Reading a paper about VaR and don't understand what $a'$ is. The link to the paper is here: https://citeseerx.ist.psu.edu/viewdoc/download?doi= The relevant passage is:

We consider n financial assets whose prices at time $t$ are denoted by $p_{i,t}$ ,is $1, . . . ,n$. The value at $t$ of a portfolio with allocations $a$ , i =$1, . . . ,n$ is then:
$$W_f(a)=\sum_{i=1}^n{a_ip_{i,t}}=a'p_t$$ If the portfolio structure is held fixed between the current date $t$ and the future date $t+1$, the change in the market value is given by $$W_{t+1}(a)-W_t(a)=a'(p_t+1-p_t)$$

Apologies for basic question, I just don't understand what $a'$ is supposed to be and why you can separate the $p_{i,t}$ term.

  • 3
    $\begingroup$ $a$ is a vector of portfolio weights (allocations) and $a'$ is $a^\top$, the transpose of the vector. Then, $\sum\limits_{i=1}^n a_ib_i=a'b$ is just the Euclidean inner product. $\endgroup$
    – Kevin
    Jun 30 at 21:30
  • $\begingroup$ @Kevin Oh gotcha, thank you. $\endgroup$
    – elbecker
    Jun 30 at 21:50
  • 2
    $\begingroup$ Also, that $p_t +1$ should be $p_{t+1}$. $\endgroup$
    – ir7
    Jun 30 at 22:16

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