Re: expected stock price/volatility question
- From: elodie.gillain@xxxxxxxxx
- Date: Fri, 09 Nov 2007 06:14:37 -0800
On Nov 8, 9:15 pm, Ray Vickson <C6...@xxxxxxx> wrote:
On Nov 8, 4:33 pm, elodie.gill...@xxxxxxxxx wrote:
On Nov 8, 6:30 pm, elodie.gill...@xxxxxxxxx wrote:
On Nov 8, 4:35 pm, Ray Vickson <C6...@xxxxxxx> wrote:
On Nov 8, 6:56 am, elodie.gill...@xxxxxxxxx wrote:
Dear Forum,
I would need some help answering the following questions.
Suppose that a stock price has an expected return of 16% per annum and
a volatility of 30% per annum.
Assuming that daily stock price changes are independent and
identically distributed (a BIG assumption, that finance scholars argue
about), we then have to worry about whether changes are additive or
multiplicative. Assuming additivity, the expected daily change is 30%/
365 (if there are 365 working days in a working year---otherwise,
change the divisor). If v is the daily variance, the annual variance
is 356*v, so the annual standard deviation is sqrt(365)*sqrt(v), and
this equals 0.30 (30%). So, you can find the daily standard deviation,
sqrt(v) = 30%/sqrt(365).
R.G. Vickson
When the stock price at the end of a
certain day is $50, calculate the following:
a.The expected stock price at the end of the next day.
I guess that I need to convert the 16% annual return into a daily
return. I think that I need to use a square root of time coefficient.
I am confused.
b.The standard deviation of the stock price at the end of the next
day.
That is 30%, right?
No.
c.The 95% confidence limits for the stock price at the end of the next
day.
I can do that when I have an answer for question a.
I greatly appreciate your help.
many thanks. I appreciate your help.
I think I understand. The daily change in stock price is distributed
normally N(return, volatility). So if the daily change is iid, then
one just adds the daily returns and volatilities, and one obtains the
annual change in stock price.
Exactly, although that depends on whether volatility means variance or
standard deviation. Variances add but standard deviations do not---
hence the square root of 365 in the previous calculation. However, if
the price changes are lognormally distributed, one should replace sums
by products, so instead of talking about the $ price increase or
decrease in a day/week/month/year, one should speak of the percentage
increase or decrease. Instead of dividing by 365 we should take the
365th root, etc.
R.G. Vickson
Hello and thanks again for your help.
I would be grateful if you could indicate a reference for that
material.
I greatly appreciate your help.
.
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