Valuing an Equity Swap Leg with Forward Equity Returns

Summary

The document asks whether an equity swap’s equity leg can be valued by discounting the projected returns between successive payment dates. It defines each period’s return using forward equity prices observed at the start of a new calculation period, then discounts those cash flows to that period’s start. The author contrasts this with the conventional floating-rate-bond interpretation, in which the leg resets to par at payment dates, and wonders whether the two approaches are equivalent as they are for floating LIBOR legs.

The text does not provide a derivation, numerical example, market data, or a resolution. It also suggests adding a spread so the equity leg and the other leg have equal value at inception, but leaves the valuation assumptions and treatment of dividends, funding, and contract terms unspecified. It is therefore useful as a framing of the valuation question, but not as a complete pricing method or evidence that the proposed formula is correct.

Key ideas

• The proposed approach discounts forward-implied equity returns over successive payment periods.
• The conventional interpretation treats the equity leg like a floating-rate bond that resets to par.
• The document asks whether the two valuation interpretations are equivalent.
• A spread is proposed to balance the equity leg against the other swap leg at inception.

Tags

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


# 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.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.