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# Pricing Equity Forwards and Futures

A forward contract is a contract that promises to buy or sell an asset on a specific date in the future at a prearranged price. We need to construct a portfolio with cash flows equal to the forward to price forwards and futures. From there, we can use the law of one price to determine the value of the forwards. Investment managers use equity index futures and swaps to hedge equity risk on a low tax basis. This section will illustrate the carry arbitrage model with equity forward pricing and valuation for equity forward and futures contracts. We assume that futures and forward contracts are priced the same way and that interest rates are compounded annually.

#### Example 1: Equity Futures Contract Prices With Continuous Compounded Interest Rates

The dividend yield on the EURO STOXX 50 is 5%, and the current stock index level is 3,200. The continuously compounded annual interest rate is 0.2%. Based on the carry arbitrage model, the three-month futures price is most likely to be:

#### Solution

The formula we will be using is:

$$F_0=S_0e^{(r_c+CC-CB)T}$$

Let us assume that the carry costs are 0 for the stock index. The carry benefit will be 5%, and the financing cost will be 0.2%. Since the dividend yield is greater than the financing cost, the future price will be lower than the spot price. The future value of the underlying adjusted carrying dividend payments over the next three months is:

$$F_0=3200e^{(0.002+0-0.5)3/12} = 3,161.829$$

#### Example 2: Equity Forward Pricing and Forward Valuation With Discrete Dividends

Kraft Heinz common stock trades for $36.40 and pays a$1.50 dividend in one month. Assume that the dollar one month risk-free is 1% on an annual compounding basis. Further, assume that the stock goes ex-dividend the same day the contract expires in one month. The one-month forward price for Kraft Heinz common stock will be closest to:

#### Solution

$$S_0$$ = 36.4, $$r$$ = 1.0% $$T$$ = 1/12 and $$FV(CB_0)$$ = 1.5 = $$CB_T$$

\begin{align} F_0 & = FV(S_0+CC_0-CB_0) \\ & = 36.4(1+0.01)^{1⁄12}+0-1.5 \\ & = 34.93 \end{align}

The value before the contract expires is the present value of the difference between the initial equity forward price and the current forward price.

## Question

Assume that a dividend payment is announced between the forward’s valuation and expiration date. If the announcement remains unchanged the current underlying price, the forward value is most likely to:

1. Remain the same.
2. Decrease.
3. Increase.

#### Solution

Payment of dividends is likely to reduce the forward price and therefore, lower the value of the initial forward contract.

Reading 33: Pricing and Valuation of Forward Commitments

LOS 33 (b) Describe how equity forwards and futures are priced, and calculate and interpret their no-arbitrage value.

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