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:

1. Use the historical daily risk factor closing price data to calculate the daily returns and hence estimate the volatilities of all the risk factors and their correlations over the entire data period.
2. Calculate the vector of portfolio betas in terms.