Why would I expect the VaR of my portfolio to be less than the weighted VaR of the individual assets?

Question 1

Why would I expect the VaR of my portfolio to be less than the weighted VaR of the individual assets?

Question 2

Outline three (3) criticisms of VaR.

Question 3

Explain the difference between Value-at-Risk (VaR) and Expected Shortfall (ES).

Question 4

Consider a position consisting of a $300 000 investment in gold and a $500 000 investment in silver.  Assume that the daily volatilities of the assets are 1.8% and 1.2% respectively, the daily mean for both is zero and that the correlation between them is 0.6.  What is the ten-day 97.5% VaR for the portfolio?  By how much does diversification reduce the VaR?

Question 5

You invest in a 3 year BB rated corporate bond with a face value of $100 and a coupon rate of 5% (paid annually).  The BB corporate yield curve is flat at 5%.  Assume all shifts in the yield curve are parallel and that the distribution of 1 day changes in the rates are  ~ N(0, 0.00002). Use the duration approximation to get the VaR(10,99%) for this bond portfolio.

 

Question 6

You invest in a 2 year Spanish government bond and a 2 year French government bond.  Both have a face value of 100 Euros and a coupon rate of 10% (paid annually).  The Spanish yield curve is flat at 5% while the French yield curve is flat at 3%.  Assume all shifts in the yield curve are parallel and that the distribution of monthly changes in the rates are  ~ N(0, 0.0001) and ~ N(0, 0.0001)  (Note: this means that they have mean zero and a standard deviation of 1%), where the two have a correlation of 0.5.  Use the duration approximation to get the VaR(1,95%) for this bond portfolio (this is the 1 month VaR).

 

 

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