Thread: Very unusual problem - any help highly appreciated

Suppose there is a stock (Stock A) and an index (Index A).

Stock A's price=$150
Index A's level=2450

The current ratio of Stock A/Index A Level = 150/2450 = 0.06122

Now supposing you look on the historic ratio chart and think that the ratio will increase from the current 0.06122 to say 0.07500 (ie you think stock A will outperform the index).

Just from knowing the expected ratio (0.07500) and the current ratio level (0.06122), would it be possible to calculate by how much % stock A outperformed the index by ?

Thanks a lot for all your help.

Originally Posted by gillchandler1

Suppose there is a stock (Stock A) and an index (Index A).

Stock A's price=$150
Index A's level=2450

The current ratio of Stock A/Index A Level = 150/2450 = 0.06122

Now supposing you look on the historic ratio chart and think that the ratio will increase from the current 0.06122 to say 0.07500 (ie you think stock A will outperform the index).

Just from knowing the expected ratio (0.07500) and the current ratio level (0.06122), would it be possible to calculate by how much % stock A outperformed the index by ?

Thanks a lot for all your help.

Right now you have A(0)/I(0)= .06122 and you believe that at some time in the future, A(t)/I(t) will be 0.07500. That tells you that (A(t)/I(t)) divided by A(0)/I(0) will be [tex]\frac{A(t)/I(t)}{A(0)/I(0)}= \frac{A(t)}{A(0)}{I(0)/I(t)}= .07500/.06122= 1.225. If we think of A= A(t)/A(0) as measuring how well A has "performed" and I= I(t)/I(0) as measuring how well the index has "performed", then we have A/I= 1.225 so we could say that, in some sense, A has "outperformed" the index by 22.5%. I'm not sure that is a useful "sense".

Hello gillchandler1

Welcome to Math Help Forum!

Originally Posted by gillchandler1

Suppose there is a stock (Stock A) and an index (Index A).

Stock A's price=$150
Index A's level=2450

The current ratio of Stock A/Index A Level = 150/2450 = 0.06122

Now supposing you look on the historic ratio chart and think that the ratio will increase from the current 0.06122 to say 0.07500 (ie you think stock A will outperform the index).

Just from knowing the expected ratio (0.07500) and the current ratio level (0.06122), would it be possible to calculate by how much % stock A outperformed the index by ?

Thanks a lot for all your help.

The answer is that there isn't a fixed percentage difference, but you can calculate one if you know the other.

Suppose that the stock is originally valued at $ and increases by %; and the index, valued at $ , increases by %. Then the values will increase by factors of and respectively. The ratio of the new values will then be

So if the original ratio, , was , and the new one is , we have

Re-arranging this equation gives:

which will give the value of for a given value of , enabling a comparison to be made. For example:

If (i.e. the index does not rise, ; i.e the stock rises by %.

If (i.e. the index rises by %), ; the stock rises by %, outperforming the index by %.

... and so on.

Grandad