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Spread calculation

In this article we will provide a method to calculate correct lotsizes of symbols in the spread. Due to popular belief, the number of lots for each symbol should always be equal to its weight in spread. If you do so, you can experience real trading results not matching your expectations.

This is because the price of instruments is usually indicated in indicative points. For each instrument, we can get two values: tick size (minimal price step) and tick cost (price change if that step occurs). For example, popular futures contract E-Mini S&P has these values at 0.25 and 12.5$ respectively. In the simplest case, when all the symbols in our spread have same both the tick size and cost, the number of lots in spread can definitely be the same for each symbol. If tick size or cost differ in one or more instruments, this should be taken into calculation:

For example:

"Weight in spread" - multiplication factor for an instrument in spread

SPRED=(w1*X1+...+wn*Xn)- (wn+1 *Xn+1+...+wn+m*Xn+m)

where wj is weight in spread and Xj is price.

"Lotsize in spread units" - is a parameter that determines the actual number of lots that will be traded when buying or selling one unit of the spread.

Let pj be tick cost, sj tick size, then number of units in a unit spread (cj) for each instrument can be calculated by the following formula:

cj=wj*sj/pj.

In some cases it is easier first to pick the needed lotsizes for symbols, and only then calculate needed spread weights. In this case, weight in spread can be calculated by following formula:

wj=cj*pj/sj.

Now, an example:

SPRED=(0,8*platinum+23*silver)-(0,6*gold+1,2*palladium)

Platinum: p=10$ (tick cost), s=0,5 (tick size). 

Silver: p=10$s=0,01

Gold: p=10$s=0,5

Palladium: p=10$s=0,5

So, platinum: c=0,8*0,5/10=0,04 (number of lots for each spread traded),

silver: c=23*0,01/10=0,023,

 

gold: c=0,6*0,5/10=0,03,

palladium:  c=1,2*0,5/10=0,06.

Of course one can increase or decrease c value at any time. For example, we can multiply each one by 10 and get platinum as 0.4 lots, silver as 0.23, 0.3 lots of gold, and palladium at 0.6 lots. So, we basically calculated necessary proportions for each of instruments in this particular spread. Of course, tick costs should be in the same currency (in our case it was USD).