I’m having difficulties how to get the theoretical Futures price to take advantage of a cash&carry arbitrage
Assume you are currently holding a position on a 6-months forward contract, taken at BM&BOVESPA, Brazil, that you entered 3 months ago and matures exactly 3 months from today, to sell gold at BRL (Brazilian real) 107.60 per gram. Looking at the current market trend, you now want to offset your outstanding position by taking a long position today in a new forward contract to take a delivery of gold in 3 months time. The current spot price of gold has a bid price of BRL 108.57 and ask price of BRL 109.73 per gram. The continuously compounded risk free interest rate is 13%. For calculations ignore storage costs of gold and use precision up to 2 decimal places.
question is : The profit / loss (BRL) in 3 months from a cash and carry strategy using a single contract of 250 grams would be:
solution is : 337.5 -=250*(114.85-113.50)
so for a cash&carry we borrow money, buy spot (109.73) and sell the forward (which price) ?
loan and interests: 109.73*e^(13%*0.25)=113.50
how do they come up with 114.85 as short forward price ?
I would be really grateful if someone could explain that.