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Question 116 capital structure, CAPM

A firm changes its capital structure by issuing a large amount of equity and using the funds to repay debt. Its assets are unchanged. Ignore interest tax shields.

According to the Capital Asset Pricing Model (CAPM), which statement is correct?

Question 809 Markowitz portfolio theory, CAPM, Jensens alpha, CML, systematic and idiosyncratic risk

A graph of assets’ expected returns ##(\mu)## versus standard deviations ##(\sigma)## is given in the graph below. The CML is the capital market line.

Which of the following statements about this graph, Markowitz portfolio theory and the Capital Asset Pricing Model (CAPM) theory is NOT correct?

(a) The market portfolio M has systematic risk only. It’s a fully diversified portfolio comprised of all individual risky assets. The market portfolio is usually assumed to be the equity index, such as the ASX200 in Australia or the S&P500 in the US.

(b) The risk free security has no risk at all. Government bonds are usually assumed to be the risk-free security.

(c) Portfolio combinations of the market portfolio and risk free security will plot on the CML and will have systematic risk only. They will have no diversifiable risk.

(d) The portfolios on the CML with a return above ##r_f## have maximum return for any given level of risk.

(e) The individual assets and portfolios with returns less than the risk free rate are over-priced, have a negative Jensen’s alpha and should be sold.

Question 810 CAPM, systematic and idiosyncratic risk, market efficiency

Examine the graphs below. Assume that asset A is a single stock. Which of the following statements is NOT correct? Asset A:

Question 988 variance, covariance, beta, CAPM, risk, no explanation

Price Data Time Series
Sourced from Yahoo Finance Historical Price Data
Date	S&P500 Index (^GSPC)					Apple (AAPL)
Date	Open	High	Low	Close	Adj close	Open	High	Low	Close	Adj close
2007, Wed 3 Jan	1418	1429	1408	1417	1417	12.33	12.37	11.7	11.97	10.42
2008, Wed 2 Jan	1468	1472	1442	1447	1447	28.47	28.61	27.51	27.83	24.22
2009, Fri 2 Jan	903	935	899	932	932	12.27	13.01	12.17	12.96	11.28
2010, Mon 4 Jan	1117	1134	1117	1133	1133	30.49	30.64	30.34	30.57	26.6

Source: Yahoo Finance.

Which of the following statements about the above table which is used to calculate Apple's equity beta is NOT correct?

Question 994 duration

Find the Macaulay duration of a 2 year 5% pa annual fixed coupon bond which has a $100 face value and currently has a yield to maturity of 8% pa. The Macaulay duration is:

Question 872 duration, Macaulay duration, modified duration, portfolio duration

A fixed coupon bond’s modified duration is 20 years, and yields are currently 10% pa compounded annually. Which of the following statements about the bond is NOT correct?

Question 999 duration, duration of a perpetuity with growth, CAPM, DDM

A stock has a beta of 0.5. Its next dividend is expected to be $3, paid one year from now. Dividends are expected to be paid annually and grow by 2% pa forever. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. All returns are effective annual rates.

What is the Macaulay duration of the stock now?

Question 904 option, Black-Scholes-Merton option pricing, option on future on stock index

A six month European-style call option on six month S&P500 index futures has a strike price of 2800 points.

The six month futures price on the S&P500 index is currently at 2740.805274 points. The futures underlie the call option.

The S&P500 stock index currently trades at 2700 points. The stock index underlies the futures. The stock index's standard deviation of continuously compounded returns is 25% pa.

The risk-free interest rate is 5% pa continuously compounded.

Use the Black-Scholes-Merton formula to calculate the option price. The call option price now is:

Question 797 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 risk-neutral probability that a European put option will be exercised?

Question 793 option, hedging, delta hedging, gamma hedging, gamma, Black-Scholes-Merton option pricing

A bank buys 1000 European put options on a $10 non-dividend paying stock at a strike of $12. The bank wishes to hedge this exposure. The bank can trade the underlying stocks and European call options with a strike price of 7 on the same stock with the same maturity. Details of the call and put options are given in the table below. Each call and put option is on a single stock.

European Options on a Non-dividend Paying Stock
Description	Symbol	Put Values	Call Values
Spot price ($)	##S_0##	10	10
Strike price ($)	##K_T##	12	7
Risk free cont. comp. rate (pa)	##r##	0.05	0.05
Standard deviation of the stock's cont. comp. returns (pa)	##\sigma##	0.4	0.4
Option maturity (years)	##T##	1	1
Option price ($)	##p_0## or ##c_0##	2.495350486	3.601466138
##N[d_1]##	##\partial c/\partial S##		0.888138405
##N[d_2]##	##N[d_2]##		0.792946442
##-N[-d_1]##	##\partial p/\partial S##	-0.552034778
##N[-d_2]##	##N[-d_2]##	0.207053558
Gamma	##\Gamma = \partial^2 c/\partial S^2## or ##\partial^2 p/\partial S^2##	0.098885989	0.047577422
Theta	##\Theta = \partial c/\partial T## or ##\partial p/\partial T##	0.348152078	0.672379961

Which of the following statements is NOT correct?

Question 434 Merton model of corporate debt, real option, option

A risky firm will last for one period only (t=0 to 1), then it will be liquidated. So it's assets will be sold and the debt holders and equity holders will be paid out in that order. The firm has the following quantities:

##V## = Market value of assets.

##E## = Market value of (levered) equity.

##D## = Market value of zero coupon bonds.

##F_1## = Total face value of zero coupon bonds which is promised to be paid in one year.

What is the payoff to debt holders at maturity, assuming that they keep their debt until maturity?

Question 319 foreign exchange rate, monetary policy, American and European terms

Investors expect the Reserve Bank of Australia (RBA) to keep the policy rate steady at their next meeting.

Then unexpectedly, the RBA announce that they will increase the policy rate by 25 basis points due to fears that the economy is growing too fast and that inflation will be above their target rate of 2 to 3 per cent.

What do you expect to happen to Australia's exchange rate in the short term? The Australian dollar is likely to:

Question 626 cross currency interest rate parity, foreign exchange rate, forward foreign exchange rate

The Australian cash rate is expected to be 2% pa over the next one year, while the Japanese cash rate is expected to be 0% pa, both given as nominal effective annual rates. The current exchange rate is 100 JPY per AUD.

What is the implied 1 year forward foreign exchange rate?

Question 320 foreign exchange rate, monetary policy, American and European terms

Investors expect the Reserve Bank of Australia (RBA) to decrease the overnight cash rate at their next meeting.

Then unexpectedly, the RBA announce that they will keep the policy rate unchanged.

What do you expect to happen to Australia's exchange rate in the short term? The Australian dollar is likely to:

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:

Question 383 Merton model of corporate debt, real option, option

In the Merton model of corporate debt, buying a levered company's debt is equivalent to buying the company's assets and:

Question 710 continuously compounding rate, continuously compounding rate conversion

A continuously compounded monthly return of 1% ##(r_\text{cc monthly})## is equivalent to a continuously compounded annual return ##(r_\text{cc annual})## of:

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 726 return distribution, mean and median returns

Question 792 mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate, log-normal distribution, confidence interval

A risk manager has identified that their investment fund’s continuously compounded portfolio returns are normally distributed with a mean of 10% pa and a standard deviation of 40% pa. The fund’s portfolio is currently valued at $1 million. Assume that there is no estimation error in the above figures. To simplify your calculations, all answers below use 2.33 as an approximation for the normal inverse cumulative density function at 99%. All answers are rounded to the nearest dollar. Assume one month is 1/12 of a year. Which of the following statements is NOT correct?

Question 926 mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

The arithmetic average continuously compounded or log gross discrete return (AALGDR) on the ASX200 accumulation index over the 24 years from 31 Dec 1992 to 31 Dec 2016 is 9.49% pa.

The arithmetic standard deviation (SDLGDR) is 16.92 percentage points 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.

If you had a $1 million fund that replicated the ASX200 accumulation index, in how many years would the median dollar value of your fund first be expected to lie outside the 95% confidence interval forecast?

Question 927 mean and median returns, mode return, return distribution, arithmetic and geometric averages, continuously compounding rate

The arithmetic average continuously compounded or log gross discrete return (AALGDR) on the ASX200 accumulation index over the 24 years from 31 Dec 1992 to 31 Dec 2016 is 9.49% pa.

The arithmetic standard deviation (SDLGDR) is 16.92 percentage points pa.

If you had a $1 million fund that replicated the ASX200 accumulation index, in how many years would the mean dollar value of your fund first be expected to lie outside the 95% confidence interval forecast?

Question 120 credit risk, payout policy

A newly floated farming company is financed with senior bonds, junior bonds, cumulative non-voting preferred stock and common stock. The new company has no retained profits and due to floods it was unable to record any revenues this year, leading to a loss. The firm is not bankrupt yet since it still has substantial contributed equity (same as paid-up capital).

On which securities must it pay interest or dividend payments in this terrible financial year?

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.

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