Normal VaR for short bond

Question

So I'm short a GBP denominated zero-coupon bond which has a face value of 1 million pounds and a remaining maturity of 6 months. Furthermore, I have to assume that the daily return of a 6-month zero GBP bond has a volatility of 0.06% (when its price is converted into Euro). The current exchange rate is 0.88 Pound Sterling per Euro and the 6-mont interest rate in GBP is 5% per annum with continuous compounding.

I now have to calculate the 10-day 99% relative normal VaR of this investment and as a hint, I have that I must start by defining the volatility of the P1L of my investment. However, I'm not sure how I can solve this particular exercise as I haven't really worked with the VaR with different currencies.

Answer 1

I would think that you would treat this as computing the VAR of a two asset case. In your case these assets would be 1/ your GBP bond and 2/ an FX position in EURGBP. You already have a vol measure for asset 1. Once you have a vol measure for the FX, you should be able to obtain the standard deviation of the combined asset via $$\sigma_{X+Y}=\sqrt{\sigma_X^2+\sigma_Y^2 +2\rho\sigma_X\sigma_Y}$$after making an estimate of $\rho$ (the correlation between the GBP bond and EURGBP), say via historical analysis.