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Financial Engineering principles - Beaumont P.H.

Beaumont P.H. Financial Engineering principles - Wiley publishing , 2004. - 318 p.
Download (direct link): financialengineer2004.pdf
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F = S (1 + T (R - Yd))
where Yd = dividend yield calculated as the sum of expected dividends in the coming year divided by the underlying equity’s market price.
Precisely how dividends are treated in a forward calculation depends on such considerations as who the owner of record is at the time that the intention of declaring a dividend is formally made by the issuer. There is not a straight-line accretion calculation with equities as there is with coupon-bearing bonds, and conventions can vary across markets. Nonetheless, in cases where the dividend is declared and the owner of record is determined, and this all transpires over a forward’s life span, the accrued dividend factor is easily accommodated.
CASH-SETTLED EQUITY FUTURES__________________________________
As with bonds, there are also equity futures. However, unlike bond futures, which have physical settlement, equity index futures are cash-settled. Physical settlement of a futures contract means that an actual underlying instrument (spot) is delivered by investors who are short the contract to investors who are long the contract, and investors who are long pay for the instrument. When
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48
PRODUCTS, CASH FLOWS, AND CREDIT
a futures contract is cash-settled, the changing cash value of the underlying instrument is all that is exchanged, and this is done via the daily marking-to-market mechanism. In the case of the Standard & Poor’s (S&P) 500 futures contract, which is composed of 500 individual stocks, the aggregated cash value of these underlying securities is referenced with daily marks-to-market.
Just as dividend yields may be calculated for individual equities, they also may be calculated for equity indices. Accordingly, the formula for an equity index future may be expressed as
F = S (1 + T (R - Yj))
where S and Yd = market capitalization values (stock price times outstanding shares) for the equity prices and dividend yields of the companies within the index.
Since dividends for most index futures generally are ignored, there is typically no price adjustment required for reinvestment cash flow considerations.
Equity futures contracts typically have prices that are rich to (above) their underlying spot index. One rationale for this is that it would cost investors a lot of money in commissions to purchase each of the 500 equities in the S&P 500 individually. Since the S&P future embodies an instantaneous portfolio of securities, it commands a premium to its underlying portfolio of spot instruments. Another consideration is that the futures contract also must reflect relevant costs of carry.
Finally, just as there are delivery options embedded in bond futures contracts that may be exercised by investors who are short the bond future, unique choices unilaterally accrue to investors who are short certain equity index futures contracts. Again, just as with bond futures, the S&P 500 equity future provides investors who are short the contract with choices as to when a delivery is made during the contract’s delivery month, and these choices have value. Contributing to the delivery option’s value is the fact that investors who are short the future can pick the delivery day during the delivery month. Depending on the marketplace, futures often continue to trade after the underlying spot market has closed (and may even reopen again in after-hours trading).
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Cash Flows
49
variation on a theme that we have already seen, and may be expressed as
F = S 11 + T1 Rh - R0))
where Rh = the home country risk-free rate R0 = the other currency’s risk-free rate
For example, if the dollar-euro exchange rate is 0.8613, the three-month dollar Libor rate (London Inter-bank Offer Rate, or the relevant rate among banks exchanging euro dollars) is 3.76 percent, and the three-month euro Libor rate is 4.49 percent, then the three-month forward dollar-euro exchange rate would be calculated as 0.8597. Observe the change in the dollar versus the euro (of 0.0016) in this time span; this is entirely consistent with the notion of interest rate parity introduced in Chapter 1. That is, for a transaction executed on a fully hedged basis, the interest rate gain by investing in the higher-yielding euro market is offset by the currency loss of exchanging euros for dollars at the relevant forward rate.
If a Eurorate (not the rate on the euro currency, but the rate on a Libor-type rate) differential between a given Eurodollar rate and any other euro rate is positive, then the nondollar currency is said to be a premium currency. If the Eurorate differential between a given Eurodollar rate and any other Eurorate is negative, then the nondollar currency is said to be a discount currency. Table 2.3 shows that at one point, both the pound sterling and Canadian dollar were discount currencies to the U.S. dollar. Subtracting Canadian and sterling Eurorates from respective Eurodollar rates gives negative values.
There is an active forward market in foreign exchange, and it is commonly used for hedging purposes. When investors engage in a forward transaction, they generally buy or sell a given exchange rate forward. In the last example, the investor sells forward Canadian dollars for U.S dollars. A for-
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