VaR of a Portfolio of Bond Futures (spread trade)

[jortiz12]

Dear Community,

I'd appreciate any guidance regarding the most efficient way to compute the VaR (say 1-day VaR at 95% confidence level) for a spread trade in two Bond Futures, with weights adjusted by duration, currency, and volatility.

As an example, consider you're given this positio:

1. LONG 373k $ in 10-year TNote Futures (CBOT)
2. SHORT 556k $ in 10-year Euro Bund Futures (EUREX)

Crucially, note that the 373 k and 556k amounts represent PVBP (Price Value of a Basis Point) exposures.

Thanks in advance.
Jose

 

[gsarm1987]

@jortiz12 I think you are asking in context of component VARs and PF VARs. first you need to know whats the PF volatility. your PF has long Tnote and short Bund. if you get that volatility, then you simply multiply by 1.645*sqrt(1/250) to get the daily VAR. check Dowd Ch 3. There are many ways to approximate the component VARs, one way to do that is given in same chapter: Weight X Duration (T-note) X volatility of T-note. if you can give me complete set of info, say correlation, PF volatility, Component volatility, i can solve it.

 

[jortiz12]

First, many thxs for your respose.
Assume EURSd =1 to make things simpler.
Assume I´m long 100 lots in TNote future (so 100 x 100,000 = 10MM USD value for this position as the TNote contract size is 100000 USD per contract) and short 125 losts Euro Bund future(so 125 x 100,000 = 12.5MM USD value for this position as the Euro Bund future contract size is 100000 EUR per contract and I´m assuming EURUSD =1).

*** This is where I may be making a fundamental mistake ***
Hence, portfolio total initial value is 10MM - 12.5MM = -2.5MM USD
So weights are:
w_Tnote = 10/-2.5 = -4
w_Bund = -12.5/-2.5 = 5
(w_Tnote + w_Bund = 1)

I've indeed (i) gathered historical daily futures data, obtained individual daily return series, calculated daily portfolio returns as - (w_Tnote * ret_Tnote + w_Bund * ret_bund) (I change signs to have right long/short direction of returns), and estimated SMA daily volatility of the "portfolio" ol_port in order to apply the normal approx VaR (%) = vol_port * z-score.
If I wanted the VaR ($), should I do VaR ($) = VaR (%) * (-2.5MM USD)???
I´m mainly interested in the VaR ($) value, not so much on the VaR (%)

Thxs vm one again (can provide excel spreadsheet with basic data and calcs)

 

[gsarm1987]

First, many thxs for your respose.
Assume EURSd =1 to make things simpler.
Assume I´m long 100 lots in TNote future (so 100 x 100,000 = 10MM USD value for this position as the TNote contract size is 100000 USD per contract) and short 125 losts Euro Bund future(so 125 x 100,000 = 12.5MM USD value for this position as the Euro Bund future contract size is 100000 EUR per contract and I´m assuming EURUSD =1).

*** This is where I may be making a fundamental mistake ***
Hence, portfolio total initial value is 10MM - 12.5MM = -2.5MM USD
So weights are:
w_Tnote = 10/-2.5 = -4
w_Bund = -12.5/-2.5 = 5
(w_Tnote + w_Bund = 1)

I've indeed (i) gathered historical daily futures data, obtained individual daily return series, calculated daily portfolio returns as - (w_Tnote * ret_Tnote + w_Bund * ret_bund) (I change signs to have right long/short direction of returns), and estimated SMA daily volatility of the "portfolio" ol_port in order to apply the normal approx VaR (%) = vol_port * z-score.
If I wanted the VaR ($), should I do VaR ($) = VaR (%) * (-2.5MM USD)???
I´m mainly interested in the VaR ($) value, not so much on the VaR (%)

Thxs vm one again (can provide excel spreadsheet with basic data and calcs)

Jose, to compute the Value at Risk (VaR) in dollars for your spread trade, you're on the right track. You can use the following steps:
-Compute the portfolio volatility (vol_port) based on historical daily returns of the spread trade.
-Apply the normal approximation for VaR (%) = vol_port * z-score (1.645 for 95% confidence level).
-If you want VaR in dollars, use VaR ($) = VaR (%) * portfolio initial value.
with your weights and portfolio initial value, it seems correct to use VaR ($) = VaR (%) * (-2.5MM USD) in your case. share your spreadsheet, that will be interesting to see