Evaluation of MACD Trading System

Its easy to attribute meaning to seemingly complex trading systems where often there is none. What follows is an exchange I had with a very experienced trader regarding a MACD (moving average convergence/divergence) system he advocated. This way of doing system simplification is known as inequality algebra. It was discussed in an issue of TASC.

XXXXX, Lets take a look at what you are really saying when you advocate that system.

XXXXX said:

I think one of the better indicators is a weekly MACD. Don't wait for a cross over the signal line, but rather just an upturn. 13 21 8.

First for those who may not know, lets explain (using SMA) the Moving Average Convergence/Divergence. MACDi is the difference between the 13-week SMAi (Simple Moving Average) of the closing prices and the 21-week SMAi of the closing prices. You're saying go long if this calulation increases (turns up)… go short if it decreases (turns down).

Algebraically you are saying this:

if (13MA1 - 21MA1) > (13MA2 - 21MA2) is TRUE
    then GO LONG (vice versa for short)

Lets simplify...

13SMA1 = (c1+C2+c3 ... c13) / 13
21SMA1 = (c1+C2+C3 ... c21) / 21


13SMA2 = (c2+C3+C4 ... c14) / 13
21SMA2 = (c2+c3+c4 ... c22) / 21

Plugging those formuala into your equation we get:

{(c1+c2...c13)/13 - (c1+C2...c21)/21} > 
{(c2+c3...c14)/13 - (c2+c3...c22)/21}

multiplying both sides by 13 gives:

{.381*(c1+c2+...c13) - .619*(c14+c15...c21)} > 
{.381*(c2+c3...c14) - .619*(c15+c16...c22)} 

which can be reduced as follows:

.381*c1 - .619*c14 > .381*c14 - .619*c22 
.381*c1 - .619*c14 + .619*c14 > .381*c14 +.619*c14 -.619*c22 
.381*c1 > c14 - .619*c22   


 c1 > 2.624*c14 - 1.624*C22   <-  simplified MACD system

So what you are saying is BUY if: this weeks close is greater than 2.624 times the close 14 weeks ago minus 1.624 times the close 22 weeks ago. Just the opposite is true for a SELL signal.

Personally I'm skeptical of such a system. Whats so special about these weeks (1, 14 and 22) and that particular relationship? TA should have some logical basis. Please tell me… why should it should perform?

This analysis applies to all MACD regardless of parameters. I would like to see XXXXX explain how one gets a "leading system" out of (potentially very) old price information. Now THAT would be a good trick!