# Using Forward Equity Returns to Value Stream of Equity Return Cash Flows

Can I value the equity leg of an equity swap using the projected forward equity returns?

In other words, for a sequence of times $t_{0}<t_{1}<\ldots<t_{n}$, where $t_{0}$ begins a brand new calculation period and $t_{n}$ is the maturity of the contract, do we have (assuming the payment frequency is the same as the calculation period frequency) $$V_{t}=\sum_{j=1}^{n}\frac{F_{j}-F_{j-1}}{F_{j-1}}\cdot D(0,t_{j})?$$ Here $F_{j}$ is the forward equity price at time $t_{j}$ calculated at time $t_{0}$ and $D(0,t_{j})$ is the discount factor for the period $[t_{0},t_{j}]$

I know that the traditional way to value the equity leg is to think of it as a floating rate bond that resets to par at the end of each payment date. Personally, I find this approach somewhat unintuitive and prefer the projected forward rates viewpoint. Since the two interpretations are equivalent for floating LIBOR legs, I suspect the same is true for the equity legs.

My presumption is that once the value of the equity leg is determined, then a spread $S$ can be added so that $$V_{EquityLeg}=V_{OtherLeg},$$ at inception of the contract.