Michael Isichenko - Quantitative Portfolio Management

Security return for day is defined as the relative change in the closing price from previous day to current day :

(1.1)

To account for corporate actions, the prices are adjusted, that is, multiplied by an adjustment factor so (1.1)give a correct return on investment after the adjustment. In general, a multi-day return from day to day equals

(1.2)

The adjustment factor is used only in a ratio across days and is therefore defined up to constant normalizing coefficient. There are two ways of price adjustment: backward and forward. The backward adjustment used, for example, in the Bloomberg terminalis normalized so today's adjustment factor equals one and changes by cax events going back in time. On a new day, all values 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)

_____________

1 2This 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.