Risk management synthetic stock index fund

[Bopha99]

Why does the combination of buying an equity index and selling futures on that index yield the risk free rate?

 

[jpsi1]

From payoff replication principal the long position in stock index futures is equivalent to long position in stock index and short position in risk free bond. You borrow at risk free rate to buy stock index to create synthetic long position in futures contract:
Long futures = (Long stock index) + (Sell risk free bond)
By rearranging this equation we have:
(Long stock index) - (Long futures) = - (Sell risk free bond)
(Long stock index) + (Short futures) = Long risk-free bond
CFAI is using similar argument in section 3.3. of Reading 26

 

[StallionDis]

Long and short

 

[Bopha99]

OK thanks. That helps

 

[S2000magician]

Go back to your Level II derivatives: the forward price on an equity index in the spot price increased at the risk-free rate.