Traffic Lights
motivated by a talk with Marty

I was told of this software that gave you Buy and Sell signals and ...

>And you bought it, right?
Hardly. It cost thousand of dollars, but in looking at the reviews of the software, I found that people thought the red and green signals that indicated whether a stock was Hot or Not ... that was neat.
 So I decided to give it a try myself, like so: We download a years worth of daily prices for some stock. We decide upon some number of days for our Exponential Moving Average. (See EMA) We calculate the gBS, like Figure 1. We pick a couple of gBS-values to determine the Buy or Sell signals. We ... >Wait! You calculate gBS? Yeah. We'll get to that in a moment. Figure 1
 It's that Hot or Not signal that I thought was neat, so you get a Traffic Light, one of the three shown in Figure 2. >Don't tell me! Green is Buy, Red is Sell and ... Amber is Hold. You got it! Neat, eh? Figure 2
Yes, like this:

There's an Explain sheet that looks like this and ...

>It does 4 stocks, too?
Yes. There's a 4-Stocks sheet where you can get something like this.
Just type in 4 stock symbols and click the do Four button.
You can change the EMA days and Buy and Sell values to see what'd happen to all four stocks. Neat, eh?

>Yeah. Wonderful, but what on Earth is gBS?
Although I was just interested in generating that neat traffic light, I needed a Buy/Hold/Sell signal, so I decided on gBS.
Let me ...

>What's gBS stand for? I can imagine the g and, come to think of it, I can imagine the BS!
Let me explain.

The idea is to identify times where the Bulls are just too active and we expect it's time to Sell.
Also, the days where the Bears are too active and it's time to Buy.
To identify these times, we do this:
 Each day we see if the High has increased. If so, we assign a 1 to the Bulls ... else they get 0. If the Low has decreased, we assign a point to the Bears ... else they get 0. This gives us a sequence of daily 0s and 1s for the Bulls ... and for the Bears We calculate the EMA for each sequence and, each day, note whether the Bulls are winning (meaning that the EMA of Bear points is large) or the Bears are winning. The gBS is the difference between these two Exponential Moving Averages. Figure 3
 The gBS might look like Figure 4 (similar to the spreadsheet, above). When gBS is large, we say: "The Bulls have overbought this stock. It's bound to drop, so I Sell." When gBS is small, we say: "The Bears have oversold this stock. It's bound to recover, so I Buy." >And that's it? That's your Buy/Sell signal? Sure. Why not? >And you actually use this stuff? Huh? You think I'm crazy! Figure 4

 gBS details

Suppose that the sequence of daily Highs and Lows are Hk and Lk for k = 1, 2, ...
We calculate the Bull Points Sk and the Bear Points Bk ... where B and S stand for Buy and Sell.

We pick N, the number of days in the EMA calculation, and calculate α = 1 - 2/(N+1).

Then we calculate, each day, the Exponential Moving Averages.
Recall the magic EMA formula, namely   EMAk = αEMAk-1 + (1-α) Zk
This implies that we're taking the Exponential Moving Average of a sequence of Zs.

For our EMAs, we calculate:
EMAk[S] = α EMAk-1[S] + (1-α) Sk   (the EMA of the Ss).
and
EMAk[B] = α EMAk-1[B] + (1-α) Bk   (the EMA of the Bs).

Then comes the difference:
gBSk = EMAk[S] - EMAk[B] = α {EMAk-1[S] - EMAk-1[B]} + (1-α){Sk-Bk} = α gBSk-1 + (1-α){Sk-Bk}

We recognize that gBSk is just the EMA of the difference: Sk-Bk.

Although we need to assign some value to gBS1, it makes little difference how we do this.
Since α < 1, after umpteen days, the initial value gBS1 is long since forgotten.

In the spreadsheet, although a year's worth of daily data is downloaded and used, only the last three months or so is plotted.
In other words, the first nine months serve to get the EMA ritual started.

>And how would that ritual have done, say at the 1987 crash?
Uh ... I have to find the data for 1987, but remember the terrible Nasdaq (^IXIC) and DOW (^DJI) performance after 1999?
There was great momentum, great hopes of making fortunes (especially in hitech), great ...

>Yeah, so? How would it have done? Would it have warned of the big drop?
You decide:

>But that's cheating! You picked the parameters so you'd get good Buy/Sell signals.
Of course. I always cheat.

 New Stuff
 Since I wrote the stuff above, the spreadheet has changed a wee mite and ... >You stopped cheating? No, I just added a (fictitious) \$100K portfolio that abides by the Buy/Hold/Sell signals. It's much more fun. >Is it any good? I give up. Is it?
I should also mention that you can weight the prices, High and Low, by the Volume of trades.
That is, instead of comparing daily Highs and Lows we compare daily log(Volume)*High and log(Volume)*Low.
That means that days when the volume of trades were really HUGE have more weight than ...

>Yeah, yeah. I get it.
Good for you.

to continue ...