Douglas Johnson wrote:

- quote -

Suppose you have $100,000, and it will in ten years

grow to $1,000,000 with certainty with investment option A
grow to $2,100,000 or stay at $100,000, each with equal probability,
with option B

Option B produces a higher expected wealth of $1,100,000, which is
$100,000 higher than that of option A, but I think most people would
prefer option A, because it has lower volatility.

If two investments have the same expected returns, the one with higher
volatility has a greater probability of falling far short of
expectations.

beliavsky[at]aol.com wrote:

- quote -

My take-away from this is that arithmetic averages are very misleading (useless)
for a sequence of percentages. I learned that lesson twenty years ago -- very
painfully.

- quote -

Why? I'm not going to beat this horse any deader, but I still can't see why
volatility is a measure of my chances of reaching an investment goal (risk).

Thanks,
Doug

Douglas Johnson wrote:

- quote -

The hypothetical stock you cited has an expected daily ARITHMETIC
return of 25%, but a GEOMETRIC return of 0%. The expected ARITHMETIC
return of a portfolio of stocks depends on the weighted (by money
invested) average ARITHMETIC return of the constituent stocks.

To give a numerical example, suppose there are 1000 stocks,
uncorrelated, each with the return distribution you cited, and you buy
the same amount of each. Each day, on average, about 500 stocks will
rise 100% and 500 will fall 50%, and the portfolio return will be
(500*100% - 500*50%)/1000 = 25%. If you rebalance the stocks each day,
your return each day will be close to 25%.

The principle involved is that for a given average arithmetic return,
the expected geometric return will FALL as the volatility RISES. The
"variance drain", defined as the difference between average arithmetic
and geometric returns, is given by the formula

variance drain = 0.5*volatility^2 .

Volatility IS important to rational investors.

beliavsky[at]aol.com wrote:


- quote -

True enough. That mythical stock is a day trader's dream, which is why it can't
exist. If you'd like use buy-and-hold, imagine a stock that goes down 50% one
day, up 101% the next, then repeats.

- quote -

Eh? How can one stock have zero net return and a portfolio of such stocks have
25% daily return?

- quote -

Could you elaborate? I still don't understand. I know academic papers use
volatility as a measure of risk. I know why -- you can measure, quantify, and
get historical data on it. I don't know why I should care. How does volatility
in a stock or a portfolio of stocks (or other investments) measure my chances of
a comfortable retirement? Or meeting any other investment goal?

Thanks,
Doug

Douglas Johnson wrote:
- quote -

If stock goes down 50% on 1 day and then up 100% the next day, its
value is the same as it was 2 days ago. So if this repeats indefinitely
the stock stays at exactly the same price :-)

But I get your point.

Anoop

"raylopez99" <raylopez99[at]yahoo.com> writes:

- quote -

Actually, I think it was for the since-somewhat-discredited CAPM.

- quote -

Not quite -- *all* the people who hold any particular stock during a
particular time will experience the same return (how else could it
be?). So it's not like someone who makes a killing on a stock during
some interval will be balanced by someone who loses everything on the
same stock in the same interval. Rather, in the universe of all
securities with the same random walk parameters, most securities will
do average, few will do very well, and few will do very badly.

In other words, I think what the statement you are referring to is
really saying is that if you have an ensemble of independent
securities that each have the same random walk parameters (i.e. same
mean, variance around the mean, etc.), let that ensemble evolve over N
periods, for each of the securities in the ensemble calculate its
average return per period, and finally histogram those returns, *then*
you'll get what you said -- a distribution that is sharply peaked
around the mean return but having low, long tails.

Or, since we're assuming a random walk (which means the security is
"self-independent", to make up a term), you could compute the avg
return of Security X over N periods, write that down, compute the avg
return of X over the next N periods, write that down, rinse, lather,
repeat, and histogram that and also get the histogram you described.

--
Rich Carreiro rlcarr[at]animato.arlington.ma.us

Elizabeth Richardson wrote:

- quote -

In appreciation of your (and Joe's) sense(s) of humor, and
perspicacity: "You can observe a lot just by watching." (Yogi Berra.)
(I think he may have later rephrased that to: "It's amazing what you
can see, just by looking.")

(Joe, watch it!)

MichaelC - Thanks for the info on MS Money. Many years ago that program
didn't meet my expectations for record-keeping because it wouldn't
track options trades, and I never looked at it again - now I will. I
wonder what methodology mutual funds use - as I recall, Congress passed
some disclosure laws a few years ago specifically addressing this.

Will Trice - XIRR looks like it will give a quick answer if I use the
summary (annual) numbers I already have. Thanks. It will understate,
but will give a comparison to the weighted and unweighted numbers I
have. The 10 separate periods will help even out the "initial
investment" number - I tried several times to apply the statistical
"best fit" line (I thought the "least squares" was the equation) but
failed on the math. One gets the same problem trying to measure a
company's rate of earnings growth - if the first number is off the
growth line, it tilts that line. Statistical techniques and I have
never been best friends.

"You've got to be very careful if you don't know where you're going,
because you might not get there."

Hello-- A quick and easy way to measure risk is to use Risk Grades
(free, last I checked) website: www.riskgrades.com/

That said, this topic is very rich in theory--I believe a Dr. Sharpe
won the Nobel for work in this area ("Sharpe's Ratio"). BTW I am a
layperson who'se familiarity with this topic comes from reading popular
books by Peter Bernstein and perusing a beat-up second hand book on
finance by Bode, Marcus and Kane, so I'm no expert.

I will leave the savants of this newsgroup with this paradox, from Bode
et al:

did you know that while it is true the longer you hold a stock (or any
risky asset that observes random walk in price), the more likely the
rate of return will converge to the mean, but it is also true the more
likely SOMEBODY (not the average, mind you) will LOSE ALL THEIR MONEY
THE LONGER THEY HOLD THE STOCK?(!).

Intuitively, the curve for rate of return for the stock gets narrower
(variance decreases) over time, but the "tails" of the curve for return
get longer (both ends of the curve, so it's also true somebody will get
filthy rich over time), and therein lies the paradox. Most people
(area under the curve) will see their rate of return converge to the
mean (thus Money magazine and AAII will encourage you to hold onto a
mutual fund, correctly predicting that it will 'come back), but a FEW
unfortunates will actually LOSE MORE MONEY THE LONGER THEY HOLD THEIR
STOCK (or mutual fund, or bond mutual fund, it doesn't matter).

Maybe one in a million/billion, but it happens.

RL

Douglas Johnson wrote:
- quote -

No, it would not be, with a buy-and-hold strategy. A stock that forever
bounces between $50 and $100 would fit your description above, but the
compounded return would be zero.

A diversified portfolio of very many uncorrelated stocks, each with an
equal chance of -50% and 100% daily returns, would have average daily
returns of 25% with low volatility. This idealized case illustrates the
value of diversification across assets with low correlations.

- quote -

For distributions that are close to symmetric, volatility is highly
correlated with down-side risk.

Will Trice <wwtrice[at]paragondynamics.com> wrote:

- quote -

This may be a good time to ask about volatility as a measure of risk. I'm
increasingly uncomfortable with it. Consider a stock that goes down 50% one day
and up 100% the next and repeats this continuously. It will be highly volatile,
but not risky. In fact, it will be very, very profitable.

I know that the market will not let such a stock exist, but it illustrates my
discomfort. How does volatility measure any risk I care about?

Thanks,
Doug

anoop wrote:
- quote -

Anoop,
One thing to keep in mind with international investing is that part of
what you're buying is currency-related risks - which can work both in
your favor and against you. When the dollar falls, foreign stocks show
positive returns to US investors even if the foreign markets were flat
over the period. And vice versa, of course.

If you pick and choose among countries you can end up losing some of the
currency diversification that comes with a broader index like MSCI-EAFE.

Personally I think that it's impossible for any manager to game this,
and it's a reason I really don't like actively managed "global" stock
mutual funds. First you need to evaluate the country's equity
investments on their own merits. But that's not enough because you also
need to evaluate whether the currency exchange rates over your
anticipated holding period are going to vary enough to significantly
affect your return (your return in US dollars). So you need to make
decisions about whether, say, the Yen will fall relative to the dollar,
the Euro relative to the Yen, and the Euro relative to the dollar, and
of course all of those vs. a dozen-odd other currencies. I don't think
that's possible. I think the best you can do is choose among the
"market-driven" weightings that are typically the basis of an index
weighting. It might look to the total market cap of a country's equity
investments, or the relative size of an economy. There's some
subjectivity to this of course but I think it beats picking the "5 least
risky countries" or something like that.

-Tad

Elle wrote:
- quote -

Barclay's seems to have ETFs for a number of individual countries.
I was hoping to be able to be able to pick the more "stable" ones
rather than invest in the entire EAFE. Again, this is something I'm
just exploring.

Anoop

<beliavsky[at]aol.com> wrote
- quote -

Interesting. I registered without difficulty and immediately brought up a
graph of the EAFE going back to 1969. They call it, as well as other
countries' indices, "price indices." These are apparently mostly measures
MSCI put together, though this doesn't mean they lack meaning, especially
since MSCI apparently applies the same principles to construct each
individual country's "index." See http://www.msci.com/equity/index2.html

Elle wrote:

<snip
- quote -

A good source of historical data on foreign stock and bond indices is
the MSCI web site, http://www.msci.com/equity/index2.html . I think the
stock data is available upon free registration. MSCI publishes foreign
stock indices in both nominal (home currency) and U.S. dollar terms.
The latter is more relevant for U.S. investors.

anoop wrote:
- quote -

I suggest instead trying to find the PORTFOLIO of country ETFs that
historically had the lowest variance. This could be done using Excel
Solver after importing the price histories into Excel from Yahoo
Finance. For an individual investor, probably nonegativity (no
shorting) constraints should be imposed.

I have written before on this newsgroup about alternatives to
capitalization weighting in domestic stock indices, such as equal
weighting or fundamental (earnings, sales, dividends, or book value).
This could be applied to weighting of foreign indices, too. The global
indices such as EAFE are cap-weighted, which has the same advantages
(low turnover) and disadvantages (possible overweighting of overvalued
markets) as cap-weighted single-country stock indices. I think chapters
18 and 19 of the very good book "Investing by the Numbers" by Jarrod W.
Wilcox discuss alternative diversification strategies for foreign
stocks. In the early 1990s, the Japanese stock market was overvalued
and therefore overweighted in global indices. I've read that some
global fund managers were able to outperform the indices by
underweighting Japan.

"anoop" <ghanwani[at]gmail.com> wrote
- quote -

I don't know that those all actually exist; do you? But that may be a nit.
One can certainly go to finance.yahoo.com, for one, and look up quite easily
what I gather are the most popular global, regional indices:
http://finance.yahoo.com/intlindices?e=americas

- quote -

I will assume you have your reasons for wanting a low volatility one. Then,
just my opinion, but, sure, it makes some sense, based on certain other
assumptions. These assumptions are similar to those of most any popular
asset allocation tool, so ISTM you're not doing anything necessarily
reckless.

My only concerns would be the aforementioned caveats about "past
performance... " yada and also the statistical significance of any
correlations (which would be measures of risk) you find. I'm not sure how
much data is available on all the indices listed above at Yahoo, for
example. A dearth of data means poor statistical significance.

"Elizabeth Richardson" <erichktn[at]worldnet.att.net> wrote in message
news:clJXe.60132$qY1.43228[at]bgtnsc04-news.ops.worldnet.att.net...
- quote -

Personally, I can't think of anything else worth trying to predict.

Mike

MichaelC wrote:

- quote -

Thanks for the pointer to IFA. I have looked at their stuff before but
had kind of forgotten about it.

Anoop

Elle wrote:
- quote -

In general, I would use it for fund picking. One strategy that comes
to mind would be to look at stock indexes of all individual countries
that make up the EAFE and invest in the least volatile of them. Not
sure if it makes sense, but that's kind of what I was trying to
evaluate.

Anoop

Will Trice wrote:
- quote -

I always have a reference handy .

http://papers.ssrn.com/sol3/papers.c...ract_id=331800
Forecasting Volatility in Financial Markets: A Review (revised edition)

SER-HUANG POON
University of Manchester - Manchester Business School
CLIVE W.J. GRANGER
University of California, San Diego - Department of Economics

You can find other papers at
http://papers.ssrn.com/sol3/DisplayAbstractSearch.cfm using the
keywords "historical volatility".