Log Calculations

[Avishek]

Hi David,

In case of questions from "stock's daily volatility over a short period under continuously compounded returns", how to calculate the log using the Texas Calculator?

Is the Log table provided or the values are provided along with the questions?

Kindly advise.

Thanks, Avishek.

 

[David Harper CFA FRM]

Hi Avishek,

If a stock closed yesterday at $10 and today at $11, the continuously compounded return is LN(11/10) = about 9.5%. On the TI, keystrokes are:

11
divide
10
= (equals) (should get 1.1),
LN button (sixth button down on first column of calculator)
= .095xxx

Generically, continuous compounded return = LN (today's price/yesterday's price) = LN(S1/S0).

As a mental check, you could look at the simple return (+10%) and your continuously compounded return should be a bit lower.

Also, as a sidebar: note the e^x function that is 2nd function using the same key. Also known as exp(x). You get that by hitting (yellow) 2nd, then LN. It shares the key because it is the inverse function. x = LN(exp(x)).

So, we can practice exp() by entering:

10
x (multiply)
.095
2nd (yellow key)
LN
= (equals, should get almost 11)

That is the strokes for 11 = 10 exp(9.5%).

OR, 11/10 = exp(9.5%) and take natural log of both sides: LN(11/10) = 9.5%.

Just be aware, to calculate 9.5% here is to calculate a SINGLE PERIODIC RETURN. We need a series of periodic returns to calculate historical volatility. But (under Hull's simplification) it is not so hard: the variance is the average of the squared periodic returns. So, if the periodic returns for 3 days are x,y,z, the variance of the series is [x^2 + y^2 + z^2]/3 and take the square root of that for the (trailing) 3 day volatility.