# synthetic cash and equity

I dont get how you can earn the risk free rate. Anyone want to explain?

Remember back to your Level II derivatives: the price of a forward contract (say, an equity forward) is the spot price increased by the risk-free rate.

I remember its from L2. But also I memorised that formula without the understanding of how the risk free rate is involved. Care to explain why we get the risk free rate? i

The forward price is:

F = S0 × (1 + rf)^T.

Suppose you have an equity position of, say, \$10,000,000, you want to create synthetic cash for 90 days, and the risk-free rate is 2%. Then you enter into the short position on \$10,000,000 of equity forward contracts; the forward price will be:

F = \$10,000,000 × 1.02^(90/365)

= \$10,048,948

Thus, in 90 days you’ll get paid \$48,948 in risk-free interest.

Hi spacebar. What helps me think about this and other related formulas is that if you earned anything other than the risk free rate it would create an arbitrage opportunity (i.e. you get the risk free rate if/when the equation is balanced; otherwise someone could arb synthetic vs actual by borrowing at the risk free rate to short one, go long the other and capture a profit).