Let us say that I want to spot trade a portfolio constituted of a pair of two stocks of respective prices (for example in USD) $S^1_t$ and $S^2_t$, and suppose for example that they co-integrate according to the relation:

$\varepsilon_t$ = $a$ $S^{(1)}_t$ + $b$ $S^{(2)}_t$

where $\varepsilon_t$ is the co-integration factor.

If for example $a$ $=$ $0.6$ and $b$ $=$ $-0.3$, and if $\alpha_t$ units of the portfolio are owned (for simplicity $\alpha_t \in \{-1, 0, 1\})$, the total value owned $\Sigma_t$ writes:

$\Sigma_t = \alpha_t (0.6\ S^{(1)}_t -0.3 \ S^{(2)}_t) + C_t$,

where $C_t$ is the cash in USD.

What does it exactly (mathematically) mean to

1) Short the portfolio,

2) Long the portfolio,

3) Liquidate the portfolio ?

  • $\begingroup$ The position is only determined once you specify a "scale factor" $\lambda$ (which you can choose based on how much money you have/how much risk you want to take). The position consist of $\lambda a$ shares of stock 1 and $\lambda b$ shares of stock 2. Usually a and b will be of opposite sign, one positive, the other negative. HTH. $\endgroup$ – Alex C Mar 17 '19 at 2:41
  • $\begingroup$ @AlexC I have modified the question. Could you provide an answer including the "scale factor" you mention ? $\endgroup$ – Arnold Mar 17 '19 at 14:33

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