Question
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 Risk Metrics 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?
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.
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 observations)
ii. Volatilities estimated using the Risk Metrics methodology
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.
Repeat questions (2) and (3) assuming that $3.5 billion AUM of Global Access portfolio is 100% invested in bonds (Balanced Fund).
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.