convert volatility of log returns to dollars

classic Classic list List threaded Threaded
3 messages Options
Reply | Threaded
Open this post in threaded view
|

convert volatility of log returns to dollars

Noah Silverman
While not specifically an "R" question, I was hoping someone in the group could help with an answer. (It is finance related and I am coding in R)


I stuck on converting volatility of log returns to an absolute dollar amount.  The main question is, "How many dollars/cents is one standard deviation give our current price and volatility of returns?"


For example (x are a series of prices)
range(x)
753.0  763.5

mean(x)
758.9125

sd(x)
2.61521
# I assume that this answers my main question with "$2.62"

Now, If I take the log returns
r <- diff(log(x))
r[1] <- 0

Then calculate the SD of the returns:
sd(r)
0.001201941

This is where I'm stuck.  How can I translate the 0.001201941 into the correct monetary value?  (Which I assume is $2.62)

Thanks!

-N




Hi,

I'm a bit confused on how to convert a garch of log returns into a dollar value.

My understanding is that garch will give us the volatility. The square root of that is the standard deviation. But just multiplying the SD times the price does not appear to produce the correct values. (They seem too large.)

To make is simpler, if I have 100 prices and first calculate the log returns:



then calculate the volatility:


I have the volatility of the log returns. How can I convert that back to a physical dollar value. I want to answer the question, "How many dollars/cents is one standard deviation given the current price and volatility of returns."

Thanks!




--
Noah Silverman
UCLA Department of Statistics
8117 Math Sciences Building
Los Angeles, CA 90095


        [[alternative HTML version deleted]]

_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-finance
-- Subscriber-posting only. If you want to post, subscribe first.
-- Also note that this is not the r-help list where general R questions should go.
Reply | Threaded
Open this post in threaded view
|

Re: convert volatility of log returns to dollars

Patrick Burns-2
Noah,

Actually I think it is about 91 cents.

r = log(P1/P0)

so:

P1 = P0 * exp(r)

and the difference is:

P0 * exp(r) - P0 = P0 * (exp(r) - 1)

I think you really want to put in the
current value of the portfolio rather
than the average.

I'm surprised by the size of the difference
in the two answers, but I don't see how
my answer isn't right.

The standard deviation of the prices is
the wrong thing but I can't currently see
just how wrong.  At least part of the
answer is the autocorrelation of the
prices.  This is related to the blog post:
http://www.portfolioprobe.com/2011/01/12/the-number-1-novice-quant-mistake/

Pat


On 20/07/2011 19:05, Noah Silverman wrote:

> While not specifically an "R" question, I was hoping someone in the group could help with an answer. (It is finance related and I am coding in R)
>
>
> I stuck on converting volatility of log returns to an absolute dollar amount.  The main question is, "How many dollars/cents is one standard deviation give our current price and volatility of returns?"
>
>
> For example (x are a series of prices)
> range(x)
> 753.0  763.5
>
> mean(x)
> 758.9125
>
> sd(x)
> 2.61521
> # I assume that this answers my main question with "$2.62"
>
> Now, If I take the log returns
> r<- diff(log(x))
> r[1]<- 0
>
> Then calculate the SD of the returns:
> sd(r)
> 0.001201941
>
> This is where I'm stuck.  How can I translate the 0.001201941 into the correct monetary value?  (Which I assume is $2.62)
>
> Thanks!
>
> -N
>
>
>
>
> Hi,
>
> I'm a bit confused on how to convert a garch of log returns into a dollar value.
>
> My understanding is that garch will give us the volatility. The square root of that is the standard deviation. But just multiplying the SD times the price does not appear to produce the correct values. (They seem too large.)
>
> To make is simpler, if I have 100 prices and first calculate the log returns:
>
>
>
> then calculate the volatility:
>
>
> I have the volatility of the log returns. How can I convert that back to a physical dollar value. I want to answer the question, "How many dollars/cents is one standard deviation given the current price and volatility of returns."
>
> Thanks!
>
>
>
>
> --
> Noah Silverman
> UCLA Department of Statistics
> 8117 Math Sciences Building
> Los Angeles, CA 90095
>
>
> [[alternative HTML version deleted]]
>
> _______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-finance
> -- Subscriber-posting only. If you want to post, subscribe first.
> -- Also note that this is not the r-help list where general R questions should go.
>

--
Patrick Burns
[hidden email]
http://www.burns-stat.com
http://www.portfolioprobe.com/blog
twitter: @portfolioprobe

_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-finance
-- Subscriber-posting only. If you want to post, subscribe first.
-- Also note that this is not the r-help list where general R questions should go.
Reply | Threaded
Open this post in threaded view
|

Re: convert volatility of log returns to dollars

Noah Silverman
Pat,

Thanks for the reply.

I believe that to estimate the dollar value of the standard deviation, the formula would be:

with r the volatility (through garch, sum of squared logged returns, etc.)

(1 - exp(r)) * Price


Of course this isn't "correct", as we can never know the true volatility, but only an estimate baed on historical returns.  But the boss asked me yesterday for this and I want to give him an answer that is as reasonable as possible.

Thanks,


--
Noah Silverman
UCLA Department of Statistics
8117 Math Sciences Building
Los Angeles, CA 90095

On Jul 20, 2011, at 11:27 AM, Patrick Burns wrote:

> Noah,
>
> Actually I think it is about 91 cents.
>
> r = log(P1/P0)
>
> so:
>
> P1 = P0 * exp(r)
>
> and the difference is:
>
> P0 * exp(r) - P0 = P0 * (exp(r) - 1)
>
> I think you really want to put in the
> current value of the portfolio rather
> than the average.
>
> I'm surprised by the size of the difference
> in the two answers, but I don't see how
> my answer isn't right.
>
> The standard deviation of the prices is
> the wrong thing but I can't currently see
> just how wrong.  At least part of the
> answer is the autocorrelation of the
> prices.  This is related to the blog post:
> http://www.portfolioprobe.com/2011/01/12/the-number-1-novice-quant-mistake/
>
> Pat
>
>
> On 20/07/2011 19:05, Noah Silverman wrote:
>> While not specifically an "R" question, I was hoping someone in the group could help with an answer. (It is finance related and I am coding in R)
>>
>>
>> I stuck on converting volatility of log returns to an absolute dollar amount.  The main question is, "How many dollars/cents is one standard deviation give our current price and volatility of returns?"
>>
>>
>> For example (x are a series of prices)
>> range(x)
>> 753.0  763.5
>>
>> mean(x)
>> 758.9125
>>
>> sd(x)
>> 2.61521
>> # I assume that this answers my main question with "$2.62"
>>
>> Now, If I take the log returns
>> r<- diff(log(x))
>> r[1]<- 0
>>
>> Then calculate the SD of the returns:
>> sd(r)
>> 0.001201941
>>
>> This is where I'm stuck.  How can I translate the 0.001201941 into the correct monetary value?  (Which I assume is $2.62)
>>
>> Thanks!
>>
>> -N
>>
>>
>>
>>
>> Hi,
>>
>> I'm a bit confused on how to convert a garch of log returns into a dollar value.
>>
>> My understanding is that garch will give us the volatility. The square root of that is the standard deviation. But just multiplying the SD times the price does not appear to produce the correct values. (They seem too large.)
>>
>> To make is simpler, if I have 100 prices and first calculate the log returns:
>>
>>
>>
>> then calculate the volatility:
>>
>>
>> I have the volatility of the log returns. How can I convert that back to a physical dollar value. I want to answer the question, "How many dollars/cents is one standard deviation given the current price and volatility of returns."
>>
>> Thanks!
>>
>>
>>
>>
>> --
>> Noah Silverman
>> UCLA Department of Statistics
>> 8117 Math Sciences Building
>> Los Angeles, CA 90095
>>
>>
>> [[alternative HTML version deleted]]
>>
>> _______________________________________________
>> [hidden email] mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-sig-finance
>> -- Subscriber-posting only. If you want to post, subscribe first.
>> -- Also note that this is not the r-help list where general R questions should go.
>>
>
> --
> Patrick Burns
> [hidden email]
> http://www.burns-stat.com
> http://www.portfolioprobe.com/blog
> twitter: @portfolioprobe

_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-finance
-- Subscriber-posting only. If you want to post, subscribe first.
-- Also note that this is not the r-help list where general R questions should go.