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The Optimal Price to Trade
Published online by Cambridge University Press: 19 October 2009
Extract
The literature on security selection and evaluation is quite extensive-Aside from the chart readers, however, there is little or no theoretical framework on the optimal trading price. The theories of technical analysts have been almost completely debunked by the evidence on the random walk nature of price performance. This state of affairs leaves the investor, who has decided to buy or sell a particular security, with very little insight as to the optimum price to trade. The random nature of price performance suggests that both higher and lower prices are likely to be obtainable in the near future. Thus, trading at the current market price may not be the best strategy. On the other hand, waiting for the stock to move decisively in the desired direction exposes one to the risk of an equally large movement in the opposite direction.
- Type
- Research Article
- Information
- Journal of Financial and Quantitative Analysis , Volume 10 , Issue 3 , September 1975 , pp. 497 - 514
- Copyright
- Copyright © School of Business Administration, University of Washington 1975
References
1 On this point see for examples Granger, C. and Morgenstern, G., Predictability of Stock Prices (Heath Lexington, 1970).Google Scholar
2 It is possible that the price reached the desired level and not all orders at that level be executed. Orders at the same price are executed in the order received. For a limit order which has been on file for some time, the chances of its execution are very good if the price reaches its level. All orders at one price must be executed before the execution of relevant orders at a still more favorable price. That is, a sell order at 27 3/4 could not be executed until all sell orders at 27 5/8 were executed. The only exception here are block trades which sometimes jump over existing orders.
3 Granger, C. and Morgenstern, O., Predictability, p. 270.Google Scholar
4 A density function of the following form was fitted econometrically:
where x = probability of Ph/Pt > x for x beginning at 1 and ranging to the limits found empirically. Fitting this to data for n ranging from 2 to 80, produced an 
which ranged from .87 to .98. Examination of residuals indicated that the principal areas of large errors were in the extreme values: x very nearly 1 or at the high end of the range. The absence of intraday data contributed to the poorer fit near x = 1, while the high range is of little interest. The form fits very well for values of x near the mean. A very good fit ( of .99) was found for the form aebx+c but such a form is much more difficult to work with mathematically. The mean of such a function is very complicated and it is not clear whether the mean is the optimum value.
5 That is, a dollar-for-dollar drop in the expected end price hits a middle ground between the optimistic assumption that a drop in the current price had no effect on the expected end price and the pessimistic assumption that the fall in the current price is matched by a proportional drop in the end price.
6 Owen, , “Analysis of Variance Tests for Local Trends in the Standard and Poor's Index” Journal of Finance (June 1968), pp. 508–514.Google Scholar
7 By fitting the stocks' performance to a linear relation of a market average, one obtains the β ratio. That is, beta; arises from regressing the stock's return P on a market index return 1 as follows: P = ∝ > + βI. For β > 1 the stock is less volatile than the market while a β > 1 indicates the stock is more volatile.
8 These data were also collected for S s P 500 stock average with very similar results for the March 1969-January 1973 period.
9 To obtain the data one would probably have to examine Barron's for each week. Even then only hourly closings are available.
10 On this point see Niederhoffer, V. and Osborne, M., “Market-Making and Reversal on the Stock Exchange.” Journal of the American Statistical Association (December 1966), pp. 897–917.CrossRefGoogle Scholar
11 The price of stocks listed OTC were also examined for any tendency to cluster. The bid and asked quotations for the primary list of OTC stocks in the May 17, 1973, Wall Street Journal were analyzed. The results appear in the table below:
For OTC stocks there is a noticeable tendency for whole numbers to be more numerous than halves; halves more common than quarters, and quarters more prevalent than eighths. Only for eighths is the tendency very pronounced. The frequency of quarters, halves, and whole numbers is approximately equal. Apparently the dealers who make markets in OTC stocks tend to think in terms of quarters of a point without much regard to whether zero, one, two or three quarters are involved. Such dealers, however, do not consider eighths of a point to be clean numbers and thereby tend to avoid them. Unfortunately, it is very difficult to place limit orders on OTC stocks. Such orders are not closely watched and there is no guarantee of execution if the stock reaches the desired level. The absence of an organized exchange makes limit orders very awkward in the OTC market. One may as well watch the daily quotes and purchase when the desired level is reached. A limit order is almost a useless device here.
12 These expected gains are based on the assumption that a buy at market is executed at the average of the bid and asked. A somewhat less attractive price is likely for a market order as the trader will have to absorb the spread. That is, if he is buying, he will have to pay the asked price while a sale will be at the bid.
13 See: Litzenberger, R. and Rao, C., “Estimates of the Marginal Rate of Time Preferences and Average Risk Aversion of Investor in Election Utility Shares: 1960–1966,” Bell Journal of Economics and Management Science (Spring 1971), pp. 265–277.CrossRefGoogle Scholar