Modern Portfolio Theory

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ngutman
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Modern Portfolio Theory

Post by ngutman »

Is anyone here dabbling with Harry Markowitz's Modern Portfolio Theory for portfolio optimization/design?
Thanks, Nathan
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Re: Modern Portfolio Theory

Post by dharrythomas »

In the past there were a number of posts about portfolio optimization. People building spreadsheets and models. I haven't seen any discussions recently.

The problem is the the correlations between asset classes change over time and the markets tend to move together when things head South. Optimizers are good for telling you what you should have done in the past, not as accurate at telling you where to go now.

Good Luck

Harry
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Kevin M
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Re: Modern Portfolio Theory

Post by Kevin M »

A lot of what some of us do is based on Portfolio Theory. MPT is the academic justification for owning a lot of stocks or bonds, and index funds happen to be the most efficient way to do that. Ditto for trying to include assets with low correlations in one's portfolio.

There are several Wiki articles on this topic (search for "risk" and "return" as well as MPT). The concept of quantifying risk and expected return was one of the major contributions of Markowitz in his 1952 paper on portfolio theory. Of course academics have punched bunches of holes in MPT (and CAPM, etc.) over the years, but I think it still serves as a useful foundation for thinking about markets.

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Re: Modern Portfolio Theory

Post by nisiprius »

I have a lay understanding of it, but after brooding on it for a while I've decided not to fuss about it beyond the basic idea of its being a really good idea to hold both some stocks and some bonds. Here's my snarky, simplistic, know-nothing dismissal of it. Oh, before I get to that, have you read Mandelbrot and Hudson, The Misbehavior of Markets: A Fractal View of Financial Turbulence? Read it! It's funny, books on investing mention Markowitz and modern portfolio theory about twenty times as often as they mention Mandelbrot, and it's not because Mandelbrot has been discredited, it's because Mandelbrot is so nihilistic.

MPT in one sense is just math. It is unarguable that IF assets #1 and #2 have returns M1 and M2, standard deviations S1 and S2, and correlation R, THEN a chart of return versus standard deviation for mixtures of 1 and 2 will trace a hyperbola. The line from the riskless asset that's tangent to the hyperbola defines the "best" proportions for mixing 1 and 2 (best by one criterion anyway). Call that mix M.

Now, decide what level of risk you want to take. If it's less than the risk of M, tame it by mixing in the riskless asset. If it's greater than the risk of M, leverage it. These mixes of M with the riskless asset are better than mixing 1 and 2 in any other proportion, and (usually) better than either 1 or 2 by itself. Free lunch!

Here's why I don't fuss with it. Reason A and Reason B.

Big reason A. "If we had ham, we could have ham and eggs, if we had some eggs." The ham is the return and standard deviation of A, the eggs are the return and standard deviation of B, and, uh, uh, uh, correlation, yeah, correlation is the ketchup. Well, we only have those for the past. For the past, it's math. For the future, it depends on the assumption that we know those MPT parameters going forward. And yet we are all familiar with the fact that even something as basic as past performance, i.e. return, is a weak predictor of future performance. Even with 80 years of stock market data, you can get a difference of almost 1% simply in the value of the "historical" rate of return if you change the starting date by just a couple of years. Just the historical value! Not even speaking about the future.

And the other parameters are worse. It takes more data to estimate standard deviation accurately. And it takes far more to estimate correlations accurately. Financial types measure them anyway, but they are proverbially unstable.

If we had ham, we could have ham and eggs, if we had some eggs, but we don't have ham and we don't have eggs. (The eggs are like those in "A Space Child's Mother Goose:" "Possible-probable, my black hen/She lays eggs in the Relative When/She doesn't lay eggs in the Positive Now/Because she's unable to postulate how.")

This means that in real life those MPT hyperbolas don't hold still, they squirm around like crazy. John C. Bogle gives this example in Common Sense on Mutual Funds, 10th Anniversary Edition:

Image

So, MPT devotees simply substitute "chasing correlations" for "chasing performance."

So, that was the big reason A. Modern portfolio theory predicts behavior of portfolios if you know the behavior of each component, in terms of mean, standard deviation, and cross-correlations. But you don't, in fact, know what the behavior of each component will be, so it's garbage in, garbage out.

Reason B: in real life, it's not usually a free lunch, just at best a free snack. if you actually do the math instead of just talking about "reducing risk," it isn't a very powerful or robust effect unless certain rather stringent conditions are met, which are rarely found in real-world asset pairs. It isn't good enough for them just to have a correlation of less than 1.00, and the reasoning that "any correlation that isn't 1.00 must be helping at least a little bit" is misleading. The effect is only powerful if assets 1 and 2 have reasonably similar return AND reasonably similar volatility/standard deviation/risk AND a really low correlation. It's not clear that there are any known asset pairs that display this robustly over long periods of time except stocks and long-term bonds.

If asset 2 has low return, then it drags down overall portfolio return so much that it's hard for anything else it does to help.

If asset 2 has low volatility, then even during those golden moments when 1 zigs and 2 zags, 1 zigs a lot and 2 zags just a little, so it helps, but it doesn't help much.

If assets 1 and 2 don't have seriously low correlation, then the effect is weak. Notice that even if they have zero correlation, that does NOT mean "when 1 zigs, 2 tends to zag." What zero correlation means is that "when 1 zigs, 2 sometimes zigs and sometimes zags; when 1 zags, 2 sometimes zigs and sometimes zags." That's actually fairly powerful but it's not at all what some people seem to think.

Something like 0.66 (the correlation between U. S. and international) means something like "they mostly zig and zag at the same time, just by different amounts."

If you really had a good robust persistent NEGATIVE correlation between two assets, that arose out of the assets natural behavior and not a synthetic result of leverage or derivatives, that would be investing magic and would work wonders--like having an asset with no real return nevertheless improve a portfolio--but I don't think any such pairs really exist.
Last edited by nisiprius on Sat Jun 15, 2013 5:25 pm, edited 3 times in total.
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Re: Modern Portfolio Theory

Post by nedsaid »

Wow, Nisiprius you have articulated well what I have tried (and failed) to say in many posts.

The engineering and math geeks on this forum too often see investing as an algebra equation, a physics formula, an algorithm. Plug and chug. Investing doesn't work that way because it is so behavioral. Mr. Bogle said it best when he said that the market is not an actuarial table.

I am all in favor of the math, the charts and graphs, efficient frontiers, the Monte Carlo simulations, etc. etc. It greatly helps illustrate market behavior in the past, why the market behaved that way, and give us some idea what the markets might do in the future. It is just that I realize that these approaches have their limitations.

This is why I expressed skepticism about mechanical investment strategies, there were some posters that bashed my points pretty hard. Pretty much what you did was what the dog Toto did in the Wizard of Oz and pulled back the curtain. It turned out the great Oz wasn't so great after all. All the numbers and calcutions just obscure the fact that all of this is based on well educated guesswork and folks fly by the seat of the pants more than they admit to. We all SWAG (Scientific Wild Ass Guess) things a bit but those of us that are more numbers and quant gifted can obscure it more than I can. I invest some "by feel" and make some educated guesses and now I realize that others do the same.

So the math, charts, graphs, models, etc. are all very helpful. I pay attention to the quants and listen to the guys like Swedroe. I just realize that all of this has limitations.
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Re: Modern Portfolio Theory

Post by magician »

nisiprius wrote:The line from the riskless asset that's tangent to the hyperbola defines the best proportions for mixing 1 and 2.
True if the highest Sharpe ratio is the proper measure of "best". That isn't universally true.
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Re: Modern Portfolio Theory

Post by nisiprius »

OK, I revised it to 'defines the "best" proportions for mixing 1 and 2 (best by one criterion anyway).' I wondered whether I could wiggle enough just by putting the word best in quotes.
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Re: Modern Portfolio Theory

Post by magician »

nisiprius wrote:OK, I revised it to 'defines the "best" proportions for mixing 1 and 2 (best by one criterion anyway).'
OK.
nisiprius wrote:I wondered whether I could wiggle enough just by putting the word best in quotes.
It was a valiant effort, I'll grant you.
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Re: Modern Portfolio Theory

Post by Frengo »

nisiprius wrote: Something like 0.66 (the correlation between U. S. and international) means something like "they mostly zig and zag at the same time, just by different amounts."
It actually means when A zags it is more probable that B zags too.
The relative amounts of zag depends on the beta.
The effect is only powerful if assets 1 and 2 have reasonably similar return AND reasonably similar volatility/standard deviation/risk AND a really low correlation. It's not clear that there are any known asset pairs that display this robustly over long periods of time except stocks and long-term bonds.


If they don't you can simply load up on the asset with lower volatility to compensate.
For instance, if bonds have 1/3 of the stocks volatility, you would have a portfolio with 3 parts of bonds and 1 of stocks.
This would minimize the overall volatility, given that the two assets partial (actually, versy small) correlation.
The problem is that bonds have a lower expected return, therefore doing so also lowers your portfolio expected return much more than if you simply went half and half.
The two things are correlated: Bonds lower expected return is due to their lower volatility, as the MPT expects.
If you really had a good robust persistent NEGATIVE correlation between two assets
You have it: long and short are perfectly anti correlated. Unfortunately the expected return of short is negative :happy
Last edited by Frengo on Sat Jun 15, 2013 7:19 pm, edited 1 time in total.
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Re: Modern Portfolio Theory

Post by Call_Me_Op »

We all use MPT. I'll summarize it for you here: diversify and rebalance.
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Re: Modern Portfolio Theory

Post by staythecourse »

Like ANYTHING that is put out by academics(not just in finance) the concept is what is important and NOT the specifics. The problem is MVO (just like that seen in medical articles) are that they are so specific and well designed they usually only work in a very SPECIFIC environment created by academic and not easy to replicate in real life.

The concept is no different then "don't put all your eggs in one basket". I do think that is an important concept as it (in my opinion) is the cause of most folks answer to "What is your biggest financial mistake" question. Folks take on either too much company risk, too much market risk, etc., etc...

The more I learn about investing the less I care about data, i.e. returns, S.D., covariance, correlation, etc...

I am starting to think the BEST level of diversification in finance comes from looking at your portfolio as how diversified is your income streams, i.e. labor income, dividends from stocks, bond interest, SS, pension, rental income, etc...

Good luck.
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Re: Modern Portfolio Theory

Post by Frengo »

staythecourse wrote: The more I learn about investing the less I care about data, i.e. returns, S.D., covariance, correlation, etc...
It is certainly true that an excessive mathematical sophistication in finance only allows one to make large errors with great accuracy, but you are taking the concept a little too far :)
If you reason in terms "this correlation is 0.57, if such and such happens it could go down to 0.43, therefore I going to..." that's quite dangerous. But the fact that HY returns are partially correlated to the stock market, let's say something around 0.3÷0.6, while treasuries and IG corporate are more or less uncorrelated, let's say -0.1÷0.1 it ain't exactly rocket science.
I am starting to think the BEST level of diversification in finance comes from looking at your portfolio as how diversified is your income streams, i.e. labor income, dividends from stocks, bond interest, SS, pension, rental income, etc...
Actually, labor income is not a financial asset, but if you are reasoning from an holistic point of view, that's right.
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Re: Modern Portfolio Theory

Post by Kevin M »

One valuable concept I took away from portfolio theory is the use of a (relatively) riskless asset in portfolio construction. That is rarely discussed here. People focus mostly on stock funds and bond funds, not on cash. That continues to puzzle me, but I know John Bogle has said that cash is not an investment, it's savings. I disagree. Maybe that is often the case, but not now. If I can earn 1% on cash and less than 1% on a short-term bond fund, then I see cash as the superior investment.

I view (non-brokered) CDs as somewhere between cash and bonds. They are not marketable, so they neither zig nor zag, thus the correlation with any risky asset is pretty much 0, which is what you're looking for in a riskless asset (it's pretty much the definition of a riskless asset in portfolio theory). There is an early withdrawal penalty, so there is some limited interest-rate risk--more than cash, but less than bonds, perhaps much less, depending on duration.

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Re: Modern Portfolio Theory

Post by Frengo »

cash is bonds, and CD's are too.
Pie charts come out prettier in 3 colors and that's why some people separate them.
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Re: Modern Portfolio Theory

Post by pkcrafter »

Frengo wrote:cash is bonds, and CD's are too.
Pie charts come out prettier in 3 colors and that's why some people separate them.
Bonds are not cash. There are three generally recognized distinct asset classes--stocks, bonds, cash.


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Re: Modern Portfolio Theory

Post by Frengo »

Who recognizes them ?

There are only two financial investment classes:
Lend your money
Give your money away in exchange of a share of property.

A $100 bill is just a bond issued at face value, paying zero interest, and with zero residual maturity. Its credit quality is the highest of all.
Last edited by Frengo on Sun Jun 16, 2013 12:19 am, edited 1 time in total.
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Re: Modern Portfolio Theory

Post by magician »

pkcrafter wrote:
Frengo wrote:cash is bonds, and CD's are too.
Pie charts come out prettier in 3 colors and that's why some people separate them.
Bonds are not cash. There are three generally recognized distinct asset classes--stocks, bonds, cash.

Paul
Cash is just a zero-duration bond.
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Re: Modern Portfolio Theory

Post by magician »

Frengo wrote:. . . let's say something around 0.3÷0.6, while treasuries and IG corporate are more or less uncorrelated, let's say -0.1÷0.1 . . . .
Are those supposed to be division signs? That would be distinctly odd.

Dashes, on the other hand, would make some sense.

(As a former rocket scientist, I like to keep these things straight.)
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Re: Modern Portfolio Theory

Post by Frengo »

magician wrote: Are those supposed to be division signs? That would be distinctly odd.
It would and they are not.
Dashes, on the other hand, would make some sense.
Sorry! I thought that as a former rocket scientist you would have confused them with subtraction signs. :^p
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Re: Modern Portfolio Theory

Post by Kevin M »

Frengo wrote:cash is bonds, and CD's are too.
Pie charts come out prettier in 3 colors and that's why some people separate them.
I agree and disagree.

I agree with the idea that cash is a zero duration bond. There is a continuum of duration/maturity, so where do you draw the line between cash and bonds? In my investment textbooks, the term "cash" isn't used. There is a differentiation between "money markets" and "capital markets", the distinction typically being about 1-year maturity.

In portfolio theory, I believe 30-day treasuries are the most common proxy for a riskless asset. Again, as I recall, the term cash is not used. The key point is that with a 30-day maturity, there is little uncertainty in the value of the asset over a short time period, and there is essentially zero correlation with risky assets (stocks and bonds). For practical purposes, money market funds and savings accounts are reasonable proxies for the riskless asset, since there is no interest-rate risk.

I completely disagree that non-brokered CDs are bonds. You can call them that, but I think it is a disservice to those trying to understand the different risk characteristics. It is a wonderful thing to call them that for those who are trying to obscure the differences. Vanguard has many bond funds; they don't have a CD fund (other than the CDs that may be owned in a money market fund). The downside of a non-brokered CD is limited to the EWP; there is no such put option for any of the bond funds I know of. As long as this is crystal clear, call CDs whatever you want.

The 3-color chart comment is just facile, and shows a complete lack of understanding of portfolio theory (which is what this thread is about). The introduction of the concept of the riskless asset was considered a significant step forward in the theory of portfolio construction. Markowitz did not include it in his original work; it was introduced as part of CAPM by Sharpe et al.

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Re: Modern Portfolio Theory

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Kevin M wrote: I completely disagree that non-brokered CDs are bonds. You can call them that, but I think it is a disservice to those trying to understand the different risk characteristics. It is a wonderful thing to call them that for those who are trying to obscure the differences. Vanguard has many bond funds; they don't have a CD fund (other than the CDs that may be owned in a money market fund). The downside of a non-brokered CD is limited to the EWP; there is no such put option for any of the bond funds I know of. As long as this is crystal clear, call CDs whatever you want.
Guess the Treasury is grossly mistaken in naming their Savings Bonds...

It all comes to understand that either you lend your money, or you use it to buy property shares of something.
If you choose to lend, there are countless different terms available: fixed coupon, variable coupon, no coupon, fixed maturity, variable maturity, insured capital, marketable, non marketable, etc.
Each peculiar characteristic of a given bond influences its risk, but all the risk for bonds is just non-payment of the stipulated sum at the stipulated time. Pluse inflation, if you want to reason in real terms. You can understand that CD's have the same typology of risk as a 30-year TIPS, if you reason in nominal terms.
On the other hand, stocks come with a much more complex array of risks and that's why they are so much more difficult to price.
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Re: Modern Portfolio Theory

Post by Kevin M »

Frengo, I don't disagree that equity and debt are the top-level distinctions between broad asset classes, and that cash, bonds and CDs are all debt. I just think it's useful to use standard terminology to distinguish between sub-asset classes. I would never tell someone I bought a bond from a bank when I actually bought a CD; it's just confusing.

The cap on downside interest-rate risk of a non-brokered CD with an early withdrawal option is a huge differentiater relative to bonds, and I think it's really useful for folks to understand that.

But this is really drifting from the main topic of this thread, which is MPT. Again, In MPT there is a clear distinction between "the riskless asset", typically a 30-day T-bill, and the risky asset classes of stocks and bonds. You may not agree with it or like it or think it makes sense, but it is what it is.

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Re: Modern Portfolio Theory

Post by Erwin »

ngutman wrote:Is anyone here dabbling with Harry Markowitz's Modern Portfolio Theory for portfolio optimization/design?
Thanks, Nathan
In order to use Markowitz's optimization model (efficient frontier), you need to know the future standard deviations and returns of each of the investment instruments (stocks, bonds, etc.). That is a big guessing game which gets complicated because if you have played with the model, you will realize rather quickly that the results, meaning the optimal allocation, is extremely sensitive to the input data (i.e., from zero allocation to a big number), so that you run the risk of garbage in, garbage out problem. Further, returns, and to a lesser degree, standard deviations are highly dynamic, so the numbers you may have used one day become irrelevant rather quickly.
Investment companies tried to use this idea in the seventies, but gave up for the reasons described above.
Thus, it has become an academic tool for research purposes.

If you want to discuss this issue further, contact me and I can explain in more detail.
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Re: Modern Portfolio Theory

Post by Frengo »

Kevin, Savings Bonds have the word "bonds" in their name and work more or less like CD's: non-marketable, with a prepayment penalty. I think calling them "bonds" is not such a stretch, or source of confusion.

As far as MPT is concerned, riskless assets are simply a convenient reference mark. We could rewrite the entire theory using 10-year Notes as a reference of risk, which would be more cumbersome but nothing substantial would change.
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Re: Modern Portfolio Theory

Post by Kevin M »

Frengo wrote:Kevin, Savings Bonds have the word "bonds" in their name and work more or less like CD's: non-marketable, with a prepayment penalty. I think calling them "bonds" is not such a stretch, or source of confusion.
Well, I also consider "savings bonds" quite different from "bonds" (unqualified); again, Vanguard does not have a savings bond fund. I also consider Series I Savings Bonds quite different than Series EE Savings Bonds (I max out my annual allotment to the former, but have no interest in the latter). That's probably why most people here talk about "I Bonds", not "Savings Bonds". But have it your way; call CDs bonds if you want. I will not.
Frengo wrote:As far as MPT is concerned, riskless assets are simply a convenient reference mark. We could rewrite the entire theory using 10-year Notes as a reference of risk, which would be more cumbersome but nothing substantial would change.
A riskless asset is not just a convenient reference mark. It is an asset that has zero correlation to the portfolio of risky assets; this is the critical distinction in portfolio theory.

But you are right in a sense. The riskless asset depends on holding period and unit of account. If your holding period is 10 years and your unit of account is nominal dollars, then a 10-year treasury is the riskless asset. My problem with that is that there is way too much inflation risk over a 10-year period, and I'm concerned with real dollars. There is very little unexpected inflation risk over a 30-day period. So in my portfolio I consider the riskless asset to be something with no credit risk and little to no interest-rate risk--something I can convert to cash relatively quickly with little to no loss of principal. A 10-year treasury does not meet the latter criterion; a savings account certainly does, and a non-brokered CD with decent early withdrawal terms comes close enough for me.

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Re: Modern Portfolio Theory

Post by Frengo »

Kevin M wrote: A riskless asset is not just a convenient reference mark. It is an asset that has zero correlation to the portfolio of risky assets; this is the critical distinction in portfolio theory.
Actually, it's distinction is that it has zero volatility. You can easily find uncorrelated risky assets.
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Re: Modern Portfolio Theory

Post by YDNAL »

ngutman wrote:Is anyone here dabbling with Harry Markowitz's Modern Portfolio Theory for portfolio optimization/design?
Thanks, Nathan
Here is what I think in a couple of quick observations:

1. MPT's central tenet - that diversification mitigates portfolio risk - collapsed in 2008 when all asset classes were mauled. Treasuries provided a haven, but according to MPT, Treasuries don’t even count - they’re just the risk-free baseline at the bottom of the return axis. Conversely, during the technology boom of the late 1990s when “risk” was a dirty word, MPT also failed in the real world. What sense does it make to diversify out of an asset class that’s returning 30%?... investors don’t experience upside volatility as risky at all - investors aren’t risk-averse per-se, they’re loss-averse.

2. MPT treats both upside and downside volatility as risk and there is a bell-shaped curve that shows the mean variance - with standard deviations - each unit above or below the mean. But, real market returns aren’t symmetrical. Stock market crashes like 1987, 2000, 2008 are supposed to be outlier events - yet reality drags Markowitz’s bell curve away from orderly distribution around the mean, and reality adds extra-bad outcomes on the negative side of the mean (fat tails). For instance, according to MPT, the S&P 500 should have shown a monthly decline of more than 15% (three standard deviations) only once in 80+ years - but it happened something like 10 times (if I recall).

The best portfolio optimization/design is known in retrospect, so:
a) Save as much as you can.
b) Diversify those savings.
c) Don't pay more than you have to.
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Re: Modern Portfolio Theory

Post by nisiprius »

Some more sour remarks. I do not intend to downplay the importance or legitimacy of Markowitz' Nobel prize or any Nobel prize. But I do think that in the field of economics, if not others, too-cozy interrelationships between academic research and commercial considerations pollute things. I can't come up with a good analogy, but imagine an automaker hiring Einstein as a consultant and then advertising that their cars are best because only their engineers can use patented CAD software, available to no other company, that calculates relativistic corrections when simulating piston movements. The theory is real, they may be telling the truth about using it, but it doesn't matter; it's just a secret miracle ingredient.

It is apparently well-known that
Fisher & Statman 1997* wrote:The Markowitz mean-variance optimization framework presents a puzzle. Although it is the standard model of portfolio constructions, investors rarely use it and, when used, it is constrained so much that portfolios reflect the constraints more than the optimization....

Portfolios constructed using historical means, variances, and correlations do not appeal to investors' intuitions. They consists of few of the many available assets, and the weights of the assets used in the portfolios are extreme--large long or large short positions. Investors are suspicious of portfolios with extreme weightings, although many like the idea of mean-variance optimization. As a result of these suspicions, mean-variance optimization is implemented with extensive sets of constraints such as the prohibition of short positions and the assignment of maximum weights for long positions.

Do optimized portfolios.... display extreme weightings because historical parameters are not good estimates of the expected parameters? This view is common in the literature...
(They go on to present an alternate view). The point is that for whatever reason,

MPT isn't really applicable in practice because it gives crazy results. So it isn't really used in practice, although people pretend to use it by "constraining" its results, either by rule or by informed intuition.

A further sour remark. I certainly don't pretend to understand the social structure of the overlapping worlds of financial economics and investment companies, but I have been doing a long, slow double-take on the interrelations thereof. It appears as if economists who make important discoveries in financial economics either found very-much-for-profit commercial enterprises or get snapped up by very-much-for-profit commercial enterprises. This inevitably is going to lead to situations where legitimate-enough work is overhyped as a hugely important secret miracle ingredient.

Harry Markowitz serves on the "advisory panel" of Research Affiliates, the firm led by Rob Arnott which creates and sells "fundamental indexes" and I-don't-know-what-all else. I am sorry to say I can't retrieve details on a quick Google, but IIRC Markowitz also has some connection with a firm that actually provides commercial mean-variance optimizer software to financial advisors. If someone happens to know the name of the firm and the product, I'd like to know it. (He also is the cofounder of CACI International,which began as a software development company that sold implementations of the SIMSCRIPT computer programming language, but seems to have become a giant defense C3 contractor or something; I don't think that's the company that sell the MVO software).

My point is that given the cross-connections between the academic and the commercial world, there are often commercial reasons to exaggerate the practical usefulness and robustness of these studies. I don't mean to single out Markowitz here; I'm just saying that I have gradually gotten queasy about the coziness between the worlds that are developing the theories and the worlds that are selling products. This works both ways. It was unsettling to me to discover that the CRSP was originally founded in order to provide data that Merrill Lynch could use in an advertisement, and that the University of Chicago’s Booth School of Business is named after the founder of DFA in recognition of the largest gift ever made to any business school. Nobody ever believes they personally are subject to funding bias, but everyone acknowledges that others are.


*Fisher, Kenneth L. and Meir Statman, "The Mean-Variance Optimization Puzzle: Securities Porfolios and Food Portfolios," Financial Analysts Journal Vol. 53, No. 4, Jul. - Aug., 1997 pp. 41-50. The point of the paper is that portfolios generated by mean-variance optimization are crazy, not so much because they are ridiculously sensitive to parameters used as input which can't be estimated accurately, but because even when they work, what they optimize is not even close to what investors wish to optimize.
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Re: Modern Portfolio Theory

Post by grayfox »

ngutman wrote:Is anyone here dabbling with Harry Markowitz's Modern Portfolio Theory for portfolio optimization/design?
Thanks, Nathan
Not long ago i took a couple of university courses in Modern Portfolio Theory. Lots of math-probability and statistics, calculus, linear algebra-which made the classes very exciting and fun. We mostly focused on the computational aspects and wrote programs in python and R. Of course also Excel.

We spent a lot of time learning how to compute statistical properties of securities markets, which we studied in depth. We also created all kinds of portfolio optimizers that I've spent a lot of time playing with. Until you've run portfolio optimizations and see how they work, you really won't understand what they do and what the limitations are.

If you are the kind of person that enjoys statistics, computer programming, playing with numbers, I highly recommend taking classes in the subject.
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Re: Modern Portfolio Theory

Post by nedsaid »

I do believe in Modern Portfolio Theory but I am realizing this is an imperfect tool. My portfolio has always reflected good diversification but I have to admit my approach was not scientific.

I started with individual stocks but I learned to be value oriented and mostly I bought stocks that yielded a dividend. The idea of getting paid with dividends waiting for the price appreciation really appealed to me.

Over time, I started buying mutual funds because I realized I needed more securities. A typical fund owns 120-200 stocks or more and this seemed like a logical progression.

Later I determined that I wanted International diversification. I read some articles on this but the reason for buying International Stock Funds was that it just seemed like a good idea. Diversify beyond your own country.

Later came bond funds as I learned more about diversification between between stocks and bonds. I wanted to decrease the risk in my portfolio.

The REIT fund came available at my favorite mutual fund company and I bought it. It seemed logical but I didn't realize it was a non-correlating asset to stocks. It just seemed like a good idea.

I later learned about indexing, the arguments for it had bullet proof logic and I started indexing parts of my portfolio.

I read articles on portfolio theory, I adopted a lot of its concepts because it just made sense. It was intuitive.

I never tried to calculate risk or plot out an efficient frontier or kept really detailed spreadsheets. It seemed to make sense to spread my funds over different asset classes. The hope was to maintain the return that I wanted and reducing volatility.
My process wasn't too scientific. Over the years, I read a lot of articles and books but have to admit that my eyes glazed over when the discussion got too much into the math.

It also helped to look at the portfolios of the Target Date Funds and the Moderate Risk funds at my favorite mutual fund company. It gave me a good idea of an appropriate portfolio for my age and risk leve.

Later, I learned about Dimensional Fund Advisors and slicing and dicing. I didn't use the DFA funds but tilted my portfolio towards small-midcap stocks and towards value. I believed the Academic research about the small cap and value premiums.

So I believe in Modern Portfolio Theory and use it to the best of my ability. Nisiprius's posts have highlighted the limitations of this approach and has shown that the math behind it is imperfect also. His posts put the finger on what I had suspected for a long time. So this is why I think the math is important but I don't obsess over it. The general principles and concepts of Modern Portfolio Theory are sound, like most anything else it is imperfect.
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Re: Modern Portfolio Theory

Post by richard »

Markowitz on how to apply MPT:
Dr. Markowitz first got to choose how to divide his assets between a stock fund and a bond fund not long after publishing his pioneering article "Portfolio Selection" in the prestigious Journal of Finance. Following his own breakthroughs, he should have made intricate calculations, based on historical averages, to find the optimal trade-off between risk and return. But, Dr. Markowitz told me, that isn't what he did: "Instead, I visualized my grief if the stock market went way up and I wasn't in it -- or if it went way down and I was completely in it. My intention was to minimize my future regret."

Dr. Markowitz paused, then added wryly: "So I split my contributions 50/50 between bonds and equities."
http://online.wsj.com/article/SB123093692433550093.html
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Re: Modern Portfolio Theory

Post by nedsaid »

So Dr. Markowitz flew by the seat of the pants the way a lot of us have. Another way of saying it was that he made a
Scientific Wild Ass Guess. He SWAGged it.

This confirms the suspicions I have long held. The process isn't as precise as we are lead to believe. The concepts and the reasoning behind Modern Portfolio Theory are very good though.
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Re: Modern Portfolio Theory

Post by FabLab »

richard wrote:Markowitz on how to apply MPT:
Dr. Markowitz first got to choose how to divide his assets between a stock fund and a bond fund not long after publishing his pioneering article "Portfolio Selection" in the prestigious Journal of Finance. Following his own breakthroughs, he should have made intricate calculations, based on historical averages, to find the optimal trade-off between risk and return. But, Dr. Markowitz told me, that isn't what he did: "Instead, I visualized my grief if the stock market went way up and I wasn't in it -- or if it went way down and I was completely in it. My intention was to minimize my future regret."

Dr. Markowitz paused, then added wryly: "So I split my contributions 50/50 between bonds and equities."
http://online.wsj.com/article/SB123093692433550093.html
Thank you, Richard, for one of my favorite posts. (Nice to hear from another 50/50er, even if it is the good Doctor M.) That and YDNAL's points a,b,c, above are all that's ever made much sense to me when planning long-term investments to meet one's retirement goals.
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Re: Modern Portfolio Theory

Post by staythecourse »

YDNAL wrote: What sense does it make to diversify out of an asset class that’s returning 30%?... investors don’t experience upside volatility as risky at all - investors aren’t risk-averse per-se, they’re loss-averse.
I don't understand what you mean here?? Yes investors are loss aversive that is why if you are one of them you do NOT want a 30% return. risk and return is the same thing as they are just different sides of volatility, i.e. standard deviation. Upside deviation is what folks call return (and love) and downside deviation is what folks call risk (and hate). They are two sides of the same coin. The same thing that gives a 30% return, i.e. stocks can and do give a 30% loss.

That is why a loss aversive investor should DIVERSIFY away from stocks, i.e. cut the left tail returns by giving up the right tail returns. Thus give up some return to get some protection from loss.

Diversification is just the means of NARROWING the dispersion of returns in a portfolio by decreasing the weighted average to the most volatile asset class, i.e. stocks, i.e. market risk. If that is done with bonds, cash, putting your money under the mattress, etc...

Good luck.
"The stock market [fluctuation], therefore, is noise. A giant distraction from the business of investing.” | -Jack Bogle
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Re: Modern Portfolio Theory

Post by gwrvmd »

My opinion on MPT: "The markets are governed by behavioral science, not physical sciences therefore do not trust market risk models" Seth Klarman...Gordon
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Re: Modern Portfolio Theory

Post by IlliniDave »

Seems to me MPT is an interesting tool to evaluate investment markets after the fact. It seems less useful looking forward. It seems to lend some backing to the intuitive techniques that predated it (e.g, diversification--Wellington, for example, has been running 2/3 stocks-1/3 bonds going back maybe to the 1930s). It certainly seems to have brought short-term standard deviation to the fore as the primary measure of risk.

I'm sure some of what I do reflects some of the ideas that have flowed through MPT, but I don't sit around and put dots on predicted efficient frontier and wring my hands over whether I should sacrifice 0.2% of annualized return for a 0.5% reduction in standard deviation and the like.
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Re: Modern Portfolio Theory

Post by magician »

Frengo wrote:
magician wrote: Are those supposed to be division signs? That would be distinctly odd.
It would and they are not.
Dashes, on the other hand, would make some sense.
Sorry! I thought that as a former rocket scientist you would have confused them with subtraction signs. :^p
;-)
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Re: Modern Portfolio Theory

Post by Kevin M »

Frengo wrote:
Kevin M wrote: A riskless asset is not just a convenient reference mark. It is an asset that has zero correlation to the portfolio of risky assets; this is the critical distinction in portfolio theory.
Actually, it's distinction is that it has zero volatility. You can easily find uncorrelated risky assets.
Again, there is a kernel of truth in what you're saying, but there's a bit of muddling too. Academics discuss portfolio theory in terms of variance, covariance, and correlation.

Yes, the riskless asset actually is defined as an asset with a variance (and standard deviation) of 0 for the given holding period. Since covariance is based on the sum of products of the individual variances of individual assets, it will be 0 (as will correlation) when combining a riskless asset with a risky asset.

Variance is measured as the standard deviation of the expected return for a given holding period. It is not based on price volatility during the holding period, but of course the variance of expected returns for a given holding period is likely to be higher for an asset with more price volatility. And of course an asset with zero variance mostly likely has zero volatility.

"Uncorrelated" as you're using it means correlation of less than 1. Correlation of 0 is a very specific case. Finding assets with correlation of less than 1 has nothing to do with the riskless asset.

I'm the primary contributor to a Wiki article that covers some Portfolio Theory, and is extensively referenced. Nothing I wrote there is my opinion (at least I tried not to interject opinion); it is based mostly on investing and finance textbooks. I admit my knowledge is a little rusty, so I might be slightly misstating a few things. You might scan it to get a better idea about where my comments are coming from: http://www.bogleheads.org/wiki/Risk_and_Return.

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Re: Modern Portfolio Theory

Post by Frengo »

Kevin M wrote: Yes, the riskless asset actually is defined as an asset with a variance (and standard deviation) of 0 for the given holding period. Since covariance is based on the sum of products of the individual variances of individual assets, it will be 0 (as will correlation) when combining a riskless asset with a risky asset.
Zero volatility is a sufficient condition for zero correlation, but it is not a necessary condition. For instance, a few roulette spins evidently have zero correlation with the stock market return. We don't use such an "asset class" for diversification because its expected value is negative.
Variance is measured as the standard deviation of the expected return for a given holding period. It is not based on price volatility during the holding period, but of course the variance of expected returns for a given holding period is likely to be higher for an asset with more price volatility. And of course an asset with zero variance mostly likely has zero volatility.
Aside from the fact that volatility is related to the square root of variance (the standard deviation), the difference is that variance is measured on a given sample, volatility is estimated based on variance measurements.
Cash is a special case, since in nominal terms has a fixed value, therefore zero variance however you measure it and consequently zero volatility.
"Uncorrelated" as you're using it means correlation of less than 1. Correlation of 0 is a very specific case. Finding assets with correlation of less than 1 has nothing to do with the riskless asset.
I thought you wrote "A riskless asset is not just a convenient reference mark. It is an asset that has zero correlation to the portfolio of risky assets"
I'm the primary contributor to a Wiki article that covers some Portfolio Theory, and is extensively referenced. Nothing I wrote there is my opinion (at least I tried not to interject opinion); it is based mostly on investing and finance textbooks. I admit my knowledge is a little rusty, so I might be slightly misstating a few things. You might scan it to get a better idea about where my comments are coming from: http://www.bogleheads.org/wiki/Risk_and_Return.
Thanks, I'll have a look.
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Re: Modern Portfolio Theory

Post by Frengo »

YDNAL wrote: 1. MPT's central tenet - that diversification mitigates portfolio risk - collapsed in 2008 when all asset classes were mauled. Treasuries provided a haven, but according to MPT, Treasuries don’t even count - they’re just the risk-free baseline at the bottom of the return axis. Conversely, during the technology boom of the late 1990s when “risk” was a dirty word, MPT also failed in the real world. What sense does it make to diversify out of an asset class that’s returning 30%?... investors don’t experience upside volatility as risky at all - investors aren’t risk-averse per-se, they’re loss-averse.
Yeah, but in finance "risk" is the possibility of an outcome different from the expected one. It can be a less desirable outcome, or more desirable, it doesn't matter.
The fact that MPT makes you get out of an asset returning 30% is actually evidence that it works: The objective of diversification is not to increase expected returns (it lowers them!), but to lower volatility. Therefore you should expect to avoid market spikes in both directions and be happy about that.
2. MPT treats both upside and downside volatility as risk and there is a bell-shaped curve that shows the mean variance - with standard deviations - each unit above or below the mean. But, real market returns aren’t symmetrical. Stock market crashes like 1987, 2000, 2008 are supposed to be outlier events - yet reality drags Markowitz’s bell curve away from orderly distribution around the mean, and reality adds extra-bad outcomes on the negative side of the mean (fat tails). For instance, according to MPT, the S&P 500 should have shown a monthly decline of more than 15% (three standard deviations) only once in 80+ years - but it happened something like 10 times (if I recall).
MPT doesn't assume a gaussian distribution.
The best portfolio optimization/design is known in retrospect, so:
a) Save as much as you can.
b) Diversify those savings.
c) Don't pay more than you have to.
And MPT tells you how to diversify for maximum effect.
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Re: Modern Portfolio Theory

Post by Frengo »

nisiprius wrote: MPT isn't really applicable in practice because it gives crazy results. So it isn't really used in practice, although people pretend to use it by "constraining" its results, either by rule or by informed intuition.
If one has not understood the theory, his/her results can certainly be crazy.
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Re: Modern Portfolio Theory

Post by Kevin M »

YDNAL wrote: 1. MPT's central tenet - that diversification mitigates portfolio risk - collapsed in 2008 when all asset classes were mauled. Treasuries provided a haven, but according to MPT, Treasuries don’t even count - they’re just the risk-free baseline at the bottom of the return axis.
I don't think so. Typically 30-day T-bills are used as a proxy for the riskless asset. Longer term treasuries are definitely in the mix of risky assets.

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Re: Modern Portfolio Theory

Post by magician »

Frengo wrote:
YDNAL wrote:2. MPT treats both upside and downside volatility as risk and there is a bell-shaped curve that shows the mean variance - with standard deviations - each unit above or below the mean. But, real market returns aren’t symmetrical. Stock market crashes like 1987, 2000, 2008 are supposed to be outlier events - yet reality drags Markowitz’s bell curve away from orderly distribution around the mean, and reality adds extra-bad outcomes on the negative side of the mean (fat tails). For instance, according to MPT, the S&P 500 should have shown a monthly decline of more than 15% (three standard deviations) only once in 80+ years - but it happened something like 10 times (if I recall).
MPT doesn't assume a gaussian distribution.
However, it does assume that the distribution can be characterized fully with only the mean and the standard deviation; thus, it does assume a symmetric distribution. Could be normal, uniform, Student's T, or something weirder, but it'll be symmetric.
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Re: Modern Portfolio Theory

Post by Frengo »

magician wrote: However, it does assume that the distribution can be characterized fully with only the mean and the standard deviation; thus, it does assume a symmetric distribution. Could be normal, uniform, Student's T, or something weirder, but it'll be symmetric.
Any distribution, however exotic it may be, has a mean and a standard deviation. What you do with that data is another matter and I don't agree that according to MPT the distribution can be characterized fully. I'd say that it can be characterized. Period.

One has to recognize that MPT doesn't give you a deterministic formula where you plug in numbers and obtain an ideal portfolio. Instead, it tells you which characteristics influence the overall behavior of you portfolio.
After all, we never know future volatility and that's the volatility that counts. Discussing if past volatility is gaussian or giraffe-shaped doesn't help.
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Re: Modern Portfolio Theory

Post by richard »

Frengo wrote:Any distribution, however exotic it may be, has a mean and a standard deviation.
http://en.wikipedia.org/wiki/Cauchy_distribution
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Re: Modern Portfolio Theory

Post by nisiprius »

Frengo wrote:...Zero volatility is a sufficient condition for zero correlation, but it is not a necessary condition. For instance, a few roulette spins evidently have zero correlation with the stock market return. We don't use such an "asset class" for diversification because its expected value is negative....
In theory, in principle, an asset class with a negative return could increase the return of a portfolio if the return weren't too negative, its volatility was similar to that of stocks, and it had a strong, persistent, robust negative correlation with stocks. (Not low, negative, and not just a little negative, a lot negative).

This theoretical possibility leads to advocates of slice-and-dice and exotic asset classes talking a lot of nonsense about things which are lousy investments in themselves improving the portfolio as a whole. The problem is that no asset pairs have strong, persistent, robust negative correlation unless they are synthetic, the result of short selling, in which case they just cancel out the risky asset leaving you with nothing but the cost of borrowing.

Unfortunately, chance being what it is, asset pairs that really have zero or low correlation can temporarily show negative correlation due to sampling error, and during the period of time when they are showing it, they do improve the portfolio--and people advocating for that asset class will point that out, cherry-picking that particular period of time.
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Re: Modern Portfolio Theory

Post by nisiprius »

richard wrote:
Frengo wrote:Any distribution, however exotic it may be, has a mean and a standard deviation.
http://en.wikipedia.org/wiki/Cauchy_distribution
Right, the Cauchy distribution doesn't. And it is a perfectly reasonable distribution--at first glance you could mistake it for the normal distribution, it's not "Cantor dust" or anything like that. And it has any number of simply physical realizations in the real world. For example, if you imagine a football field illuminated by a single row of fluorescent fixtures hanging overhead and lined up with the 50-yard line, that football field is lit up by a Cauchy distribution of light.

And, this is the book that has a sort of down-the-memory-hole "unbook" status in investing: Mandelbrot and Hudson, The Misbehavior of Markets: A Fractal View of Financial Turbulence. As far as I know, it hasn't been discredited. It's just ignored, because it's so painful to think about. This book does talk about the Cauchy distribution, and he gives good evidence for suggesting that real-world markets have behavior that is not, thank goodness, as wild as the Cauchy, but are much wilder than the normal distribution and all of the gently moulded variations of it. The concern is not that real-world distributions might be lognormal instead of normal or anything like that. It is that they might be outside the range of all the "tame" distributions (on which the central limit theorem can do its stuff), somewhere in between the land of the statistically well-behaved and the Cauchy.

And to my mind there is awfully good evidence that financial economists and practitioners make the same mistakes over and over and over again: they discover/invent wonderfully clever new systems for extracting profit from statistically tame situations, get funding, start applying it, and at first it seems to be a magic money well. But as time goes on it becomes harder and harder to extract the oil so, since it seems to so tame and under such good control, they leverage it up and up and up. And then, pow! They hit the financial "turbulence" of Mandelbrot's book title. The way you can tell that this is happening--that they have misjudged the basic nature of their financial processes is that they always say the same thing: some variation on "This was a ten-sigma event," or "this was a twenty-five sigma event."
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Re: Modern Portfolio Theory

Post by richard »

Good things about MPT:
- teaches that diversification is a good thing
- teaches that if you want more return, you'll have to take more risk

Bad things about MPT (Markowitz mean variance model):
- simplistic model that does not come close to capturing the real world
- uses volatility as a proxy for risk
- encourages an engineering approach to investing - the belief that often basic analyses of data will yield useful results
- leads to arguments over definitions, such as what constitutes a riskless asset
- widely taught because it's easy, which leads to "it's in textbooks so it must be true"
- even its creator does not actually use it for portfolio decisions
- encourages belief that more risk will lead to higher return
- name suggests it is a current model, rather than a model from the 1950s that has been superceded
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Re: Modern Portfolio Theory

Post by grayfox »

Kevin M wrote:
I'm the primary contributor to a Wiki article that covers some Portfolio Theory, and is extensively referenced. Nothing I wrote there is my opinion (at least I tried not to interject opinion); it is based mostly on investing and finance textbooks. I admit my knowledge is a little rusty, so I might be slightly misstating a few things. You might scan it to get a better idea about where my comments are coming from: http://www.bogleheads.org/wiki/Risk_and_Return.

Kevin
Nice work! I especially like your discussion of risk in the section Risk as the uncertainty of returns The charts comparing T-Bill, 10-YearBond and Stock returns do a good job of showing the increasing uncertainty of riskier assets. It's good that you put all on the same scale.

Image

Before I studied MPT, I thought that using standard deviation as a measure of risk was pretty worthless. A simplication so that the theory and math would work out. Just because one thing goes up and down more each day than another thing does not seem to make it more risky, in my view.

However, after studying Portfolio Theory in school, I now think that SD does capture the risk of investing very plainly. It's the uncertainty of the result that makes it risky. Anyone with any sense will demand a bigger payoff (higher expected return, risk premium) for something with a less certain outcome. Duh! :oops:

Harry Markowitz deserves his Noble prize. :beer
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Re: Modern Portfolio Theory

Post by pkcrafter »

richard wrote:Good things about MPT:
- teaches that diversification is a good thing
- teaches that if you want more return, you'll have to take more risk

Bad things about MPT (Markowitz mean variance model):
- simplistic model that does not come close to capturing the real world
- uses volatility as a proxy for risk
- encourages an engineering approach to investing - the belief that often basic analyses of data will yield useful results
- leads to arguments over definitions, such as what constitutes a riskless asset
- widely taught because it's easy, which leads to "it's in textbooks so it must be true"
- even its creator does not actually use it for portfolio decisions
- encourages belief that more risk will lead to higher return
- name suggests it is a current model, rather than a model from the 1950s that has been superceded
Thanks, Richard, an excellent (useful!) summary.

KevinM, nice contributions to the Wiki.

greyfox wrote:
However, after studying Portfolio Theory in school, I now think that SD does capture the risk of investing very plainly. It's the uncertainty of the result that makes it risky. Anyone with any sense will demand a bigger payoff (higher expected return, risk premium) for something with a less certain outcome.
The key here is you studied MPT in school and you can relate to volatility, but the majority of investors on this forum don't understand volatility as risk as well as you do, they relate to loss. People don't care about probability, frequency, or what happens 2/3rds of the time, but they don't like losing a lot of money.

And to throw another sticky wrench into the mix, we also need to know the difference between uncertainty and risk.

Paul
When times are good, investors tend to forget about risk and focus on opportunity. When times are bad, investors tend to forget about opportunity and focus on risk.
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