t=1) was 3% pa, given as an effective annual rate.

Which of the following statements is NOT correct? The bond investment produced a:

(a) Nominal income return of 1% pa ##\left( =\dfrac{1}{100} \right)##.

(b) Nominal capital return of 0.5% pa ##\left( =\dfrac{100.5-100}{100} \right)##.

(c) Nominal total return of 1.5% pa ##\left( =\dfrac{100.5-100+1}{100} \right)##.

(d) Real income return of 0.9708738% pa##\left( =\dfrac{ 1/(1+0.03)^1}{100} \right)##.

(e) Real capital return of 0.4854369% pa ##\left( =\dfrac{ (100.5-100)/(1+0.03)^1}{100} \right) ##.

Question 779  mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

Fred owns some BHP shares. He has calculated BHP’s monthly returns for each month in the past 30 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 0.8% per month using this formula:

###\bar{r}_\text{monthly}= \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( r_\text{t monthly} \right)} }{T} =0.008=0.8\% \text{ per month}###

He also found the standard deviation of these monthly returns which was 15% 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} =0.15=15\%\text{ per month}###

Assume that the past historical average return is the true population average of future expected returns and the stock's returns calculated above ##(r_\text{t monthly})## are normally distributed. Which of the below statements about Fred’s BHP shares is NOT correct?

(a) The returns ##r_\text{t monthly}## are continuously compounded monthly returns.

(b) The mean, median and mode of the continuously compounded annual return is expected to equal 0.8% per month.

(c) The annualised average continuously compounded return is ##\bar{r}_\text{cc annual}=12×0.008=0.096=9.6\%\text{ pa}##. The annualised standard deviation is ##\sigma_\text{annual} = \sqrt{12}×0.15=0.519615242 = 52\%\text{ pa}##.

(d) If the current price of the BHP shares is $20, they're expected to have a median value of $52.2339 ##(= 20×e^{0.008×12×10})## in 10 years.

(e) If the current price of the BHP shares is $20, they're expected to have a mean value of $13.5411 ##(= 20×e^{(0.008 - 0.15^2/2)×12×10})## in 10 years.