Quantitative Portfolio Management. Michael Isichenko

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rel="nofollow" href="#fb3_img_img_c5a7bc1c-dc62-501f-baea-374e050021a3.png" alt="upper A Subscript d"/> are recomputed.

      Another way is forward adjustment, in which scheme

starts with one on the first day of the security pricing history and then changes as

(1.3)

      Cax events are understood as those with

or . The past history of the forward adjustment is not changed by new entries. Therefore, the forward adjustment factor can be recorded and incrementally maintained along with price-volume data. If backward adjustment factor is desired as of current date, it can be computed as

      (1.4)

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      1 2 This is clearly not enough for updating an actual trading portfolio for newly spun off regular or when-issued stock. For this, portfolio managers usually rely on maintenance performed by the prime broker.

The rationale for Eq. (1.3) is as follows. Dividend and split for day

are always known in advance. One perfectly logical, if impractical, way to reinvest a dividend (including a monetized spin-off) per share is to borrow cash to buy additional shares of the same stock at the previous day close and then return the loan the morning after from the dividend proceeds. To stay fully invested, the total dividend amount must equal the loan amount , therefore

      (1.5)

      In terms of value at hand, this manipulation is equivalent to a

stock split. If there is also a post-dividend split , one-day adjustment factor equals

(1.6)

and formula (1.3) follows.³

      Some quant shops have used a similar reinvestment logic of buying

shares of stock at the new closing price resulting in a somewhat simpler day adjustment factor,

(1.7)

This formula is fine as far as only daily data is concerned, but applying this adjustment to intraday prices results in a lookahead (Sec. 2.1.1) due to using a future, while intraday, closing price

. Intraday forecast features depending on such adjustment factor can generate a wonderful forecast for dividend-paying stocks in simulation, but production trading using such forecasts will likely be disappointing. Formula (1.6) differs from the “simple” Eq. (1.7) by a typically small amount but is free from lookahead.

Dividend (including any spin-off) values

found in actual historical data can occasionally reach or exceed the previous close value causing trouble in Eq. (1.3). Such conditions are rare and normally due to a datafeed error or a major capital reorganization warranting a termination of the security and starting a new one via a suitable entry in the security master (Sec. 2.1.2), even if the entity has continued under the same name.

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      1 3 Eqs. (1.3) and (1.6) apply to the convention that a dividend is paid on a pre-split (previous day) share. A post-split dividend convention is used by some data vendors and requires a straightforward modification of the adjustment factor. Simultaneous dividends and splits are infrequent.

      Price adjustment is also used for non-equity asset classes. Instead of corporate actions, futures contracts have an expiration date and must be “rolled” to continue position exposure. The roll is done by closing an existing position shortly before its expiration and opening an equivalent dollar position for the next available expiration month. For futures on physical commodities, such as oil or metals, the price of a contract with a later expiration date is normally higher than a similar contract with an earlier expiration due to the cost of carry

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