Fight Finance

Question 56  income and capital returns, bond pricing, premium par and discount bonds

Which of the following statements about risk free government bonds is NOT correct?

(a) Premium bonds have a positive expected capital return.

(b) Discount bonds have a positive expected capital return.

(c) Par bonds have a zero expected capital return.

(d) Par bonds have a total expected yield equal to their coupon yield.

(e) Zero coupon bonds selling at par would have zero expected total, income and capital yields.

Hint: Total return can be broken into income and capital returns as follows:

###\begin{aligned} r_\text{total} &= \frac{c_1}{p_0} + \frac{p_1-p_0}{p_0} \\ &= r_\text{income} + r_\text{capital} \end{aligned} ###

The capital return is the growth rate of the price.
The income return is the periodic cash flow. For a bond this is the coupon payment.

Question 242  technical analysis, market efficiency

Select the most correct statement from the following.

'Chartists', also known as 'technical traders', believe that:

(a) Markets are weak-form efficient.

(b) Markets are semi-strong-form efficient.

(c) Past prices cannot be used to predict future prices.

(d) Past returns can be used to predict future returns.

(e) Stock prices reflect all publically available information.

Question 248  CAPM, DDM, income and capital returns

The total return of any asset can be broken down in different ways. One possible way is to use the dividend discount model (or Gordon growth model):

###p_0 = \frac{c_1}{r_\text{total}-r_\text{capital}}###

Which, since ##c_1/p_0## is the income return (##r_\text{income}##), can be expressed as:

###r_\text{total}=r_\text{income}+r_\text{capital}###

So the total return of an asset is the income component plus the capital or price growth component.

Another way to break up total return is to use the Capital Asset Pricing Model:

###r_\text{total}=r_\text{f}+β(r_\text{m}- r_\text{f})###

###r_\text{total}=r_\text{time value}+r_\text{risk premium}###

So the risk free rate is the time value of money and the term ##β(r_\text{m}- r_\text{f})## is the compensation for taking on systematic risk.

Using the above theory and your general knowledge, which of the below equations, if any, are correct?

(I) ##r_\text{income}=r_\text{time value}##

(II) ##r_\text{income}=r_\text{risk premium}##

(III) ##r_\text{capital}=r_\text{time value}##

(IV) ##r_\text{capital}=r_\text{risk premium}##

(V) ##r_\text{income}+r_\text{capital}=r_\text{time value}+r_\text{risk premium}##

Which of the equations are correct?

(a) I, IV and V only.

(b) II, III and V only.

(c) V only.

(d) All are true.

(e) None are true.

Question 275  derivative terminology, future

The 'futures price' in a futures contract is paid at the start when the futures contract is agreed to. or ?

Question 449  personal tax on dividends, classical tax system

A small private company has a single shareholder. This year the firm earned a $100 profit before tax. All of the firm's after tax profits will be paid out as dividends to the owner.

The corporate tax rate is 30% and the sole shareholder's personal marginal tax rate is 45%.

The United States' classical tax system applies because the company generates all of its income in the US and pays corporate tax to the Internal Revenue Service. The shareholder is also an American for tax purposes.

What will be the personal tax payable by the shareholder and the corporate tax payable by the company?

(a) Personal tax of $6.43 and corporate tax of $45.

(b) Personal tax of $15 and corporate tax of $30.

(c) Personal tax of $16.5 and corporate tax of $45.

(d) Personal tax of $31.5 and corporate tax of $30.

(e) Personal tax of $45 and corporate tax of $0.

Question 619  CFFA

To value a business's assets, the free cash flow of the firm (FCFF, also called CFFA) needs to be calculated. This requires figures from the firm's income statement and balance sheet. For what figures is the balance sheet needed? Note that the balance sheet is sometimes also called the statement of financial position.

(a) Net income, depreciation and interest expense.

(b) Depreciation and capital expenditure.

(c) Current assets, current liabilities and cost of goods sold (COGS).

(d) Current assets, current liabilities and capital expenditure.

(e) Current assets, current liabilities and depreciation expense.

Question 722  mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

Here is a table of stock prices and returns. Which of the statements below the table is NOT correct?

Price and Return Population Statistics
Time	Prices	LGDR	GDR	NDR
0	100
1	50	-0.6931	0.5	-0.5
2	100	0.6931	2	1
Arithmetic average		0	1.25	0.25
Arithmetic standard deviation		0.9802	1.0607	1.0607

 

(a) The geometric average of the gross discrete returns (GAGDR) equals 1 which is 100%.

(b) ##\text{GAGDR} = \exp \left( \text{AALGDR} \right)##. The GAGDR is equal to the natural exponent of the arithmetic average of the logarithms of the gross discrete returns (AALGDR).

(c) ##\text{GAGDR} = \left( P_T/P_0 \right)^{1/T}##. The GAGDR equals the ratio of the last and first prices raised to the power of the inverse of the number of time periods between them.

(d) ##\text{LGAGDR} = \text{AALGDR}##. This is always true, regardless of the distribution of the prices or returns and the number of return observations. The logarithm of the geometric average of the gross discrete returns (LGAGDR) is always equal to the arithmetic average of the logarithms of the gross discrete returns (AALGDR).

(e) ##\text{LAAGDR} = \text{AALGDR} + \text{SDLGDR}^2/2##. This is always true, regardless of the distribution of the prices or returns and the number of return observations. The logarithm of the arithmetic average of the gross discrete returns (LAAGDR) equals the arithmetic average of the logarithms of the gross discrete returns (AALGDR) plus half the variance of the LGDR's.

Question 885  foreign exchange rate, no explanation

A Brazilian lady wishes to convert 1 million Brazilian Real (BRL) into Chinese Renminbi (RMB, also called the Yuan or CNY). The exchange rate is 3.42 BRL per USD and 6.27 RMB per USD. How much is the BRL 1 million worth in RMB?

(a) RMB 21,443,400

(b) RMB 1,833,333

(c) RMB 592,089

(d) RMB 545,455

(e) RMB 46,634

Question 948  VaR, expected shortfall

Below is a historical sample of returns on the S&P500 capital index.

S&P500 Capital Index Daily Returns Ranked from Best to Worst
10,000 trading days from 4th August 1977 to 24 March 2017 based on closing prices.
Rank	Date (DD-MM-YY)	Continuously compounded daily return (% per day)
1	21-10-87	9.23
2	08-03-83	8.97
3	13-11-08	8.3
4	30-09-08	8.09
5	28-10-08	8.01
6	29-10-87	7.28
…	…	…
9980	11-12-08	-5.51
9981	22-10-08	-5.51
9982	08-08-11	-5.54
9983	22-09-08	-5.64
9984	11-09-86	-5.69
9985	30-11-87	-5.88
9986	14-04-00	-5.99
9987	07-10-98	-6.06
9988	08-01-88	-6.51
9989	27-10-97	-6.55
9990	13-10-89	-6.62
9991	15-10-08	-6.71
9992	29-09-08	-6.85
9993	07-10-08	-6.91
9994	14-11-08	-7.64
9995	01-12-08	-7.79
9996	29-10-08	-8.05
9997	26-10-87	-8.4
9998	31-08-98	-8.45
9999	09-10-08	-12.9
10000	19-10-87	-23.36
Mean of all 10,000:		0.0354
Sample standard deviation of all 10,000:		1.2062
Sources: Bloomberg and S&P.

 

Assume that the one-tail Z-statistic corresponding to a probability of 99.9% is exactly 3.09. Which of the following statements is NOT correct? Based on the historical data, the 99.9% daily:

(a) Absolute non-parametric VaR is 6.62% per day.

(b) Relative non-parametric VaR is 6.6554% per day.

(c) Absolute parametric VaR is 6.173521% per day.

(d) Relative parametric VaR is 3.727158% per day.

(e) Non-parametric expected shortfall is 9.706% per day.

Question 970  foreign exchange rate, no explanation

Examine the below graph.

Which of the below statements is NOT correct?

(a) The currency quote AUD/GBP is called a ‘cross rate’.

(b) The AUD appreciated against the GBP over the period from 1955 to 2018.

(c) The AUD depreciated against the USD over the period from 1955 to 2018.

(d) The y-axis on the ‘AUD/USD’ chart would be measured in AUD per one USD.