MARKET RISK MANAGEMENT

*TAKE YOUR TIME, READ QUESTIONS AND ANSWER CORRECTLY*

QUESTION 1

A binary option pays off $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%. Note that some of the subsequent values were assumed and not calculated.

1. The risk-neutral probability of the payoffs (d2) is(1)............?.

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

2.Assume that d2 was calculated as - 1.4250 (minus 1.4250), use the tables to determine N(-d2), and use interpolation.

The probability is, therefore (2)...........?.

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

3. What will the value of the option be if N(-d2) were determined to be 0.1072?

The value of the option is $ (3)............?.

Round your answer to two decimal places (e.g., 12.23)

QUESTION 2

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

TRUE

FALSE

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

TRUE

FALSE

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

TRUE

FALSE

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

TRUE

FALSE

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

TRUE

FALSE

QUESTION 3

1. A financial institution owns a portfolio of options dependent on the US dollar-sterling 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 $ (1).........?.

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

2. A fund manager announces that the fund's 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 (2) win / lose ?, R (3)..........? or more during a three-month period.

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

QUESTION 4

1. Suppose we estimate the one-day 97.5% VaR from 1,100 observations as 5 (in millions of dollars). By fitting a standard distribution to the observations, the probability density function of the loss distribution at the 97.5% point is estimated to be 0.04.

The standard error of the VaR estimate is $ (1)...........? million.

Round your answer to two decimal places (e.g.,0.15million)

2. A financial institution owns a portfolio of options dependent on the US dollar-sterling exchange rate. The delta of the portfolio with respect to percentage changes in the exchange rate is 6.5. If the daily volatility of the exchange rate is 0.5% and a linear model is assumed.

The estimated 10-day 99% VaR is $ (2).........?.

Round your final answer to two decimal places (e.g., 12.23)

*TAKE YOUR TIME, READ QUESTIONS AND ANSWER CORRECTLY*