Question:

DGI Investors is responsible for managing the investment portfolio of Carnegie University Trust which has a market value of $ 100m. The new appointed chairman of the University Trust, Bolger Rodman wants to assess the risk of the portfolio and any possibility of risk management. During a discussion with the team of DGI Investors, Bolger raised the following queries.

Statement 1

"I have come across an investment report where Value at Risk (VAR) measure has been used as a measure of market risk. How appropriate is VAR for the trust's portfolio."

Statement 2

"There are methods of estimating VAR estimate. I would like to know the three methods to estimate VAR. I think Analytical VAR method is the most suitable method to estimate VAR when there are derivative products in the portfolio as they follow a normal distribution"

Statement 3

"The expected 1-day return for the $100,000,000 portfolio is 0.00095 and the historical standard deviation of daily returns is 0.0011. The daily value at risk at 5% significance is the same for a monthly value at risk at 5% significance."

Statement 4

"The daily value at risk will increase with an increase in the expected 1-day return and daily VAR will decrease with an increase in the historical standard deviation."

Statement 5
"A portfolio's VAR will be larger when it is measured at a five percent probability than when it is measured at a 1 percent probability."

Bolger is very concerned with a forward rate agreement that the University trust is about to enter in the coming week for the financing of the business school.

The details of the Forward Rate Agreement are as follows:

Carnegie will borrow $ 10,000,000 in six months at LIBOR for 1 year and LIBOR is currently 5%. The trust enters an FRA with a reference rate of 5% and a notional principal of $ 10,000,000. Assuming in three months into the contract, however, LIBOR has climbed to 6%. Assuming the risk-free rate is 4%.

Required:

For the February Committee meeting you have been asked to cover the following issues in the agenda concerning Carnegie University Trust portfolio:

(i) Define in detail Value at Risk as a measure of market risk and the key elements involved when interpreting VAR.

(ii) Based on statement 2, outline the three methods used to calculate VAR and if Bolger is correct with the statement relating to the use of analytical method for derivative products,

(iii) Using the data in statement 3, calculate the daily VAR and monthly Value at Risk.

(iv) Critique the validity of statement 4 in relation to the effect on VAR for an increase in expected return and secondly an increase in historical standard deviation.