I've finally gotten to the point will I would like to optimize my
portfolio using MPT.
I'm looking for some software (preferably free) that would allow me to
run what/if scenarios.
Nothing fancy, since I'm planning on investing is ~5 Vanguard Funds
(Large/Small/International/Growth/Value), but I'm curious what the
historical performance of various weightings would produce in relation
to the risk.
Any pointers would be appreciated.
IMO the assumptions necessary to such an effort will tend to
involve a high margin of error. E.g. you'll have to choose a
timeframe for the average return of each category of stocks,
and then weigh how meaningful this timeframe is. Some of
these categories also do not even offer much historical
data, so for them the statistical significance of
"historical return" and related parameters is going to be
low. For categories where data is sparse, the caveat "past
performance is no guarantee of future performance" becomes
I am sure one can buy such software, but mostly I think it
will enrich its manufacturers, not you or anyone else.
They're really selling snake oil, to a large extent, IMO.
I suggest you experiment a bit with the free online asset
allocating tools linked at
. This would be a wise choice IMO in particular because you're considering "just" the five Vanguard funds, which seem a fine set of choices to me, one which I doubt can really be beat except via luck in the future. Note the discrepancies from one tool to the next, even when using ostensibly the same set of assumptions. To me, these differences do not mean one tool is better than the next. Instead, it means that the margin of error is somewhat wide when allocating one's assets. It's a crap shoot as to how much tweaking will yield the optimum portfolio for the future.
If you have the return series, you can use Solver in Excel to compute
the historical optimal portfolio using by minimizing the portfolio
return variance subject to the constraint of the return exceeding a
target level and the portfolio allocations summing to one. I think
some web sites discuss this.
Given expected returns, volatilities, and correlations one can use the
online tool of William Sharpe (of CAPM fame) at
to find the optimalportfolio.
A programmer can use the fPortfolio package
the free R statistical program or can write a program in C++ orFortran (there are other possibilities) and use one of the publicdomain optimization codes in those languages. The inputs for portfoliooptimization are estimated with error, as noted by another poster. Awalk-forward test where portfolio weights are computed at each timestep using information known at the time can show whether portfoliooptimization is useful in a given context.
Can't help you much on the free part, but we use SunGard's Planning
Station and AllocationMaster modules. They do what you are asking. You
can enter in a real or hypothetical set of asset holdings and it will
give an expected return and std dev. The fund info is pulled from the
internet. All you need is a symbol. It also runs Monte sims. SunGard
offers a free 30-day trial to financial planners.
The software focuses on Modern Portfolio Theory, which most others
seem to neglect. Plug in the assets to be analyzed and you can see
where the porfolio lies on an efficient frontier. We usually find that
the clients portfolio doesn't even lie on the frontier, meaning that
there is a portfolio that can achieve higher expected returns for
equal risk or equal returns for less risk. Holding all other variables
constant, that's hard to argue with.
Thanks to all that answered. Sounds like it's time to break out
Solver (per Beliav)...
As Kastnna indicates above, the goal is to get on the efficient
frontier. Even though most of the big indexes have increasing
correlation recently (small/large caps & international funds), there
is enough to make it worthwhile.
It's been a few years since I did optimization (heck, it's been a few
years since I calculated correlations and volitilities, but heck,
since I believe in MPT, and am staking my financial future on it, I
better understand the magic inside the black box.
IMHO the issue is not optimization per se, but rather exploring how the
components of your portfolio interact with each other to move you towards
the efficient frontier - towards it, not on it!
The MVO software available at
is inexpensive and good to
use for this.
The REAL problem with doing this is to get historical monthly total return
data for each of the funds in your portfolio (or candidates for possible
substitution or addition to it). I have spent considerable effort doing this
over the years and now have 14 years of data on some 90+ funds I look at.
These are put together from Reuters data service as well as manual
corrections based on data as needed from fund web sites, yahoo, etc.
Emphasis on MANUAL data corrections. All the data services are good on NAV
values, usually dividends, but very poor on capital gains distributions.
That is the weakness of this approach.
A. Bruce King
A good place to look for total returns of indices, especially style
indices, is the site of
Professor Ken French,
One could test how high the correlation is between those returns and
those of comparable index funds.
The major databases of mutual fund returns used by academics are those
of CRSP and Morningstar, and there is a paper comparing their accuracy
One can get more accurate estimates of volatility and correlation
using daily rather than monthly returns, with the caveat that the
computed correlations of foreign and domestic stock funds may be
downwardly biased due to nonsynchronous trading -- adjustments can be
made to account for this.
How does using daily returns vice monthly produce "more
The only way to gage accuracy is if the actual values of
volatility and correlation are known. One can (and people
do) use statistical science to generate numbers from the
data, but the leap from economics to an assumption that
market numbers reflect science is enormous.
On Feb 22, 10:01 pm, "Elle"
Theoretically, sampling a Brownian motion at a higher frequency
more accurate estimates of its volatility.
Empirically, the study
Financial Markets, Institutions, and Instruments 6 (1), 1997.
(p53 of the PDF file)
"With regard to calculating historical volatilities from daily versus
data, the table shows that for the longest horizon, 24 months,
computing the volatility forecast
from 5 years of monthly historical data gives the most accurate
forecast, while for the 6 month
horizon, forecasts constructed from (some amount of) daily historical
data had the lowest RMSE.
At the 12 month horizon, results were mixed, with monthly beating
daily for 2 series, daily
beating monthly for one, and one tie. Again, the GARCH model performed
very well for the
S&P 500 index volatility, but not for the other series, with RMSEs
increasing sharply for longer
So if one is willing to change allocations at a frequency of every 6
months or higher, volatility estimates using daily data may work
better. Its an empirical question.
One can study whether volatilities computed using daily vs. monthly
data produce better forecasts of future volatility (which is also
measured with some error) and whether portfolios constructed using
daily volatility estimates have a better risk/return tradeoff.
Please excuse my naivete, but I was reading Bernstein's _The
Intelligent Asset Allocator_ and he writes that it's really only
possible to determine the portfolios that lay on the efficient
frontier in the past. IIRC, he goes so far as to say something along
the lines that those forecasting the efficient frontier might also be
talking with Elvis.
Given this, I assume this software helps determine if a portfolio
_was_ on the efficient frontier. Bernstein indicates that chances are
that it wouldn't have been. But how useful is looking backward for
performance? He also indicates that future efficient frontiers are
very different than those in past.
I'm probably missing something since there's obviously a market, but
why would someone use this software?
Discussing things with you is a waste of time. You are always
demanding proof of statements made by others but rarely provide
evidence for your own half-baked theories and assertions. Judging from
your comments in this newsgoup you know little about investing or
financial theory but make a lot of strong accusations ("snake oil"
salesman, "numerologists"). Professor Figlewski, the author of the
paper I cited, is a respected researcher in finance. The paper I cited
is a good introduction for someone interested in volatilty
forecasting, but it is certainly not the last word. It does not try to
"sell" anything -- don't smear him!
I have a CFA and PhD in physics, have worked as a derivatives
professional for about 10 years, and I read the major finance
journals. I have been posting to this newsgroup for some time, and
people check my history to determine my credibility. You seem to
believe there is no expertise in finance other than your own. The
newsgroup would be much better off without you.
I don't know about "demanding," but I do think that the
value of this group hinges largely upon critical examination
of posts and asking questions where things are not clear,
like my query about your claim that market behavior is
necessarily that of Brownian motion. I noticed you ignored
this point, when of course there is a meaningful discussion
that might shed more light on from where you are coming and
from where I am coming.
I don't care about credentials. Answer the questions, or
not, and be revealed in these fashions. I am actually still
surprised at your confusion over the meaning of statistical
I don't think you know my theories. Either way, ask a
question about them, and I will try to respond.
Indeed. Any thoughtful person will note this. It's the basis
for the disclaimer, "Past performance is no guarantee of the
I do think that's a fair statement to keep in the back of
OTOH, I think an understanding of economics, mass psychology
in the markets, and similar does allow one to hypothesize
meaningfully about what the future holds for stocks and
bonds. Nothing's guaranteed, but people need to plan, so we
do our best, on the assumption--outlandish or not--that
people do not change too much, so our societies won't change
much (or they change imperceptibly slowly as far as markets
are concerned, over the course of a lifetime), and there
will always be a demand for the latest gizmo or super-duper
service, which is often an offshoot of today's large
company. (So sayeth the "large value" category of investor.)
Like most things, the software isn't perfect. EF is a comparative
tool. The most common use is to compare a clients portfolio to the
efficient frontier. Of course this means that we must have both the
client's portfolio (simple to obtain) and an efficient frontier (not
simple to obtain). It also shows how other hypothetical portfolios and/
or changes to the clients portfolio will bring it closer to or farther
from the EF.
Bernstein's argument is valid but somewhat utopian (read: childish).
He suggests that because perfection cannot be reached (a truly
efficient frontier), the whole theory should be scrapped. The
software's EF is probably not perfect but if its close, and especially
if its better than the clients current holdings, then its an
improvement. And that's a good start.
A chance to improve your situation is beneficial even if it is not
In three years I have yet to see a client's portfolio that lies to the
left of the program's efficient frontier.
In article ,
I don't think that is his argument; at least that is not how I read it.
He points out that what emerges from MVO programs is highly sensitive
to the details of the current/recent volatility and correlation data.
With the consequence that from a largish universe of asset classes,
the generated points on the EF are not stable over time, even relatively
short periods of time.
His discussion may be misleading (almost necessarily so, I think, in
that it is popular in nature and does not really go into what the
optimizers do and what constraints can be placed on them). I wonder
(and do not have one around to play with to examine this) whether
these things do well if limited to a preselected smallish ( In three years I have yet to see a client's portfolio that lies to the
Well, by definition it can't be. And almost any "seat of the pants"
portfolio could probably be improved, as you suggest, by looking at
MVO optimizations, allowing consideration of (but not automatically
indulging in) substitutions of assets not considered by the client.
Bernstein certainly doesn't reject the notion of the efficient frontier;
I read him as cautioning readers not to use MVO programs uncritically.
Sorry Michael, I did a pretty poor job of clarifying myself above. I
worded it pretty poorly.
FWIW, we can plug in as many or as few asset/indexes as we choose. The
asset mix we use to simulate an efficient frontier consists of a bunch
of ETFs that attempt to approach the market portfolio as close as
possible. As you implied, the difficult part is generating a perfectly
efficient frontier that actually has a tangency to the market
portfolio. I an almost certain that our frontier is not 100%
efficient. What we have found to date, is that no one has brought us a
portfolio that is any closer. Our market portfolio was created by some
very bright minds that actually collaborated with Mr. Markowitz while
designing the software.
Keep in mind, we use MPT as a sales tool not as a scientific research
method. We don't have to be perfect (no one is), we just gotta be
better than everyone else. Our new prospect meetings hopefully go
something like this:
1. The potential client brings us a portfolio
2. We enter it into the system
3. We show the client that a more efficient portfolio can be created
using about 12 ETFs.
4. The client decreases risk without sacrificing returns.
5. We get new client, new client gets more efficient portfolio than he
had before. Everyone's happy!
How confident are you that the efficient portfolios you generate for
do better, AFTER they are constructed, than the portfolios clients
come in with?
Have you studied the level of outerpformance, in terms of Sharpe
How come you don't word this to reflect the reality of what
you're generating? E.g. "the new client gets an allocation
that, by certain historical measures, would have been more
efficient than his old allocation."
I support diversifying so as to increase returns and reduce
risk and expect your service is worth it (assuming the cost
is reasonable). But I feel a little more honesty about the
uncertainty of what the future holds is appropriate.
Especially when academics like Robert Shiller are going
around saying that, given a choice between (1) an all-stock
or (2) all-inflation "protected" bonds portfolio, he'd
choose the bonds.