For a price of $13, Carla will sell you a share which will pay a dividend of $1 in one year and every year after that forever. The required return of the stock is 10% pa.

Bonds X and Y are issued by different companies, but they both pay a semi-annual coupon of 10% pa and they have the same face value ($100), maturity (3 years) and yield (10%) as each other.

Which of the following statements is true?

In these tough economic times, central banks around the world have cut interest rates so low that they are practically zero. In some countries, government bond yields are also very close to zero.

A three year government bond with a face value of $100 and a coupon rate of 2% pa paid semi-annually was just issued at a yield of 0%. What is the price of the bond?

A European company just issued two bonds, a

- 3 year zero coupon bond at a yield of 6% pa, and a
- 4 year zero coupon bond at a yield of 6.5% pa.

What is the company's forward rate over the fourth year (from t=3 to t=4)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.

**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 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 874** utility, return distribution, log-normal distribution, arithmetic and geometric averages

Who was the first theorist to endorse the maximisiation of the geometric average gross discrete return for investors (not gamblers) since it gave a "...portfolio that has a greater probability of being as valuable or more valuable than any other significantly different portfolio at the end of n years, n being large"?

**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:

Suppose the current Australian exchange rate is 0.8 USD per AUD.

If you think that the AUD will appreciate against the USD, contrary to the rest of the market, how could you profit? Right now you should:

**Question 989** PE ratio, Multiples valuation, leverage, accounting ratio

A firm has 20 million shares, earnings (or net income) of $100 million per annum and a 60% debt-to-**equity** ratio where both the debt and asset values are market values rather than book values. Similar firms have a PE ratio of 12.

Which of the below statements is **NOT** correct based on a PE multiples valuation?