Both sides move up or down the same amount
If gold and silver move the same amount on a percentage basis, the returns on the two sides of the trade should offset each other. For example, if both went up 10%, the 10% gain on the long gold position would be offset by the 10% loss on the short silver position, leaving you at breakeven.
If both fell by 10%, the profit on the short silver position would be offset by the loss on the long gold position. Hence, the two positions hedge each other.
Both sides move up
If gold moves up 10% and silver climbs 8%, the 10% gain on gold would be partially offset by the 8% loss on silver, leaving you with a 2% gain.
If silver moves up 10% and gold only advances by 8%, the gain on gold would be more than offset by the loss on silver, leaving you down by 2%.
Both sides move down
Consider that both metals fall and gold drops by 8%, while silver falls by 10%. The gain on the short silver position would be partly offset by the loss on the long gold position, leaving you with a 2% net gain.
If silver were to fall 8% and gold were to drop 10%, however, the loss on the gold position would more than offset the gain on the silver position, leaving you down by 2%.
Both sides move your way
Suppose you catch a break and gold advances 10% while silver declines 8%. The 10% gain on the long gold position, coupled with the 8% gain on the short silver position gives you an 18% return on the pairs trade.
Both sides move against you
One major risk in pairs trading is that you could get squeeze if both sides of the trade go the other way. Suppose gold falls by 8% and silver climbs by 10%, the 8% loss on the gold position coupled with the 10% loss on the silver position would hand you an 18% loss on the pairs trade.
