Forward Portfolios

Forward Rate Agreements
A forward rate agreement is an agreement to fix a forward interest rate for an interest period starting at a specified future date and for a specified notional.

A FRA is a combination of borrowing for a longer period and simultenously lending the same amount for a shorter period or via versa
To map to standardized points, we can decompose the cashflows into three components

For example, a long position in a 3 x 6 FRA on $10,000,000 is equivalent to:
borrowing $10,000,000 for 6 months on a discount basis and
simultaneously investing the proceeds for 3 months

Assuming that 6 month LIBOR is 4% per annum
the present value of borrowing $10,000,000 for 6 months would be:

10,000,000 / (1 + 0.04 x (365/360/2) ) = $9,801,252

For the purpose of calculating VAR the matix would be

[ -9,801,252 , 9,801,252 ]

Example

You have purchased a 6 x 12 FRA with a notional of $100m
and
6-month LIBOR is 1.75% per annum
12 monthh LIBOR is 2.25% per annum
price volatility of 6-month LIBOR is 0.6% per annum
price volatility of 12-month LIBOR is 1.2% per annum
correlation between 6-month and 12 month LIBOR is 0.7

What value (plus/minus) should be entered into the matrix