1. A binary option has a pays-off of $165 if a stock price is greater than $65 in three months. The current stock price is $50 and its volatility is 40%. The risk-free rate is 4% and the expected return on the stock is 10%. What is the real-world probability that the payoff will be received?

The real-world probability of the payoffs (d2) is Answer.

Enter the amount, either negative (e.g., -5.6789) or positive (e.g., 5.6789), rounded to four decimals.

The probability is, therefore Answer.

Enter the four-decimal cumulative probability (e.g., 0.5832).

2. 1. Value at Risk (VaR) and Expected Shortfall (ES) aims to provide a single number that summarise the total risk of the portfolio.

TRUEFALSE

2. Backtesting for Expected Shortfall (ES) is easier than for Value at Risk (VaR).

TRUEFALSE

3. The historical simulation involves the use of todays data as a guide to what will happen in the future.

TRUEFALSE

4. Periods of high volatility in the market will tend to give higher values for Value at Risk (VaR) and Expected Shortfall (ES).

TRUEFALSE

5. An advantage of the Monte Carlo simulation is that it does not have to assume the risk factors are normally distributed.

TRUEFALSE

A portfolio consists of both MTN and RMB shares. The 10-day 95% VaR for the portfolio of MTN shares is R2 505 400, the 10-day 95% VaR for the portfolio of RMB shares is R894 500 and the 10-day 95% VaR for the portfolio of both MTN and RMB shares is R3 303 000, respectively.

The benefit of diversification is equal to R Answer

Enter a numerical number without spaces or commas for thousand separators (E.g 17224)

If MTN and RMB were perfectly correlated, then the VaR for both portfolios of MTN and RMB would be Answer more thanless thanequal to the VaR for the MTN portfolio plus the Var for RMB portfolio.

1. A financial institution owns a portfolio of options dependent on the US dollarsterling exchange rate. The delta of the portfolio with respect to percentage changes in the exchange rate is 6.1. If the daily volatility of the exchange rate is 0.5% and a linear model is assumed. The estimated 10-day99% VaR is $Answer.

Round your final answer to four decimal places (e.g., 0.2345)

2. A fund manager announces that the funds three-month 99% VaR is 8.2% of the size of the portfolio being managed. You have an investment of R1,000,000 in the fund.

There is a 1% chance that you will Answer winlose, RAnswer or more during a three-month period.

Enter a numerical number without spaces or commas for thousand separators (E.g 24000)