Consider a UK fund currently holding an international equity portfolio with the following characteristics:
£1m invested in UK stocks in the FTSE 100 index, with a % portfolio beta relative to the FTSE 100 of 1.5
£2m invested in European stocks in the STOXX 50 index, with a % portfolio beta relative to the STOXX50 of 1
£3m invested in US stocks in the S&P 500 index, with a % portfolio beta relative to the S&P 500 of 1.75
£4m invested in Chinese stocks from the SSE index, with a % portfolio beta relative to the SSE index of 2.25
Suppose the risk factor returns follow correlated normal i.i.d. processes.
Tasks: (Each task carries a weight of 20% in your final grade)
Use the historical daily risk factor closing price data in the Excel spreadsheet provided at the top of this page to calculate the daily returns and hence estimate the volatilities of all the risk factors – and their correlations – over the entire data period.
Calculate the vector of portfolio betas in £ terms.
Define the normal linear Value-at-Risk (VaR) model and apply the model to calculate the 1% 10-day total systematic VaR for this portfolio. Interpret your result and discuss how it changes with the holding period and significance level.
Decompose this total VaR into Equity and Foreign Exchange (FX) VaR components. Explore how the VaR decomposition changes with different values for the risk factor correlations and explain your results. Why do some values for correlation fail to produce meaningful answers?
Now perform a stress test for the portfolio by selecting some different values for the volatilities and correlations which are appropriate to stressful market conditions, and again comment on your results.
