Question

Days are business days and a month has 21 such days. All stocks pay no dividends ?

Estimate a non-dividend-paying stock’s annualized volatility (use 252 trading days) using its prices in the past nine months.

Month Stock Price per share

1    80

2    64

3    80

4    64

5    80

6 100

7    80

8    64

9    80

Then, predict the value of the stock on the 10th business day of the 10th month with approximate probability 90%.

Answer 1

steps tobe performedin excel after putting values in the spread sheet.

Step 1: Caluculate monthly return  % Change by

(previous month price - current month price) / previous month

Step 2: Calculate Standard deviation by using formula STDDEV( range select)

Step 3: Convert monthly standard deviation in daily by using rule of square , trading day each month = 252/12 =21 days

Daily Stddev = Monthly Std dev / Sqrt(21)

Step 4 .

Convert daily STDdev into annualy Stad deviation = daily stddev * Sqrt (252)

Month	Stock Price	% change
1	$80
2	$64	-20.0%		Monthly STd Dev	0.24053512
3	$80	25.0%		Daily STd Dev	0.05248907
4	$64	-20.0%		Annual Std Dev	0.83323809
5	$80	25.0%
6	$100	25.0%
7	$80	-20.0%
8	$64	-20.0%
9	$80	25.0%

2nd part of question:

The 10 th day price in 10 the month should be calculted by = monthly standard dev+ 10 * daily std dev

Month	Stock Price	% change
1	$80
2	$64	-20.0%
3	$80	25.0%
4	$64	-20.0%
5	$80	25.0%
6	$100	25.0%
7	$80	-20.0%
8	$64	-20.0%
9	$80	25.0%
10	$62	-23%

10th day of 10 month with 90% as probability = $ 62  * [ 10 * daily Stddev) * 0.90

=$ 69.12 = $69.