N1569
BSc EXAMINATION
Financial Risk Management
There are FIVE questions and each has FOUR parts. Each part carries 5 marks.
Each question should take you 24 minutes, so 6 minutes per part.
1. (a) You want to measure the market risk of a portfolio containing hundreds of cash
flows. How would you select the risk factors, and how would you map the cash flows to these risk factors?
(b) Given the 15-month interest rate is 3.5% per annum and it has a volatility of 60
basis points (bps), find the present value (PV) and the present value of a basis point (PV01) of a cash flow of $3m 15 months from now. Justify your answers.
(c) Use the appropriate Excel workbook to map this cash flow to vertices at 1 and 2
years, in such a way that both PV and volatility are preserved under the mapping.
You are given that the 1-year rate is 4% and has volatility 65 bps, the 2-year rate is 3% and has volatility 50 bps, and the correlation between the 1-year and 2-year rates is 0.9. Justify your answer.
(d) Use the appropriate Excel workbook to calculate the present value of a basis point (PV01) of the mapped cash flows in part (c) and comment on your results.
2. (a) Which model would you use to measure Value-at-Risk (VaR) for an equity portfolio and why?
(b) What issues would you expect to arise from this choice, if any?
(c) Calculate the 1% daily historical VaR of the S&P500 index using daily returns
between 1 January 2010 and 31 December 2023. How does this compare with the normal VaR? Give your answers as a % of the portfolio value.
(d) Scale this 1% daily VaR to a 10-day VaR under the assumption that the daily returns on the S&P 500 are independent and identically distributed. Would the scaled VaR remain unchanged if you were to assume the daily returns were positively autocorrelated? Justify your answer.
3. (a) What is Value at Risk (VaR)? Describe its parameters.
(b) Describe the purpose of the Excel spreadsheet “Rolling Normal VaR”
(c) Change the spreadsheet so that the 30-day standard deviation is replaced by a 10-day standard deviation, leaving the VaR parameters unchanged. Describe the effect on the graph and explain why we observe this effect.
(d) Describe the purpose of the “VaR Model Comparison" spreadsheet and discuss the results therein.