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April 21st, 2014, 03:32 AM   #1
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how to use subindices

Hi,

I am not sure how to use subindices in a correct notation. Let's say I would like to calculate the return of a stock from day $\displaystyle t-1$ to $\displaystyle t$. That's how I'd write it:

$\displaystyle r_t=\frac{S_t}{S_{t-1}}.$

With $\displaystyle S_t$ being the stock price at time $\displaystyle t$. How could I define a return over not one period but $\displaystyle T$ periods. Would something like that be correct?

$\displaystyle R_{t,t-T}=\frac{S_t}{S_{t-T}}$

Is it possible not to use double indices and write it in a shorter way?
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April 21st, 2014, 07:55 AM   #2
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Notation does have conventions (that are often different for different areas of mathematics), but in general you can use any notation you like as long as you explain it clearly.

In your example, I might define $r_i$ to be the return of a stock from day $t−i$ to day $t$ and then we get
$$r_1=\frac{S_t}{S_{t-1}}$$
and
$$r_T=\frac{S_t}{S_{t-T}}$$

On the other hand, if you are planning on varying $t$ but not $T$, I would define $r_i$ to be the return of a stock from day $i−T$ to day $i$ and then we get
$$r_1=\frac{S_1}{S_{1-T}}$$
and
$$r_T=\frac{S_T}{S_{0}}$$

If you are going to vary both, then you might need a different notation. Perhaps $r(t, i)$ to mean the return of a stock from day $t−i$ to day $t$. Or $r_{t,i}$ or $^t_ir$. Whatever you feel is clearest and best suits your purpose.
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