Hedged Return on a stock position

[jesswong]

Why profit or loss on a hedged stock position is cal as the following equation?
V(t)S(t)-V(0)S(0)- V(0)( F(t)-F(0) ). For the last term, why use the ( F(t)- F(0) ) instead if F(t)- S(t)?
Where v(t) is spot value at maturity ,F(t) is the forward rate at maturity .

 

[cpk123]

VtSt - V0S0 = Position gain/loss
you hedge with the V0 position of the stock (sell that much forward)
and you agreed to sell at F0. At termination it is worth Ft
So gain/loss on your hedge = V0 (Ft - F0)
and since you sold the hedge -> -V0 (Ft - F0)

 

[jesswong]

For the last term , why the Ft is not comparing with St , as Ft is the result of the hedging and St is the result of not hedging ?

 

[cpk123]

Ft - F0 is your gain / loss on the forwards position.