Application Two: Price Prediction
5.2 Margin Models
In this section we will apply the insights and methodology we developed for sector models to a second example, margin trading. One way that investors take larger bets than they otherwise might be able to do is to buy or sell stocks on margin.
5.2. MARGIN MODELS 119 Buying stock on margin amounts to paying only a percentage of the total cost of the purchase, and implicitly borrowing the remainder. Similarly selling stock on margin means that the investor need only leave a percentage of the proceeds of a short sale in their account as protection against an increase in the cost of closing out the position.
In this way margin trading provides the investor with greater leverage than ordinary trading, and thus is often adopted by speculative investors.
The Japanese equity market is well known, historically at least, for the speculative fever that regularly attacks the favored \stock of the month", where that stock's price undergoes a breathtaking rise and eventual fall which cannot typically be justied from any fundamental considerations of the underlying company. To some extent these speculative price \bubbles" are thought to be caused by the (again, at least historical) tendency of the largest four brokerage houses in Japan to use their large numbers of salespeople to push particular stocks on investors. Can we use margin trading information as a surrogate for this speculative behavior and predict these disproportionate price movements? This is the goal of our modeling eorts in this section.
5.2.1 The Data
The data used for these experiments is the total balance of margined shares held (either long or short) at the end of each week for the 40 stocks introduced in Sec-tion 5.1.9, along with the corresponding stock returns, for the 111 week period from January 8, 1989 to February 17, 1991. Let us denote the margin buying balance as B =fbtg, the margin selling balance as S =fstg, and the target stock price again as P =fptg. Exploratory analysis of this data indicate some support for our theory of a relation between margin data and price bubbles. For instance, quick jumps in margin buying and selling often occur around large jumps in price, although the exact timing of these variables is not clear (see Figure 5-8).
To model this data we again use the stock returns rather than the raw prices.
Sim-120 CHAPTER5. APPLICATION TWO:PRICE PREDICTION
Dec88 89 Jan 89
Feb 89 Apr 89
May89 Jul 89
Aug89 Sep89
Nov 89 Dec90
Jan 90 Mar 90
Apr 90 Jun 90
Jul 90 Aug90
Oct 90 Nov 91
Jan 91 Feb
10001500200025003000 024681012Price
Margin Buy Balance Margin Sell Balance
Figure 5-8: Weekly margin and price data for Nippon Chemical. Left axis shows price per share in yen, and the right axis shows margin balance expressed as a percentage of shares outstanding. Dashed vertical line shows split of data into training and out of sample testing sets.
5.2. MARGIN MODELS 121 ilarly after some experimentation with various transformations of the margin balance data, we use the \return" of that as well, although this has a less obvious mean-ing. As before we denote these returns as rbt log(bt=bt;1), rst log(st=st;1), and rpt log(pt=pt;1). For the purposes of out of sample testing, we divide the data set at the same date as our daily sector models, yielding a training set of the rst 90 weeks of returns data and a test set of the last 20 weeks.
5.2.2 Models
Following similarmodel identication steps as in Section 5.1, a reasonable multivariate model of the margin data was found to be
rpt = + f(rpt;1;rpt;2;rbt;1;rbt;2;rst;1;rst;2) +t (5:12) i.e. using the values of the previous two weeks of each series to predict the price for this week. As usual, the unfortunately small size of the database encouraged us to focus attention on models with small numbers of parameters. The linear OLS versions of this model, for instance, have 7 parameters. For RBF models we chose to use 4 gaussian nonlinear units with xed centers and xed input weights, thus yielding 11 free parameters (4 gaussian scale parameters and 7 output coecients).
Perhaps not surprisingly, we were not able to nd good models for all of the 40 stocks in our sample. For instance, looking at the OLS models described by Equation (5.12), the F-test of the model tness as a whole could not reject the null hypothesis at the 95% signicance level for 28 out of 40 of the models. We believe our inability to nd good models for some of these stocks is due simply to the fact that not all of the stocks encountered substantial margin trading activity during our training period. To support this belief, we note a rank correlation of -0.27 between the F-statistic p-value for our OLS models and the median percentage of weekly total trading volume that are margin buy trades. Thus we continue our analysis with only
122 CHAPTER5. APPLICATION TWO:PRICE PREDICTION
B&H ARMA(0,1) OLS RBF BUY&HOLD
4.04
ARMA(0,1) -0.99 0.46
OLS -2.01 -1.66 -1.39
RBF 4g 1.00 1.67 2.16
3.15
Table 5.4: Approximate t-statistics for ARR measures across 12 margin models of each type. Diagonal elements are one-sided tests against the risk free ARR rate of 7.78% for this period. O diagonal elements are paired t-tests that the average ARR of the \row" model type is higher than the average ARR of the \column" model type.
Bold entries exceed the overall 95% condence level of 3.11 for 10 simultaneous t-tests each with 11 degrees of freedom.
the 12 stocks that from our F-test seem to have reasonable margin models. Out of sample results for all of our model types across these 12 stocks are shown in Figure 5-9. RBF models perform the best for this period, and accumulate an average annual rate of return of 293% with an average one way break even transaction cost of 2.14%.
These results indicate that the nonlinear RBF models may be more appropriate for this problem than the others, although we note that the overall bull market during this period makes the buy and hold strategy a stronger than usual choice. The matrix of t-test results on the rate of return for each strategy across an equal weighted portfolio of the 12 stocks are shown in Table 5.4.