Why do many MATLAB examples model stock price returns instead of absolute changes?

Many MATLAB examples about fitting ARIMA models use price2ret to transform a stock time series to a return time series and then apply the estimate function to fit an ARIMA model. Why are price returns fit instead of absolute price changes?

Answer 1

[Rick Rosson]

Suppose you own a portfolio containing two stocks, with a total value of $5,000 each. Suppose further that the price of one stock rose yesterday by $5.00 per share, while the other one rose by $3.00 per share. Which stock contributed more money to your portfolio as a result of yesterday's market changes?

The question is impossible to answer without knowing either the number of shares of each company you hold, or the initial price per share of each stock.

If, on the other hand, I had told you that the first stock rose by 2 percent while the second rose by 4 percent, you would have known immediately that the second stock had performed better and had contributed more of a net increase in value to your portfolio than had the first stock.

Absolute changes in per share stock prices are meaningless. The change in price relative to the initial price -- in other words, the percentage rate of return -- is what actually matters.

[Danny]

Thank you for the response. From a forecasting perspective, it is important for prices to not go negative and for absolute price changes to be greater when stock price is higher (on the other hand, percentage price change is likely independent of stock price level). Is modeling return (and converting to price) also important because it implies stock price cannot go negative and that price changes are greater at higher prices? Modeling absolute price changes seems to allow stock price to go negative and does not capture how absolute changes evolves with price level.

[Rick Rosson]

Yes, all valid reasons. In fact, if you ensure that the percentage rate of return is always greater than -100 percent, then the price of the stock will never go negative. And this requirement is independent of the current price of the stock.

[Rick Rosson]

One other thing to keep in mind: when computing the percentage rate of return, don't forget to include any cash dividends that the company pays in the total return. You should include the cash dividends on the so-called "ex-dividend" date, not on the announcement date or the payment date.