Q1 Would you be able to help me with the below question?

Consider an investor who holds a position that includes $500,000 invested in a 10-year Japanese government bond futures contract (YGB) and $500,000 invested in a Japanese stock index futures contract (YXF). Their annual volatilities are 6 and 18 percent respectively, with a correlation of -0.4. Assume that returns are normally distributed and VaR should be measured at 99 percent level.

1) What is the portfolio VaR
2) What is the portfolio gain from diversification benefits?
3) What is the marginal and component VaR of YCB and YXF?
4) Which of the two assets is better to be removed if you want to reduce VaR?
5) What is the incremental VaR from setting YGB to zero?

Q2 A large all-equity pension fund company with AUM of $500Billion that is closely following S&P 500 index is facing a possibility of new regulatory changes in its management of market risk. The new regulation would require capital charges to cover possible tail event losses based on the realistic assessmentof market risk of the company. A CRO (Chief Risk Officer) of the fund is given a task to assess a range of possible costs with regard to such charges.

It turns out that the CRO of the fund is an old buddy of yours from school times and regards you as a world-class expert. With no hesitation she then turns to you for help. Given your close friendship (and a hefty paycheck she offers) you eagerly decide to provide feedback.

In your recommendation, you may want to consider the following:

- Access to daily price data of the S&P 500 index (attached data_exam.xlsx)
- Various choices of risk measures
- Specificity of the data in terms of its distribution and volatility structure
- Tradeoffs between profitability and risk of the implemented charges
- Possible adjustments in the portfolio strategy
- Supporting your answers with graphs / tables.