Fight Finance

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 282  expected and historical returns, income and capital returns

You're the boss of an investment bank's equities research team. Your five analysts are each trying to find the expected total return over the next year of shares in a mining company. The mining firm:

• Is regarded as a mature company since it's quite stable in size and was floated around 30 years ago. It is not a high-growth company;
• Share price is very sensitive to changes in the price of the market portfolio, economic growth, the exchange rate and commodities prices. Due to this, its standard deviation of total returns is much higher than that of the market index;
• Experienced tough times in the last 10 years due to unexpected falls in commodity prices.
• Shares are traded in an active liquid market.

Your team of analysts present their findings, and everyone has different views. While there's no definitive true answer, whose calculation of the expected total return is the most plausible? Assume that:

• The analysts' source data is correct and true, but their inferences might be wrong;
• All returns and yields are given as effective annual nominal rates.

(a) Alice says 5% pa since she calculated that this was the average total yield on government bonds over the last 10 years. She says that this is also the expected total yield implied by current prices on one year government bonds.

(b) Bob says 4% pa since he calculated that this was the average total return on the mining stock over the last 10 years.

(c) Cate says 3% pa since she calculated that this was the average growth rate of the share price over the last 10 years.

(d) Dave says 6% pa since he calculated that this was the average growth rate of the share market price index (not the accumulation index) over the last 10 years.

(e) Eve says 15% pa since she calculated that this was the discount rate implied by the dividend discount model using the current share price, forecast dividend in one year and a 3% growth rate in dividends thereafter, which is the expected long term inflation rate.

Question 307  risk, variance

Let the variance of returns for a share per month be ##\sigma_\text{monthly}^2##.

What is the formula for the variance of the share's returns per year ##(\sigma_\text{yearly}^2)##?

Assume that returns are independently and identically distributed (iid) so they have zero auto correlation, meaning that if the return was higher than average today, it does not indicate that the return tomorrow will be higher or lower than average.

(a) ##\sigma_\text{yearly}^2 = \sigma_\text{monthly}^2##

(b) ##\sigma_\text{yearly}^2 = \sigma_\text{monthly}^2 \times 12##

(c) ##\sigma_\text{yearly}^2 = \sigma_\text{monthly}^2 \times 12^2##

(d) ##\sigma_\text{yearly}^2 = \sigma_\text{monthly}^2 \times \sqrt{12}##

(e) ##\sigma_\text{yearly}^2 = \sigma_\text{monthly}^2 \times {12}^{1/3}##

Question 521  NPV, Annuity

The following cash flows are expected:

• 10 yearly payments of $80, with the first payment in 6.5 years from now (first payment at t=6.5).
• A single payment of $500 in 4 years and 3 months (t=4.25) from now.

What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate?

(a) $573.977303

(b) $598.028469

(c) $624.484752

(d) $700.028893

(e) $736.685218

Question 656  debt terminology

Which of the following statements is NOT correct? Lenders:

(a) Buy debt.

(b) Own debt.

(c) Are owed money.

(d) Write debt.

(e) Have debt assets.

Question 689  future, hedging

An equity index fund manager controls a USD1 billion diversified equity portfolio with a beta of 1.3. The equity manager fears that a global recession will begin in the next year, causing equity prices to tumble. The market does not think that this will happen. If the fund manager wishes to reduce her portfolio beta to 0.5, how many S&P500 futures should she sell?

The US market equity index is the S&P500. One year CME futures on the S&P500 currently trade at 2,062 points and the spot price is 2,091 points. Each point is worth $250. How many one year S&P500 futures contracts should the fund manager sell?

(a) 970

(b) 1,530

(c) 1,552

(d) 2,487

(e) 2,522

Question 858  indirect security, intermediated finance, no explanation

Which of the following transactions involves an ‘indirect security’ using a ‘financial intermediary’?

(a) Alice buys Alan’s shares using their share brokers and the securities exchange.

(b) Bell buys Bob’s house using his real estate agent.

(c) Carla lends Carlos money at an interest rate of 10% pa for 3 years.

(d) Dora lends money to her bank at 2% pa and the bank lends the funds to David at 5% pa.

(e) Eve buys Ernie’s government bond using their brokers and the securities exchange.

Question 931  confidence interval, normal distribution

A stock's returns are normally distributed with a mean of 10% pa and a standard deviation of 20 percentage points pa. What is the 90% confidence interval of returns over the next year? Note that the Z-statistic corresponding to a one-tail:

• 90% normal probability density function is 1.282.
• 95% normal probability density function is 1.645.
• 97.5% normal probability density function is 1.960.

The 90% confidence interval of annual returns is between:

(a) 30% and -10% pa.

(b) 32.9% and -32.9% pa.

(c) 35.64% and -15.64% pa.

(d) 42.9% and -22.9% pa.

(e) 49.2% and -29.2% pa.

Question 961  stock split, bonus issue

Which one of the following statements is NOT correct? A 1-for-4 bonus issue:

(a) Will increase the number of shares by 25%.

(b) Will decrease the share price by 25%.

(c) Is equivalent to a 5-for-4 stock split.

(d) Is equivalent to a 25% stock dividend.

(e) Has no effect on the firm's cash flow.

Question 981  margin loan, Basel accord, credit conversion factor

Margin loans secured by listed stock have a Basel III risk weight of 20%.

For margin loans that cannot be immediately cancelled by banks and asked to be repaid, the credit conversion factor (CCF) is 20%.

Suppose you have a stock portfolio worth $500,000, financed by:

• $300,000 of your own money; and
• $200,000 of the bank’s funds in the form of a margin loan which can only be cancelled by the bank after 5 days notice. The margin loan’s maximum LVR is 70%.

How much regulatory capital must the bank hold due to your margin loan? Assume that the bank wishes to pay dividends to its shareholders, so include the 2.5% capital conservation buffer in your calculations.

(a) $2100

(b) $4200

(c) $4800

(d) $5670

(e) $6300