Business Question

1. The file 433.Assignment 01.csv (available at Canvas) contains daily data on S&P500 index and the Vanguard Total Bond Market Index Fund from 1987 to 2014. The Vanguard Bond fund is designed to provide broad exposure to U.S. investment-grade bonds. To be more specific, the fund invests about 30% in corporate bonds and 70% in U.S. government bonds of all maturities (short-, intermediate-, and long-term issues).

  • a. Compute daily volatilities of the S&P500 return and bond returns, using a “3-year rolling window’. (that is, for every t, compute those quantities from t — 3 years to t. Clearly, you need to begin in 1990.)
  • b. For the same time span, compute daily volatility of the S&P500 returns and bond returns using the RiskMetrics methodology.
  • c. Plot your results from La) and 1.b). Comment on your findings. How do estimates from RiskMetrics compare with those from using a rolling window?

2. Consider PM Jorgan’s Global Access portfolio with $3.5 billion AUM at the end of 2007. Say that today is December 31, 2007. Assume for simplicity for now that it is all invested in the S&P 500 index.
a. What was the 1 day 99% Value at Risk (VaR) on this portfolio? Compute VaR using both these methodologies:

  • i. Volatilities estimated using a 3-year rolling window (with equal weights for all obser-vations)
  • ii. Volatilities estimated using the RiskMetrics methodology

3. One day horizon is too restrictive. What is the 5-day 99% VaR? How about the 30-day (one month) 99% VaR? Compute these numbers using both methodologies enumerated in the previous question.

4. Repeat questions (2) and (3) assuming that $3.5 billion AUM of Global Access portfolio is 100% invested in bonds (Balanced Fund).

5. Let today be December 29, 2014. Assume now that $3.5 billion AUM of Global Access portfolio is 50% invested in stocks and 50% invested in bonds (the Vanguard Total Bond Fund). Will the 1-day 99%ile VaR of this portfolio be higher than a portfolio that is 100% invested in stocks? Will the VaR of the 50:50 portfolio be higher than a portfolio that is 100% invested in bonds? It is not necessary that you provide a quantitative answer; a qualitative answer would suffice. However, you should clearly articulate your rationale.