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Posted by Will Trice on September 22, 2006, 6:46 pm
Elle wrote:
> Go to the custom setting. Manually put in the fixed bond's
> settings of 6% return and 7% standard deviation. Compare in
> a second window to the bond setting, using 5 years and 20
> years. This software is extrapolating somehow from the
> short-term volatilities and not indicating long term SDs
> derived from historical data. All it is demonstrating is a
> reversion to the mean with enough 'rolls of the dice' ( =
> years of stock or bond returns), which is what one would
> expect from a Monte Carlo simulation.
Not sure I follow you here. I used the custom setting as you suggest
above, and not surprisingly, it gives more-or-less the same answer.
As to reversion to the mean, this is what you would expect over the long
term. Why do you think SDs get narrower over long time periods?
-Will
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Posted by Elle on September 23, 2006, 6:16 am
Re the site
http://www.moneychimp.com/articles/risk/longterm.htm and
long term volatilities of stocks and bonds
> Not sure I follow you here. I used the custom setting as
> you suggest above, and not surprisingly, it gives
> more-or-less the same answer.
Right, not exactly the same, because the Monte Carlo trials
vary somewhat on each run. All the software is doing, I bet,
is dividing the SD for the short periods by sqrt(long
period/short period) and generating the random distribution
of the same using MC trials. The software assumes, somewhat
misleadingly, that stock and bond returns comport to a
random distribution. The result is that the site above is
contrived and says nothing about whether the actual long
term volatility of bonds is below that of stocks.
Regardless, my "tunnel vision" post of a day or so ago
offers an explanation of why the relation between stock and
bonds' long term volatilities is probably moot and so one
cannot easily find anything credible and truly dispositive
on either your claim or my claim.
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Posted by Will Trice on September 23, 2006, 11:49 am
Elle wrote:
> Right, not exactly the same, because the Monte Carlo trials
> vary somewhat on each run. All the software is doing, I bet,
> is dividing the SD for the short periods by sqrt(long
> period/short period) and generating the random distribution
> of the same using MC trials.
If this were true then it would not be a Monte Carlo simulator.
Instead, each pass will take n random draws against a Gaussian
distribution for the n year simulation, each draw using the input
average and standard deviation (i.e. the single year arithmetic average
and the standard deviation of that average). It will then calculate the
total return using all the draws and dump the result in one of the
histogram bins on the chart. Rinse, repeat. After many passes like
this the histogram chart will fill out (that's why you see it grow). No
need to divide by the square-root of anything, although doing this would
avoid having to use the Monte Carlo simulator.
> The software assumes, somewhat
> misleadingly, that stock and bond returns comport to a
> random distribution.
Well, they do. It just may not be Gaussian, or known, or stable. If
you recall from a thread a while back, I'm a big proponent of not using
Gaussian distributions when modelling short-term returns. But even the
biggest fat-tail distribution guru admits that, long-term, the
distributions of asset returns gets to be pretty darn Gaussian. And
even short-term, Gaussian distributions are useful for gross modelling.
> The result is that the site above is
> contrived and says nothing about whether the actual long
> term volatility of bonds is below that of stocks.
In an earlier post I showed results from actual data that this is indeed
the case.
>
> Regardless, my "tunnel vision" post of a day or so ago
> offers an explanation of why the relation between stock and
> bonds' long term volatilities is probably moot and so one
> cannot easily find anything credible and truly dispositive
> on either your claim or my claim.
Sorry, I don't know which post you're referring to, but why don't you
believe the published data that you cited? Namely, the Campbell paper,
"Strategic Asset Allocation". He talks about actual data in the
second-to-last paragraph on page 6.
-Will
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Posted by Elle on September 23, 2006, 1:53 pm
> Elle wrote:
> > All the software is doing, I bet, is dividing the SD for
> > the short periods by sqrt(long period/short period) and
> > generating the random distribution of the same using MC
> > trials.
>
> If this were true then it would not be a Monte Carlo
> simulator. Instead, each pass will take n random draws
> against a Gaussian distribution for the n year simulation,
> each draw using the input average and standard deviation
> (i.e. the single year arithmetic average and the standard
> deviation of that average).
I am proposing that it is using the SD computed as I
describe above. This is not an SD derived from historical
data.
snip stuff with which I do not necessarily agree.
>> The result is that the site above is contrived and says
>> nothing about whether the actual long term volatility of
>> bonds is below that of stocks.
>
> In an earlier post I showed results from actual data that
> this is indeed the case.
You suggested some evidence exists for this to be the case
for long bonds. Please try to be complete and fair. Also, do
not assume this means I insist anything about shorter
maturity bonds. Too often IMO you're trying to force me into
defending a view that I never embraced fully. This is an
exploration. Also, only in the last half-day or so have you
offered to produce any citations of your own. To do a full
analysis would ultimately, in my experience, test the
moderators' patience, meaning there is no assurance that
submissions will be posted. Though any resentment on their
part in such instances is generally understandable. All
things considered, I do not have incentive to continue.
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Posted by Will Trice on September 26, 2006, 2:50 am
Elle wrote:
> I am proposing that it is using the SD computed as I
> describe above. This is not an SD derived from historical
> data.
So you object to the initial conditions under the "bond" setting?
(Perhaps it is a bit of a coincidence that the standard deviation is
007%...) Set the standard deviation to whatever your heart desires. If
it is less than the standard deviation for stocks, the result will be
the same, the long term standard deviation for bonds will be less than
that for stocks (though as they get real close, this will be hard to
discern)
-Will
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