stock price gives you betterreturn and less risk to return ratio. Do it and you will have better chance to win!7.2 Moving upWhat should we do if your stock moves up during the first day? Trend is your friend - thisis the old Wall Street saying. Should you buy more shares following this proverb or you shouldsell early and take the profit? To answer these questions we performed a computer analysis. Letus show some results.We will consider oversold stocks, i.e.CLO1 < K1*CLO0We will also suppose that during day #2 the stocks moved up. The closing price on day#2 CLO2 should be larger than CLO1CLO2 > K2*CLO1
41Consider the average price changes relative to CLO2 price for different values of K1 and K2. Theresults are presented in the Tables.Table 7.2 "Remaining" returns (in %), i.e. the differences X - CLO2 in the case of price growthduring the day #2. The risk to return ratios are shown in parentheses.K2 = 1K1 = 1
K1 = 0.95
K1 = 0.9
OPE3 - CLO2
0.9 (3.7)
1.6 (2.1)
2.3 (1.7)
CLO3 - CLO2
0.7 (7.4)
1.3 (5.1)
1.6 (4.7)
OPE4 - CLO2
1.2 (5.2)
2.0 (3.9)
2.5 (3.5)
CLO4 - CLO2
0.8 (9.3)
1.2 (7.2)
1.2 (7.9)
OPE5 - CLO2
1.3 (6.2)
1.9 (5.0)
2.2 (4.7)
CLO5 - CLO2
1.0 (9.1)
1.4 (7.4)
1.4 (7.7)
K1 = 1
K1 = 0.95
K1 = 0.9
OPE3 - CLO2
1.4 (3.0)
1.9 (1.7)
2.6 (1.5)
CLO3 - CLO2
1.0 (6.6)
1.5 (4.8)
1.8 (4.2)
OPE4 - CLO2
1.5 (4.9)
2.1 (3.8)
2.5 (3.6)
CLO4 - CLO2
0.7 (12)
0.9 (10)
1.2 (8.5)
OPE5 - CLO2
1.2 (7.8)
1.6 (9.8)
2.2 (5.0)
CLO5 - CLO2
0.8 (13)
1.1 (9.1)
1.4 (8.0)
K1 = 1
K1 = 0.95
K1 = 0.9
OPE3 - CLO2
1.9 (2.5)
2.4 (1.5)
3.0 (1.3)
CLO3 - CLO2
1.3 (6.0)
1.8 (4.1)
2.7 (3.0)
OPE4 - CLO2
1.8 (4.9)
2.4 (3.7)
3.3 (3.1)
CLO4 - CLO2
0.7 (13)
1.2 (8.0)
1.6 (6.6)
OPE5 - CLO2
1.2 (8.4)
2.0 (4.9)
2.9 (3.8)
CLO5 - CLO2
0.5 (20)
1.5 (6.7)
2.0 (6.0)
K2 = 1.05
K2 = 1.10
These tables can be useful for reference. You can see that the risk to return ratiodecreases with time. So, it is not a good idea to hold stocks which moved up on day #2 for along time. For better presentation let us show Figure 7.1, which illustrates the stock-timeperformance. The opening and closing prices are shown for days #3, #4, and #5.
42
Figure 7.1 Price changes for oversold stocks which moved up during the day #2.Squares - CLO1 < CLO0Circles - CLO1 < 0.95*CLO0Triangles - CLO1 < 0.9*CLO0One can see that a trader can obtain maximum returns by selling stocks at OPE3 or OPE4prices. However, from table 7.2 one can conclude that it is better to sell at OPE3 because of thelower risk to return ratio.Conclusion: If you bought the oversold stock and it moved up significantly during the day#2 it is a good idea to sell this stock on the morning of day #3. At this point the average returnis close to maximum and the risk to return ratio is minimal.7.3 When to sellSo, sometimes you need to break the rules of trading strategies depending on stockperformance. Your annual return can be larger if you take into account large upside or downsidestock moves.Here we'd like to discuss an additional advantage of selling earlier after big upsidemoves. For the Basic Trading Strategy you should hold stocks for three days. So, your tradingcapital should be divided into three parts to trade every day. If you sell stocks in two days youneed to divide your capital into two parts. This is important if your trading capital is small andbrokerage commissions represent a substantial contribution to transaction cost.Another advantage of selling early is accumulation of cash reserve. If you are using theBasic Trading Strategy and after a large upside stock move you sold early, you can use thismoney to increase positions as we described in Section 7.1.
43Chapter 8
Limits and Stops8.1 General remarks8.2 Limit orders and average returns8.3 Stop orders and average returns8.1 General remarksIn Chapter 1 we briefly considered the general idea of using stop and limit orders to sellstocks. We mentioned that when there is high growth probability the stop order should beplaced far away from the current stock price. In a bear market, when the growth probability islow, the stop should be very close to the current stock price.Let us write some equations to demonstrate this statement. If you do not like equationsyou can skip this section and start reading Section 8.2.Consider the problem which was mentioned in the first chapter. You buy stock at some currentprice and sell it when its price touches stop or limit prices.SL___________________|_________|___________|____________________stopcurrentlimitpriceHere, S and L are the differences between the current stock price and the stop and limitorder levels. Let P(L) be a probability of first touching the limit level. If this happens, you win. Itcan be shown that if the probability of stock growth and decline are equal, then the averagereturn is equal to zero for any values of L and S.The situation is different if the growth probability p is not equal to the decline probabilityq. To have some idea about the dependence of your profit on the stop order level let us considera very simple model. Suppose, the stock price changes by 1 dollar. In this case p is theprobability of an upside move and q is the probability of an downside move. The probability ofwinning P(L) can be written asP(L) = 1 - [1-(p/q) L] / [1-(p/q) S+L ]The average return R for this strategy is equal toR = L*P(L) - S* [1 - P(L)]This is a case when the market is bullish or you have a nice trading strategy which allowyou to select stocks with high probability of growth. Let us plot the average return as a functionof the stop order limit S. As an example, consider a case when p = 0.6 and q = 0.4 and L = 5.
Figure 8.1 Average return as a function of the difference between the current stock price andthe stop order level. The growth probability is larger than the probability of decline.
44You can see that to have a maximal profit (= 5 in this case) you should place a stoporder very far away from the current stock price.In bear market the situation is opposite. The Figure 8.2 shows the average return in thecase of p = 0.6 and q = 0.4. i.e. when the probability of growth is less than the probability ofdecline.
Figure 8.2 Average return as a function of the difference between the current stock price andthe stop order level. The growth probability is smaller than the probability of decline.You can see that the average return is always negative in this case and to reduce the lossone should place a stop order close to the current stock price.8.2 Limit orders and average returnsstocks
Using limit orders to sell stocks is a bad idea. Consider the strategy for trading oversoldCLO1 < K1*CLO0
LIM is the stock price limit to sell during day #2 or day #3. The limits should beLIM < MAX2LIM < MAX3where MAX2 and MAX3 are maximal prices on days #2 and #3. If the prices do not touch thislimit, you are selling at the price OPE4. The results are in Table 8.1, where the control returns(no limits for sale) are shown. The limits are chosen as 5 and 10% and 1+V , where V is thestock volatility.Table 8.1
Using limit orders to sell stocks in comparison to the standard strategy CLO1-OPE4(Return0).
K1
LIM
Return
Return0
0.95
(1+V)*CLO1
2.43 (4.0)
3.67 (3.1)
0.9
1.05*CLO1
2.86 (3.4)
5.77 (2.3)
0.9
1.1*CLO1
4.28 (2.6)
5.77 (2.3)
0.9
(1+V)*CLO1
4.53 (2.6)
5.77 (2.3)
You can see that for any limit the average return is less than for a return for standardstrategy and the risk to return ratio is higher. So, do not use limits to sell stocks. You can missthe large price moves.Another way of using limit orders can be profitable. You can try to to catch the minimumat day #2 to double your position. Consider trading oversold stocks CLO1 < K1*CLO0. LIM is thestock price limit to buy additional shares during day #2 if
45LIM > MIN2The results are in Table 8.2, where the control returns (no additional buying) are shown.Table 8.2
Using limit orders to buy additional shares of stock in comparison to the standardstrategy CLO1-OPE4 (Return0)
K1
LIM
Return
Return0
0.95
(1-V)* CLO1
4.33 (2.6)
3.67 (3.1)
0.9
(1-V)*CLO1
6.63 (2.0)
5.77 (2.3)
In contrast to the previous limit strategy, this strategy is more profitable and less riskythan standard strategy CLO1 - OPE4. So, if you see the large price drop of your stock during thetrading day, do not wait until market closing. Take a risk and try to buy more shares at somelocal price minimum. If you do not have time to watch the stock for the whole day, you canplace a limit order to buy more shares during the trading day. When the stock price touches thelimit the shares will be bought automatically.8.3 Stop orders and average returnsIn Section 8.1 we considered a theoretical model to calculate the average return as afunction of stop levels. Real life is more complicated. The growth probability can be different forday #2 and day #3. The total price change includes 2 or 3 overnight moves. All this makes thedependence of return on the stop order level very complicated.To illustrate the problem let us show the results of computer modeling. We studied an 11year history of 250 stocks from S&P 500 index. We took such a long history in order to haveenough statistics to perform a study for different market conditions. Using strategy CLO3 - CLO0we calculated the total (11 years) returns for different stop levels. Figure 8.3 shows the resultsof our calculations. Return0 is the return without using stop orders.
Figure 8.3 The dependence of 11 year return for 250 stocks on the stop order level. Return0 isthe return calculated without using stop orders.One can see that placing stop orders very close to the current stock price very slightlyreduces the total return. However, the best results were obtained for the strategies that don'tuse stop orders.
46Chapter 9
Small Stocks9.1 Statistics for small stocks9.2 Risk and return9.3 Small stocks trading strategies9.1 Statistics for small stocksWe define small stocks as stocks with closing prices less than $10 on the day of theanalysis (day #0). The number of these stocks is very large but for trading we select those witha trading volume of more than 100,000 shares on the day of the analysis. We will call thesestocks active small stocks. The number of active small stocks is about 3 times less than thenumber of active stocks with a price of more than $10 and a volume more than 200,000. So,one can expect that the number of trades per month for strategies using small stocks will beless than the number of trades for our basic strategy.The average daily return of small active stocks is higher than for "normal" stocks, i.e. forstocks with prices higher than $10. For the period 1995 - 1999 the average daily returns areequal to:S&P 500Active stocksSmall active stocks
0.089 %0.13 % +/- 1.2 %0.38 % +/- 1.4 %
This effect is probably related to abnormal activities of selected stocks. Usually, for manyof them the trading volume is much lower and some activities attract many traders who hope tofind a good bargain and make a large quick profit.To confirm this statement let us show the average closing prices of active small stocksduring 5 days after the day of analysis (day #0).<CLO1 - CLO0> = 0.38 %<CLO2 - CLO0> = 0.55 %<CLO3 - CLO0> = 0.66 %<CLO4 - CLO0> = 0.74 %<CLO5 - CLO0> = 0.81 %The difference between closing prices is diminishing with time, and by the fifth day afterthe day of analysis it becomes even less than for the S&P 500 index.Figure 9.1 illustrates the difference in behavior of active stocks (price > $10, volume >200,000) and small active stocks (price < $10, volume > 100,000)
47
Figure 9.1. Closing price differences CLOk - CLO0 (k = 1, 2, 3, 4, 5) for active stocks and forsmall active stocks. Day #0 is the day of the analysis.So, the statistics for the active small stocks are similar to the statistics for active stockswith prices > $10 described early. However, the price changes for small active stocks are largerwhat can be used to obtain higher returns per trade.In the next section we consider methods of stock selection which allow to reduce risk of smallstock trading and increase trading returns.9.2 Risk and returnLet's try to apply to trading small stocks the ideas which have been described in theprevious chapters. Consider potentially bullish stocks selected by the same criteria we used forselecting active stocks with prices higher than $10 (see Chapter 4 for details). We will defineoversold small stocks as stocks from the list of potentially bullish small stocks with a price dropduring day #1:CLO1 < CLO0Consider some statistics for oversold small stocks. We suppose that traders buy oversoldsmall stocks at the market closing on day #1. So, we will present the oversold small stock pricechange relative to the CLO1 price. The risk to return ratios are shown in parentheses. Closingand opening prices will be considered.Table 9.1 Closing prices of oversold small stocks relatively to CLO1 (in %).CLO1 < CLO0
CLO1 < 0.95*CLO0
CLO1 < 0.9*CLO0
<CLO2 - CLO1>
1.88 (6.2)
2.81 (5.1)
4.35 (4.2)
<CLO3 - CLO1>
3.58 (4.3)
5.37 (3.5)
7.58 (3.1)
<CLO4 - CLO1>
4.57 (3.8)
6.65 (3.1)
8.57 (3.0)
<CLO5 - CLO1>
4.92 (4.0)
6.90 (3.4)
8.44 (3.3)
48Table 9.2 Opening prices of oversold small stocks relatively to CLO1 (in %).CLO1 < CLO0
CLO1 < 0.95*CLO0
CLO1 < 0.9*CLO0
<OPE2 - CLO1>
1.87 (3.9)
2.69 (3.6)
4.37 (3.2)
<OPE3 - CLO1>
3.36 (4.0)
4.94 (3.3)
7.33 (2.9)
<OPE4 - CLO1>
4.99 (3.4)
7.39 (2.8)
10.2 (2.6)
<OPE5 - CLO1>
5.83 (3.2)
8.25 (2.79)
10.8 (2.7)
The returns look very attractive, but these returns are pure returns - no transaction costshave been taken into account. For small stocks these costs can be very significant. The bid-askspreads can be 5% and more. Our estimation shows that the average spread for small stocksfrom our list of potentially bullish small stocks is equal to about 2.5%. Table 9.3 shows anexample of the bid-ask spreads for some small stocks.Table 9.3 Bid - ask spreads for small stocks from the list of potentially bullish small stocks onJune 4, 1999.Ticker
Price
Bid-Ask Spread in %
HPH
2.38
2.63
VCSTW
2.10
6.06
EFCX
1.44
2.20
BDT
2.5
2.50
NRMI
4.63
2.63
VVID
2.63
3.57
JBOH
9.00
0.69
VCST
5.13
3.66
NAVR
8.88
1.39
FEET
6.38
0.98
COOL
9.88
0.63Average = 2.45%
If we subtract the average transaction cost from the returns, then the risk/return ratioswill be substantially higher. However, <OPE4 - CLO1> return is profitable even for these largetransaction costs.9.3 Small stocks trading strategiesYou can use a part of your capital to trade small stocks. Taking into account the largetransaction cost we recommend trading small stocks only when they are very oversold. Youshould consider only stocks with 5 - 10% price drops during day #1. The old trading strategyCLO1 - OPE4 is the best one for small stocks. It works for transaction costs up to 8%!However, you should remember: because of the large transaction cost the risk/returnratio for small stocks is larger than for stocks with prices greater than $10.It is worth considering trading small stocks if you do not see any opportunity in "normal"stocks. Do not spend a large part of your trading capital to buy small stocks. Wait for bigopportunities in small stocks when the potential return is very high. Buy small stocks with smallbid-ask spreads.To make the risk of trading small stocks lower you can consider very low risk strategies.One of them is buying more shares when there is a large price decline during the day #2 asdescribed in Chapter 6. Let us show some statistical data for this strategy.
49Suppose you bought some oversold small stock at the market closing on day #1 at theprice CLO1. This stock is very oversold, so that CLO1 < 0.9*CLO0. Nevertheless, the stock wentdown more than 5% or 10% during day #2. We will show the predicted returns if you buyadditional shares at the price CLO2. The risk to return ratios are in parentheses.Table 9.4
The average returns <X - CLO2> (in %) of oversold small stocks in the case of aprice drop during day #2.CLO2 < 0.95*CLO1
CLO2 < 0.9*CLO1
OPE3-CLO2
3.8 (2.2)
5.4 (1.7)
CLO3-CLO2
6.2 (3.1)
9.1 (2.5)
OPE4-CLO2
9.8 (2.2)
13.1 (1.9)
CLO4-CLO2
11.6 (2.4)
17.3 (1.9)
OPE5-CLO2
13.5 (2.0)
17.2 (1.9)
CLO5-CLO2
15.6 (2.0)
20.9 (1.8)
One can see that buying additional shares after a price drop during day#2 is rather safeand profitable. Even high transaction costs do not play significant role for these trades. The onlybad thing is that these buying opportunities are very rare. During 1995 - 1999 we found only 80potentially bullish small stocks with double price dropsCLO1 < 0.9*CLO0CLO2 < 0.9*CLO1However, the expected returns are so high that it is worth watching small stocks everyday to catch such opportunities.
50Chapter 10
Selling Short10.1 How to define overbought stocks10.2 Statistics for overbought stocks10.3 Selling short strategies10.1 How to define overbought stocksSelling short is a risky game. You borrow shares and sell them just after borrowing. Aftersome time you buy back these shares. If the stock price went down during this time, you arelucky. You buy shares at a lower price and the cost price is lower than the sell price. Your profitis the difference between the sell price and the cost price.The things can go in the opposite direction. The stock price can go up and you will beforced to buy the shares back at a higher price and you will lose money. There is no upside pricelimit for stock, and your losses can be very high.There are many other disadvantages to selling short. One of them is the uptick rule. Youare able to sell short some stock if the current bid price is higher than the previous bid price. So,when stock is falling you should wait for pull back to open a short position.There are some other problems with selling short. You need larger capital to open a shortposition. Many securities are restricted for selling short during a certain period of time. Forexample, "Yahoo!" was prohibited for selling short for a couple of weeks in 1999.This is why selling short is not popular among individual investors and traders. About 8090% of short positions are held by professionals. Nevertheless, selling short can be veryprofitable, and using this tool you are able to make money even when the market is falling.After this introduction it is clear that we should be very selective in earmaking a stock forselling short. We cannot reverse the list of potentially bullish stocks. The criteria of overboughtstocks should be stronger.We suggest establishing the list of potentially bearish stocks using the followingconditions:1. Stocks should be active. The trading volume should be more than 200,000 shares perday.2. Closing stock prices on the day of analysis should more than $10.3. Stocks should be overbought in 16 and 32 day frames.4. Stocks should rise during the previous day.Mathematically, one can write condition #3 as:D16 > 1D32 > 1T16 > T16av + σ16TT32 > T32av + σ32Twhere σ16T and σ32T are the standard deviations of 16 and 32 day trends. In other words, thestocks should be in T-D cell #4 for 16 and 32 day frames. One can find more about these termsin Chapter 2.Note that stocks should be oversold in 16 or 32 day frames to be included in the list ofpotentially bullish stocks. So, the conditions for being bearish are stronger than those for beingbullish. The list of potentially bearish stocks is smaller than the list of potentially bullish stocks.We did this to increase the safety of selling short.What is the optimal time to start selling short and to close the short position? Is it worthselecting stocks using even more stringent conditions? To answer these questions let's considerthe results of computer analysis.
5110.2 Statistics for overbought stocksThe trading strategy for selling short is different from the strategies for buying stocks.First of all, you should open a short position at the market opening. Morning prices are usuallyhigher. Very often after strong growth during trading day #0 (the day of the analysis) stockscontinue their rally on the morning of the next day, and this time is the best to start sellingshort.In our computer analysis we consider stock price changes relative to the OPE1 price. Twomethods of stock selection will be analyzed. One was described in the previous section: stocksshould be overbought in the 16 and 32 day scale. The second selection method: stocks shouldbe overbought in 4, 16 and 32 day scales. So, the additional condition is added:D4 > 1T4 > T4av + σ4TSome data can be found in Table 10.1. Thesetatistical data are the result of the analysis foryears 1995 - 1999.Table 10.1 Price (in %) of potentially bearish stocks relative to the OPE1 price (=100%) for twoselection methods.1. Stock are overbought in 16 and 32 day scales2. Stock are overbought in 4, 16 and 32 day scalesSelection-1
Selection-2
<CLO1>
99.2
98.2
<CLO2>
98.8
97.5
<CLO3>
98.5
97.3
<CLO4>
98.6
97.2
<CLO5>
98.8
97.4
<OPE2>
99.5
98.6
<OPE3>
99.0
98.0
<OPE4>
98.9
97.7
<OPE5>
98.9
97.7
Number of selected stocksper day
8.5
1.2
Conclusions:1. Our method of determining oversold and overbought stocks works. Even in bull market onecan buy overbought stocks and make some profit from selling short.2. The idea of fractal market analysis also works. Adding the overbought condition for anadditional time frame improves the stock selection method.3. The number of stocks in the list of potentially bearish stocks is very small if one uses threeoverbought conditions (4, 16, 32 day frames).4. It is better to close a short position at the market closing.5. Return from selling short is small if one uses only stocks from the list of potentially bearishstocks. Some additional conditions are necessary to improve the average return.What is the best strategy for selling short? This question will be considered in the nextsection.10.3 Selling short strategiesIn the previous section we have shown that using three time frame overboughtconditions substantially reduces the number of stocks in the list of potential candidates forselling short. Later, we will consider only stocks selected by using 16 and 32 day frames. Thenumber of such stocks is 7 times larger and statistically is more reliable. One should note that
52stocks which are overbought in 3 time frames (32, 16 and 4 days) are better for selling short,and you can use a larger part of your trading capital to sell short these stocks.We also mentioned that one should introduce an additional condition for stock selectionto improve returns. This condition is very simple. The potential winners for selling short shouldhave higher prices at the market opening on day #1 with respect to prices at the market closingon the day of the analysis (#0).OPE1 > K1*CLO0Table 10.2 shows the price changes depending on the coefficient K1. Only closing pricesare shown because they are lower than opening prices.Table 10.2 The price changes (in %) of the potentially bearish stocks relative to the OPE1 price.The risk to return ratios are shown in parentheses.OPE1 > CLO0
OPE1 > 1.05*CLO0
OPE1 > 1.1*CLO0
<CLO2 - OPE1>
-2.1 (5.0)
-5.3 (3.6)
-7.5 (3.4)
<CLO3 - OPE1>
-2.4 (4.8)
-6.9 (3.1)
-10.1 (2.5)
<CLO4 - OPE1>
-2.3 (5.6)
-7.2 (3.1)
-11.5 (2.3)
<CLO5 - OPE1>
-2.0 (6.9)
-6.6 (3.6)
-11.4 (2.4)
You can see that selling short is a rather profitable game if you use the right strategy.Potentially bearish stocks become really bearish if they move up during the night after the dayof the analysis. The optimal time to close your short position is the market closing on day #3 or#4. The risk to return ratio is low and the return is large enough to make a profit even withlarge transaction costs.What should you do if the stock went up on the morning of day #2? The answer is inTable 10.3.Table 10.3 The price changes (in %) of the potentially bearish stocks relative to the OPE2 pricein case OPE2 > OPE1. The risk to return ratios are shown in parentheses.OPE1 > CLO0OPE2 > OPE1
OPE1 > 1.05*CLO0OPE2 > OPE1
OPE1 > 1.1*CLO0OPE2 > OPE1
<CLO3 - OPE2>
-2.6 (3.8)
-8.0 (2.1)
-13.4 (1.4)
<CLO4 - OPE2>
-2.8 (4.1)
-9.0 (2.2)
-15.9 (1.3)
<CLO5 - OPE2>
-2.6 (4.9)
-8.6 (2.7)
-16.4 (1.5)
You can see that in the case of rising price during day #1 you can increase your shortposition. The expected return is large and the risk to return ratio is small.
53Chapter 11
Other trading strategies11.1 How many days to hold?11.2 How many stocks to buy?11.3 Upgrades and downgrades11.4 Trading tips11.1 How many days to hold?We define the basic trading strategy as a method of buying certain selected stocks andholding them for three days. You can ask: why three days? Maybe two or four days would bebetter?To answer this question let us consider some results of our theory of trading. As anexample, consider the basic trading strategy. For this strategy the trading capital should bedivided into three parts A, B, and C. Your initial trading capital TC is equal toTC = A + B + CAfter N days (for example, N =