Part 5 (1/2)

In addition to executing the ETF instead of the short leg of the pair, we need to consider whether the position size of the short leg should change. The position size was intended to equalize the risk of both legs and was calculated based on the average true range of each stock price over the recent past. If we subst.i.tute an ETF with significantly different volatility, then the long and short positions will not have offsetting risk. Then it seems logical that we would recalculate the position size using the volatility of the ETF.

In many cases, only the closing prices are available for the ETFs. If the high, low, and close are available, then the volatility calculation would be performed in exactly the same way as the underlying stocks, using the average true range. However, if only the closing price is available, as it was for our data, then the average true range becomes the average of the close-to-close differences, which would be a much lower volatility value. With only the closing prices, we went ahead and tested the use of both ETFs as a subst.i.tute for short sales. The results, using the standard values of a four-day momentum and 40 entry threshold, are shown in Table 3.24.

TABLE 3.24 Comparison of ETF shorts using ETF volatility to determine position size.

Although the chart shows that ITB and XHB are very similar, and the correlation of their returns is .957, the effect of subst.i.tuting them for the short sales yields very different results. The ITB ETF performs better than the benchmark case, and the XHB results are much worse. Profits per share increase from 1.7 cents to 4.0 cents, and the ratio gains from 0.131 to 0.149. At the same time, using XHB turns those profits into net losses. When we look at the individual pairs, we see that the ratio for KBH-TOL jumped from 0.589 to +0.919 using ITB but was little changed with XHB, and both ETFs performed very badly when used for LEN-HOV. In fact, ITB has a very different performance overall.

We can conclude that using an ETF as a subst.i.tute for short sales can work, but each ETF needs to be tested because just looking at the chart doesn't tell us enough.

PORTFOLIO OF HOME BUILDER PAIRS.

The final step in creating performance expectations is to build a portfolio from the results of the 10 pairs. This will show our antic.i.p.ated returns and the risk a.s.sociated with those returns. We expect that the risk will be reduced due to diversification, but we also know that these stocks are highly correlated, and the reduction might be small.

Because the construction of a portfolio is important, we will go through the process in six steps. The values for the pair LEN-TOL will be used as an example. The first steps can also be followed in Table 3.25.

1. Create a series of daily profits or losses for each pair of stocks. The net profit for the pairs is the sum of the gain or loss in one stock (the number of shares held on day t times the change in price from day t through day t + 1) plus the gain or loss in the other stock. If you are using capped results, then the daily profits and losses reflect the net return after capping the position size. The capped results are shown in the second column (B) of Table 3.25.

TABLE 3.25 Construction of NAVs from daily profits and losses for LEN-TOL.

2. Find the annualized volatility of the daily profits and losses in (1). For this pair, first create a column with the daily differences in the PL (column 3). Then find the standard deviation of those differences, 18.03. To annualize, multiply that value by to get 286.21. Note that this annualized change seems lower than expected because there were many days with no trading, giving zero returns on those days.

3. Find the investment size needed to trade this series at your target volatility. If the target is 12%, divide the annualized standard deviation in (2) by 0.12. The capped series yields an investment of $2,385. The capped series actually has lower volatility and a lower investment than the noncapped returns. This lower investment will translate into an increase in portfolio returns. When using futures in the next chapter, we will be able to adjust the leverage freely while keeping a close eye on risk.

4. Create the volatility-adjusted returns in column 4. Divide each PL difference (column 3) by the investment size calculated in step 3.

5. At this point, we have volatility-adjusted each pair to the target volatility of 12% using the capped returns, so that each PL series has an equal risk. We now create a NAV series (column 5) from the capped PL for each of the pairs. Starting with the value 100, we multiply the previous day's NAV by the value 1 + Returns for the current day. For example, on January 13, the strategy had a positive return of 0.00461, or about 46 basis points. Up to this point, there were no trades. We get the new NAV value as follows: On the next day there was another gain of 0.00587. The new NAV would be: 6. Repeat steps 1 through 5 for each pair of stocks.

When all the changes are processed, the final NAV for the pair LEN-TOL is 343.56. Because this is a compounded rate of return, results will sometimes increase faster or slower than the simple profit and loss returns, as seen in Figure 3.20, which shows the NAVs of both the noncapped and capped results.

FIGURE 3.20 LEN-TOL comparison of capped PL and capped NAV.

FIGURE 3.21 All 10 capped NAV streams from home builder pairs.

Putting the Portfolio Together When the individual pairs results have been converted from PL to NAVs, we get the NAV streams shown in Figure 3.21. All show good returns at the same target volatility of 12%. The final step in creating a portfolio is to begin with the daily returns for each pair, shown in column 4 of Table 3.25. Our portfolio will equally weight the returns for each pair because we believe that all have the same chance of being profitable in the future. You may know that modern portfolio theory states that a portfolio should be maximized using the information ratio, the annualized returns divided by the annualized risk. Then those pairs that have a better payoff (higher return for the same risk) should be given more of the investment, which is the same as giving them a larger weight or larger allocation.

Although modern portfolio theory was religiously accepted when it was first proposed by Markowitz, the years have tempered enthusiasm for it. No one has actually proved that it has predictive ability, only that the optimized returns are better than any other combination. We shouldn't be surprised that optimized returns are better.

We prefer to a.s.sume that we don't know which of the 10 pairs will give the best returns next year. They all seem good, and the economy, as well as individual corporate management, always seems to surprise us. The best company this year can be out of business next year. Had we heavily favored Enron in an energy portfolio, we would have been both disappointed and broke.

This portfolio will equally weight all pairs. This approach is called removing returns from the picture. It's simpler than portfolio optimization, we can do it on a spreadsheet, and it a.s.sumes less. Because of that, we also believe that the results, or expectations, are more realistic. The steps are simple: If you don't already have the daily returns for each series, you can start with the NAVs and calculate the daily returns, r, as For each day, average the returns of all 10 pairs. This is the same as equally weighting the results. We'll call the average daily return of the portfolio of 10 pairs R. Note that you will not equally weight the pairs if the liquidity of one or more stocks is restrictive.

Create the portfolio NAVs from the average returns using the same formula that was given in step 5 when creating the individual NAVs. The final portfolio NAV using capped returns is 327.77 and using noncapped is 173.36, both shown in Figure 3.22.FIGURE 3.22 Final portfolio NAVs for home builders using noncapped and capped returns.

Find the annualized rate of return The ending capped NAV was 327.77, and the total number of days was 2,530, then The number of years is a decimal number, the result of dividing the total number of trading days by the number of trading days in a year (typically 252). The annualized return for this portfolio is 12.55%, without commission costs or other fees.

The information ratio, the final measurement of return for risk, is A ratio of 2.34 is comfortably high and likely to remain above 1.5 even after costs are deducted. Any value over 1.0 means that you are getting more return for each unit of risk. The information ratio for a pa.s.sive investment in the S&P index may be as low as 0.4 over a long period of time, and even lower in recent years that include the 2008 decline.

The final NAV stream for the portfolio of capped pairs is smoother than the individual streams because of the unexpected diversification gained from the different pairs and the final annualized volatility of only 5.35%, down from 12%. Unless you choose one of the available leverage options, such as financing part of the position with borrowed funds, you can't boost the returns because the capped result is already using all of the investment.

EXECUTION AND THE PART-TIME TRADER.

Success of a short-term trading program depends on the timely execution of orders. Even though this program uses only the closing prices to generate signals, it's not likely to be successful if calculations were done after the market closed, then entered the next morning on the open. An extreme price on the close is very likely to have corrected by the next opening. It might work if executions were done in the aftermarket on the same day, provided trading was done in small numbers. However, we could be pleasantly surprised.

The most likely way of executing this program is to enter prices shortly before the close, calculate the new positions, and enter those orders for execution on the close or as soon as possible. As long as the pair satisfied the entry threshold, you should have a good trade. If there are differences between the price entered and the final closing price that would have affected the position size, adjustments can be made after the close; however, that may be unnecessary.

You may also want to choose a different time of day to trade, preferably a few minutes after a key economic report, such as a Federal Reserve Open Market Committee (FOMC) meeting. Statements of interest rate changes and policy are released at 2:15 P.M. on the second day of the meeting, usually a Tuesday. Capturing prices and trading somewhere between 2:20 and 2:30 P.M. is likely to take advantage of price distortions during a short but volatile reaction. Similarly, you might want to trade after the official close on a day when the first chip manufacturer announces quarterly earnings. There is a 15 minute window where you might find greater price distortions between similar companies.

Pairs trading does not require that you enter a trade on the close. The method holds up, or might even be better, if you can take advantage of obvious s.h.i.+fts in prices. Exiting from a trade, however, is still best on the close.

STOP-LOSSES.

Many traders are concerned about unexpected price moves causing large losses, and they often try to solve this problem using a stop-loss. Normally, you would use a stop-loss for a trend trade or fundamental position, one where you are net long or short. For a pairs trade, you have equal, balanced positions, long and short, in related stocks. Any price shock will affect both stocks and should cause offsetting profits and losses unless that shock was related specifically to only one of the stocks in the pair. Whether one stock of the pair moves more or less than the other is arbitrary.

But what if the pair continues to post a loss and that loss gets larger? How do you deal with controlling the maximum loss? It's not possible to handle this with a stop-loss because both stock prices are moving, and the loss is relative to the difference between the two. You could monitor the profits or losses and close out the trade if the losses persisted. But the nature of the method is that the stochastic indicator adjusts to higher or lower prices and establishes a new norm. Then a smaller relative price change will trigger an exit.

Using stops changes the performance profile of a system. Pairs trading has a high probability of a profit, and there are many smaller profits and a few larger losses. If you use a stop, then there will be more losing trades, and in some cases you will have captured a loss when the trade would have eventually produced a profit. The balance of the system will be altered, and there is no a.s.surance that the final result will be profitable.

TRADING INTRADAY.

Our application has used closing price data; however, intraday price changes can generate many more trades, and taken to an extreme, it is similar to the high-frequency trading done by the big investment banks. Those trades are entered and exited in milliseconds and costs are negligible, but the principles are the same. In the previous section, ”Execution and the Part-Time Trader,” we discussed that trading after economic or corporate announcements could be an advantage.

A compromise between daily and milliseconds is hourly data. The strategy posts prices each hour and looks for the stochastic difference to generate a trade. Of course, profits per trade would be smaller because the holding period would also be shorter, so your costs would be the limiting factor rather than the opportunities.

KEY POINTS TO REMEMBER.

This chapter was as much about the process as about the strategy. It was intended to be a step-by-step explanation of the process needed to take an idea and create a trading strategy.

We began with what we believe to be a sound premise, that pairs trading is based on the fundamental concept that two stocks in the same sector, affected by the same macrofundamentals, will perform similarly. Because of that, we skipped the process of using in-sample and out-of-sample data, which would be a requirement if we were exploring for a new solution. Instead, we tested our method on one market and one sector, then applied it to other markets and other sectors. It is a weaker out-of-sample approach but we felt that it was sufficient.