# How can factor certificates achieve constant leverage?

How does a bank which offers a factor certificate with unlimited maturity, e.g. a certificate which promises the holder to change in value in a constant proportion with respect to a change in the underlying, achieve this constant factor? For example a factor 2 long certificate on gold increases by 2% if gold increases by 1%. So far, I figure that this resembles margin trading with a price calculated something like that:

$$Price_0 = Underlying_0 - Loan.$$ This evolves over time according to: $$Price_t = Underlying_t - Loan*(1+r)^t$$

The initial difference between the price and the value of the underlying define the factor (or leverage) for the "start" but as the underlying moves this factor changes and there is no additional cash flows from or the holder of the certificate until she sells it. Truly the formulae may be oversimplified but I wonder how these products actually achieve such feature?

Thx for any help!

• As the price of gold goes up you have to borrow more (or buy additional gold futures, if you are leveraging by using futures). And vice versa when gold price goes down. It is a dynamic strategy. – Alex C May 18 '16 at 22:47
• @AlexC Thx for the comment, that helps! – Tim May 19 '16 at 16:06