A project's Profitability Index (PI) is less than 1. Select the most correct statement:
Harvey Norman the large retailer often runs sales advertising 2 years interest free when you purchase its products. This offer can be seen as a free personal loan from Harvey Norman to its customers.
Assume that banks charge an interest rate on personal loans of 12% pa given as an APR compounding per month. This is the interest rate that Harvey Norman deserves on the 2 year loan it extends to its customers. Therefore Harvey Norman must implicitly include the cost of this loan in the advertised sale price of its goods.
If you were a customer buying from Harvey Norman, and you were paying immediately, not in 2 years, what is the minimum percentage discount to the advertised sale price that you would insist on? (Hint: if it makes it easier, assume that you’re buying a product with an advertised price of $100).
Suppose you had $100 in a savings account and the interest rate was 2% per year.
After 5 years, how much do you think you would have in the account if you left the money to grow?
Question 584 option, option payoff at maturity, option profit
Which of the following statements about European call options on non-dividend paying stocks is NOT correct?
The current gold price is $700, gold storage costs are 2% pa and the risk free rate is 10% pa, both with continuous compounding.
What should be the 3 year gold futures price?
The symbol ##\text{GDR}_{0\rightarrow 1}## represents a stock's gross discrete return per annum over the first year. ##\text{GDR}_{0\rightarrow 1} = P_1/P_0##. The subscript indicates the time period that the return is mentioned over. So for example, ##\text{AAGDR}_{1 \rightarrow 3}## is the arithmetic average GDR measured over the two year period from years 1 to 3, but it is expressed as a per annum rate.
Which of the below statements about the arithmetic and geometric average GDR is NOT correct?
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?
A firm conducts a two-for-one stock split. Which of the following consequences would NOT be expected?
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 |
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10,000 trading days from 4th August 1977 to 24 March 2017 based on closing prices. |
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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: