Your portfolio is (probably) not efficient

I want to have a rational asset allocation so I did a bit of reading about modern portfolio theory.
There is this nice idea of plotting all the risky assets on two axis: risk vs. return
Then for each fixed level of return, you can find the unique combination of assets that minimizes the risk. That defines a point for each return levels, and gathering all these points you get an “efficient frontier”, where all the “good” portfolios are. You want your portfolio to be on this frontier if you’re a rational investor.

A further claim is that the Total Stock Market portfolio (like VT) lies on the efficient frontier. That means that if you only have VT in your portfolio, it’s a bit boring, but also maximally efficient. So you should give your own shoulder a deserving pat.

But this last point is actually very wrong.
Let me explain: a portfolio on the efficient frontier is defined by the weights that are associated to each asset, and the only constraint on these weights is that they have to sum up to 1.

Since these weights are somewhat random numbers only constrained by “sum = 1”, one would assume that some of these weights can be negative.
In Impossible Frontiers, two finance professors show that indeed as soon as you have more than > 100 assets to pick from it becomes extremely likely that some of the weights are negative numbers, and that this is the case for all the portfolios on the efficient frontier.

But, by definition the Total Stock Market portfolio has positive weights on every assets. So it does not lie on the efficient frontier. And as long as your portfolio in not shorting at least one stock, it also cannot be on the efficient frontier.

So none of our portfolios are efficient. I find this thought very liberating :slight_smile:


Take what you read online about MPT with a grain of salt until you have played with it yourself.

It’s a cute theoretical tool and teaches a few important lessons about diversification, but is not particularly useful for practical portfolio optimization at least in the form that’s commonly taught.

It requires you to have the clairvoyance of knowing expected future returns and correlations between assets. And it’s quite sensitive to small perturbations in these inputs - small changes may produce very different output recommendations from the optimizer. So there’s no the efficient frontier, it’s only as good as the inputs you feed into the model - which you’d normally fit from historical data but correlations may change overnight especially during crisis.

By whose definition? And where did such huge assets classes as debt, commodities and real estate go?


Knowing that MPT is okay to explain diversification but doesn’t travel much further like @kilyn said, the more accurate claim would be to say that the “market porfolio” lies on the efficient frontier. This theoretical market portfolio contains the whole market, not just the shares on VT since other assets (and asset classes!) are not taken into account.

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Thanks @Ed_Waadt and @kilyn for correcting me. In the paper Impossible Frontier the authors indeed talk about the “market portfolio” (the portfolio of all assets in which each asset’s weight is proportional to its total market capitalization).

If you believe the conclusion of that paper, then the “market portfolio” cannot be on the efficient frontier as it’s not shorting any asset and all the portfolios on the efficient frontier must be shorting at least one asset.

As @kilyn said the real efficient frontier is essentially unknowable. Furthermore, even if an oracle were to tell us the correct expected returns and covariances, the frontier moves every day.
So holding a portfolio on it would never be cost-effective.

The point is not that VT was not efficient. Its not possible to have a fully efficient portfolio, but this is not due to the point observed in the misleading paper stated above but simply a matter of information and timing challenges. The point is two-fold:

  • assuming efficient markets, its impossible to systematically beat the market; BUT
  • the market doesnt consist of shares only but all liquid assets with a risk premium
    => An efficient Portfolio consists of an unknown blend of risky asset classes; a shares only investment introduces inefficiencies

When we go into details, we need to consider that the paper is flawed. Whilst an assets with marginal zero weight may be hardly imagined, a negative weight one could only be explained with an asset that is either about to go bust; or that will experience a material de-valuation. In any other scenario, a negative weight does not make sense. In such scenario (bust or de-valuation) where assets risk or return would go belly up; such assuming efficient markets implied an immediate reduction / voiding of the assets market cap to adjust to the change in return/risk. A negative weight therefore only makes sense for a i) marginally small amount of time required for Mr Market to absorb the information, ii) in case of a market inefficiency or iii) asymetric information.

This actually highlights the underlying issue which is that both return and risk may not be determined but only retrospectively observed and approximated. Hence, its impossible to establish an ideal portfolio as such would need to be based on unknown risk and return data. Assuming efficient markets however, the market will constantly translate retrospectively observed data and resulting adjustment to approximate risk/return into a change in the assets market cap; leading to a situation where a market cap represents the best possible proxy to an efficient portfolio given „known“ data. Indexing is therefore the best alternative to beeing the allknowing Mr. Market himself.

What puzzles me is that many investors in this forum go all-in on shares only. Going 100% in shares is simply a speculation on a certain market segment (shares) of the entire market (risk carying assets). The rationale behind 100% assets is maximized return but not a maximized risk weighted return. The same logic could be applied further by cutting shares into additional segments that historically warrant higher returns like small caps or Nasdaq. Whilst small cap premium might (depending on the research) be historically observed, they are not guaranteed as there is no undisputed fundamental reason for the premium to prevail. Same applies to Shares vs. e.g. Real Estate returns. What if Mr. market at any given point in time and after centuries decides that RE shall have the higher return?

Taking the Shares vs. Small Caps example to showcase the point. Whilst many investors probably agree that Small Caps might imply higher prospect returns than All Shares. Who would dare to claim that their risk weighted return was higher? Hard to do… right? Even if currently observed (which is not the case) its even harder to claim that such was just given and prevailed. The exact same thought could be applied on Shares vs. All Risky Assets. Would anyone dare to claim that shares had a higher risk weighted return than e.g. 25% Shares, 25% Real Estate, 25% Bonds and 25% Gold? We could still claim so but huh… just looking at recovery time from max drawdowns; that might be bold. And even if we could claim so… how could we justify that this overperformance prevailed?

Why not simply going even more „passive“ than just shares only? Clearly… its impossible to establish a market cap global allocation over all risky assets. Besides, such would be screwed given market unequalities and incentives, e.g. tax relieve on real estate. So the second best to an all passive global allocation is probably to use observed, estimated risk/return as well as correlation figures from investable asset classes and to build a corresponding portfolio that gets close to the desired target return yet optimizes risk and return.

And what if you not just want to get close to but actually the maximum return? Well… its still more efficient to use such optimal risk/return portfolio that is somewhat close to the desired target return… and then simply leverage or de-leverage accordingly. Leverage doesnt need to imply debt, hefty interest or margin calls (dont do that) but can be self-funded. Latest beyond the first 10 years of work, most people establish both an investment portfolio as well as a fairly moderate safety cushion that within reason could be used for „self funded leverage“.

If you still insist on max return and don‘t have such safety cushion for self leverage… in my experience you then either are at the beginnig of your investment journey where future investments compared to current investments are major… aka your future income constitutes kind of a low risk asset that you use to re-balance against (so you follow a ballanced approach without noticing as your alternative otherwise would have been to on day 1 take a loan equivalent to your next 10 years savings and immediately invested all). Or if you already had certain wealth where your future investments p.a. did not exceed e.g. 10% of your current investments and you still invested 100% on shares… well then good luck with your investment strategy and I wouldnt want to comment on what I thought of such approach. But just remember that max returns of shares over all risky assets are observed but not guaranteed and you highly likely experience a worse risk weighted return than possible.

Or in simple words… do never go 100% all in on shares; unless you anual new investments materially exceed 10% of your current investments.


The Tea Lover

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In the paper I mentioned, having a negative weight for one asset simply means taking a short position on that asset. The authors give an example on page 8 after Proposition 2: with only 3 assets you can already build cases where portfolios on the efficient frontiers have negative weights. (This other paper has a similar example).

In their analysis the authors of the first paper show that as the number of assets increases, all the portfolios on the efficient frontier are going to have at least one negatively weighted asset. Hence the market portfolio cannot lie on the efficient frontier (because as you said that portfolio cannot have negative weights).

The paper aims at disproving that the market portfolio is efficient. It’s a critic of that conclusion of a strong version of the efficient market hypothesis.

Does this amount to the same as doing factor investing, e.g., small cap (VBR)? When you leverage your portfolio you increase both the return and the volatility If, as you mentioned, you manage to get a risk-free loan with no interest, both return and volatility are simply multiplied by your leverage. If you invest in small cap, you also in effect increase both return and volatility. Is there a difference (aside from comparing the sharpe ratios)?

First thank you very much for this very interesting post.

And i would add something i read on bogleheads: indexing (with low cost etf) is a strategy offering 100% safety not to underperform the market, while active investing is 100% sure to not always overperform.

The 2. Säule (Pensionskasse) is a not negligible part of total portfolio and in most cases by far not 100% shares (max 40% i would guess). So in real life in CH you will never be all in. Or did you mean something else?

Guess my criticismn on the paper was not fully clear. The reason why you would want to go short on an asset, when building an efficient portfolio, was either:

  1. the asset‘s value was beyond the fair value established given „known“ return/risk data. This is exactly the point above where we talk about either an interim adjustment anomaly that dissolves once Mr. Market prices in the „known“ risk and return, market inefficiency we should for the simplicity assume was not present or asymetric information. Assuming efficient markets, these effects are neglible and should be ignored.
  2. an attempt to indirectly build up leverage. From an efficiency point of view, such however doesnt make much sense. Assuming efficient markets, its more efficient to directly lever but not to shortsell risky assets.

When we consider the above, and the fact that return/risk may not be measured but only observed and estimated… we may conclude that the idea of marginal zero weight assets is questionable and that negative weight assets in an efficient portfolio does not make much sense. Hence, please disregard the paper. This puts market cap weighted indexing back to its position as the best proxy to an efficient portfolio… if only we knew the entire asset universe, asset caps and distortions introduced e.g. by tax treatments :slight_smile:.

With regard to maximizing targeted return vs. risk weighted return; the example would be that instead of investing 50% of your wealth only but all of such in shares where we expect a max. return of 6%… its more efficient to invest 60% of your wealth but these 60% in a multi-asset portfolio that you set up with a target return of 5% only. Meaning that you use your safety cushion to lever yourself up a bit. Whilst your resulting target return in both cases was 6%, the risk/volatility of the „Not-Only-Shares“ Portfolio was lower.

With regard to Pension Fund as a „Non-Shares-Asset“. Remember that the objective of investing in multiple asset classes is two-fold. On one hand, we would want to tab on to different sources of risk premium; which might potentially be more efficient than the risk/return profile of shares. But even if the risk/return was worse than the one of shares; combining two asset classes can improve efficiency given diversification resulting from low correlation. These efficiency gains are further accentuated in case we can apply smart re-balancing. Unless we talk about an 1E solution or a vested benefits account, a pension fund will not provide you with the ability to indirectly re-balance your portfolio. We therefore lose a material source of efficiency if our multi-asset solution consists of Non-Shares in the form if a Pension Fund only. Your asset allocation should encompass all your assets that you may both invest and controll. Therefore, I propose to consider 3a as part of an overall asset allocation but at the same time to disregard the pension fund. Do not count your pension fund as money market / bonds as you cant truly re-balance. Therefore, make sure that your remaining assets (as per the above) are not 100% in shares unless you are at the early stages of investing.

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Can you explain further what you mean by “self funded leverage”?

Would you like to explain where your >10% come from?


Another Tea Lover

Great to have a Tea Chat here!

The thinking was fairly simple. The key success factor is time you are exposed to risk and return carrying assets. A rational investor would therefore not just invest his current savings but as well his discounted, future savings. If you e.g. assume that you each future year manage to save 20k, you should discount these future savings at your anticipated portfolio return plus foreign capital cost plus a risk premium re. uncertainity of savings (e.g. 5% p.a return plus 3% credit cost plus 5% risk premium; 13% p.a.) and directly invest the bulk of e.g. 200k in year one (which implies leverage aka that you take on a loan to invest)

A sensible investor will NOT do this as it was way too risky to invest on the back of a loan, right? The thing is that the sensible investor mixes up risk tolerance with investment principles. Such sensible investor states he sticked to the „do not invest using foreign capital“ principle whilst in reality and probably even without noticing he meant that he simply didnt have the risk tolerance to go all in on risk.

Learning: Should you at the beginning of your savings be hestitant to take out an investment loan… you likely wont have the risk tollerance to be all-in on risk as you reach the end of your investment career. Its both expensive and painful by the way if you only retrospectively learn this lession…

If an early investor doesnt invest on lended cash - this is generally due to a combination of both, not having the appetite to go all in on risk as well as the personal rejection of the principle go buy on leverage. The principle part implies that an early investor is initially under-invested in risky assets vs. what his risk tollerance would allow him to do. Its always good to regularely review your asset allocation in the context of the combined current as well as discounted future assets as this represents your genuine asset allocation and whether your investments are on track.

As a conclusion of the above, an early investor should in the first years invest all he can into risky assets as he by doing so will reduce his underinvestment vs. his desired asset allocation. This way will he over time get closer towards his his desired asset allocation.

There will be a moment in time where current assets catch-up with discounted future assets. This is definitely the time to ensure that investments are entered in a way that we are geared towards reaching the finally desired asset allocation and that we don‘t overshoot on risky assets. At this point in time, remember that unless you on day 1 heavily take out leverage, the long term asset allocation that matches your risk appetite will likely not constitute 100% of risky assets. As we will not, and for illusion reasons should not, every year refresh our view on the „holistic asset allocation considering discounted, future savings“… the best is to just wait until your annual new investments are in the range about 10% of your current investments. As you reach such moment in time, you are probably close to a situation where current savings balance with future savings and you should definitely have a look at your total asset allocation and how you going forward invest your current savings - eg. 50/50 on risky vs. non-risky assets.

Therefore the rule of thumb that you should invest all in on risky assets as long as new investments form a material part of current investments but that you should no longer invest 100% in risky assets as soon as new investments make up for a smaller part of your current savings only.

Please let me take a sip of tea first before we dive into the topic of self leverage…

Kind regards,

The Tea Lover


I agree with you on this premise.


I partially disagree. I would say that one component of your risk tolerance is always bound with your current life situation. I would say to discuss that further we somehow need a mutual definition of risk.

That is one of the reason I am trying to get my investment approach straight in my mid twenties.


Agree, but keep in mind that the future is uncertain. Your discounted life-time-income in t=0 doesn’t have to be the same as your realised life-time-income in t=100.

Don’t agree on this point, but it really depends on your risk definition.

Your explanation makes sense, but it seems to have a lot of assumptions which aren’t that obvious for me.

In what kind of tea are you into?

Kind regards,

Another Tea Lover


Very interesting read, thanks! I hope you’ve had your sip of tea, @TeaCup, because self leverage is a topic I’m very willing to explore.

A limitation to leveraging from day one that you didn’t mention is access to capital. As a young person with what I think a stable job and a high risk tolerance, I am actively searching for ways to get leverage to invest. I may not have explored every option but that seems pretty difficult in Switzerland.

At day one, you can’t get a lombard loan because you have no assets to back it. You can’t get a mortgage because you likely don’t own a house yet. All the other commercial kinds of loans I’ve found require heavy amortization that makes it unsustainable to hope to get good returns by investing them. That leaves friends and family loans, which bear another kind of risk in that they can put a strain on your relationships (we’re back in risk tolerance territory, though).

That makes leveraging yourself from the onset unsustainable as a swiss resident, I feel, but I’ll gladly take all suggestions as to where to find credit where the cost of credit doesn’t cancel the benefits from it.

As your wealth grows, then you can start to access lombard loans and mortgages that allow you to get leveraged but as your wealth grows and you get older, the total mass of your future savings diminishes, as well as the total expected returns on the amount you can invest, making it less relevant to get leverage as opposed to right at the start of your investment journey.

There’s probably a period of time during which it would make sense to get whatever leverage you can when you can start to access it but by the time you reach it, forces of habits are likely to have set in and you’re also likely to rationalize why it’s not worth it going into leverage anymore.

I may be wrong but I’d say that the limits we put on access to credit, which are a good thing to prevent careless people to get into unsustainable debt, play a big role in why not more people go into leveraging themselves and investing according to their risk tolerance from the start. Have I forgotten to take a source of credit into account?

Edit: Aaaand… a quick trip in the “Should I buy TSLA shares” thread reminded me that I have forgotten to take leveraged ETFs into account. I’ll have to study that, though they bear yet a different kind of risk (namely, for me, investing in foreign assets subject to financial/taxation treaties fluctuation - I haven’t been able to find a leveraged swiss ETF investing in swiss assets but there again, I may not have searched deeply enough).


Have you looked at “Lifecyle Investing”? It’s a book about implementing that strategy (time diversification via leveraging heavily when young). Famously, the user “markettimer” on boglehead tried that approach in 2007 (It didn’t work out).

If you don’t want to take a loan, you can in effect have a leveraged position via futures contracts or options. That’s what the authors of Lifecycle Investing describe in chapter 1 (The implied interest rate for these contracts is usually lower than IB margin loan rate)


He didn’t try that approach exactly, he had much more leverage and increased it through the dips instead of resetting the leverage as the strategy advises.

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Basic derivatives come always with a lever of at-least 10. But keep in mind a lever works in both directions…

Not true. SQ offers me already lombard loans and i have atm less than 10k invested.


Another Tea Lover

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Gonna check that out. Thx

I must admit I haven’t read the book. I have read market timer’s thread and he did it using 0% credit card opportunities (at first, then high interest credit cards because it is a slippery slope) and derivatives. We don’t have credit card offers that would offer significant leverage. Derivatives are complex tools that I don’t pretend to understand (I’d have to study it but won’t set the required time aside just now due to other priorities). It feels to me like they’re adding yet another layer of risk by not representing a tangible asset, being just a contract instead. How would this additional risk enter the calculation of risk-adjusted returns smoothed on a lifetime?

Sure, that’s the risk part of the equation, which must be accounted for in the need, ability and willingness to take risk, considered on a lifetime basis. I wouldn’t take on leverage now, when times are quite uncertain.

Thanks for the clue. I haven’t been able to find it on their website so what are their margin requirements (how much are they willing to loan you for 10k invested and what would trigger a margin call)?

As a whole, I think that not all debt is created equal and that it translates in the ability and willingness we have to take risk. A young person with good human capital but low wealth may have high need to take risk. She may not have much to loose, so a good ability and willingness too but risking family relationships (family loan) isn’t the same as risking bankruptcy which, in turn, is not the same either as risking loosing whatever amount of money we have invested… As well, I may have the ability to take on more fiscal risk with more wealth, because I can hire an attorney, but have a much lower ability to take that kind of risk at the start of my journey.

I’m comfortable with the risk of my investments loosing value (or even going to zero). I’m not sure it’s quite the same as being willing to risk bankruptcy (taking on loans), the ability to travel aborad (investing in foreign assets I don’t know enough that may carry legal consequences in the long run) or mortgaging relationships. Which basically means that I’m not that big a believer in life cycle investing, unless one can access cheap low risk loans, which should be very hard to find because someone with the ability to loan you money to invest at a profit with low risk on the loan should be able to secure a better return for himself by investing it himself.

The bottom line of my thinking? The credit market is efficient and it’s very hard to find a truly interesting loan on a risk adjusted basis.

Oh dear, I by no means wanted to motivate anyone to invest on leverage. My observation is that many in this board go all-in on shares (when young) but carry through until old and then get crunched in a market crash as they only then realise they invested way too risky. Start with risky investments (but no leverage) and then slowly move towards a more moderated asset allocation… that is my pitch.

When we talk about leverage, we must always make sure that:

  1. we can not be called upon at the worst point in time
  2. we don‘t need to pay any volstility related risk premiums

This means no leveraged ETF (as they are daily „called“ and huge rollover losses result) nor buy options given the volatility premium. If you truly want to lever, the in my view only credible way is private/family loans, maxed out morgage (if you own a flat) or lombard credits. I would personally not do so.

Talking about the referred case. This stupid guy not only levered… but I understand he levered using funds that he could be called upon and he payd volatility risk premiums. Two no-no‘s. His third mistake was that he went for a constant stock exposure, which in a downturn can be catastrophic.

The constant exposure comes from a great idea aka balanced investments where the non-shares part is only virtual yet used as a way of anty-cyclically buying shares. But constant exposure is putting things to an extreme as it implies 99% of virtual cash investments and 1% of shares only. If he had taken e.g. 50% each, he would have not bought that bad into falling markets and his liquidity would have had probably lasted longer. So the point is that he just in any dimension went way too extreme.

Will post more structured re. Balanced investment and self-leverage thereof tomorrow… but in the meantime please do not lever yourself!


Ps: I am a fan of strong Assam tea :slight_smile:


Despite what I probably sound like, I basically get to the same point from the other side of the train thought. There’s a world of difference between the thought exercise of borrowing future money to invest it now and actually doing it: the people lending you that money are doing it to get their own profit. To them, you are the risk. They want to be compensated for it.

On a risk adjusted basis, getting a loan should not be more efficient than investing your own money (and since the other party is likely to have more time, skill and means than us when making a loan contract, they’re likely to have more ability to pull things at their advantage, so us to end up with the short end of the deal).

The story has a happy ending: 13 years later markettimer is now thinking to retire with 1.5M.
Of course, there is more to that story than lifecycle investing and I would not want to try myself that kind of extreme leverage, but I think one conclusion is that young people have the capacity to recover from liquidation of their portfolio (as the present value of their future earnings is still in the millions).

(Fun aside: Jack Bogle recommending young investors to leverage 2:1 at 5:40)

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