Explain why each position in the following pairs of positions is a hedge against the other.

(a) long 200 shares of MSFT and long 1 MSFT put (at any strike price and at any future expiry)

(b) short 200 shares of MSFT and short 2 MSFT puts (at any strike price and at any future expiry) (This is not a smart investment strategy!)

(c) short 200 shares of MSFT and long 2 MSFT calls (at any strike price and at any future expiry)

(d) long 200 shares of MSFT and short 2 MSFT calls (at any strike price and at any future expiry)

(e) long a portfolio of gold-mining stocks (ABX, RGLD, FNV, AEM) and long puts at any strike price and at any future expiry in GLD

(f) a short straddle

(g) a long strangle