Post Modern Portfolio Theory: Engineering targeted

By Ray Dalio
The drive to solve institutional investors' two biggest problems – too much concentration in equities and too low projected returns – has prompted many more investors to ask how they can engineer portfolios to achieve specified return and risk targets. As a result, interest in and understanding of financial engineering has recently accelerated. The purpose of this article is to explain the approaches we use to engineer portfolios. In it, we break returns down into a few basic building blocks, we describe these building blocks and we show you how they can fit together. Because there are only a few building blocks that are easy to understand, and because there are only a limited number of ways they can fit together, understanding our approach to financial engineering is easy. That is also why it can be fully explained in just a few pages.
What this article will not be able to do, due to space limitations, is show you a) the substantial amount of research that that was done to stress-test these concepts and b) the various nuts and bolts steps that you could take to implement these concepts. For example, there are various ways that one can separate alpha from beta that we will not have the space to explain here. So, we ask you to focus on the principles first, and if you find them worthy of further consideration, dig deeper later.
For lack of a better term, I will call the engineering process explained in this article Post-Modern Portfolio Theory (PMPT) just because it builds on the concepts of portfolio theory, but goes a couple of steps beyond. In a nutshell, while the traditional application of Modern Portfolio Theory a) combines asset classes based on their expected returns, risks and correlations and once the asset allocation mix is determined b) picks the best possible managers of these asset classes, PMPT is different in that a) alphas and betas are separated, b) the sizes of each are altered to more desirable levels and c) much more diversified portfolios of each are derived. As a result, a PMPT portfolio will have returns and risks that are more calibrated to suit the investor's objectives and it will be much more diversified than the traditional portfolio.

Some Basic Building Blocks
Let's suppose that you want to engineer a portfolio that will have a targeted return of 10% and you want to do this with the lowest possible risk. What will you do?
Since the returns of your portfolio will be equal to the weighted average of the return streams that make it up, you will have to decide on a mix of return streams that will average 10%. The three basic building blocks that we want to break all returns into are:

q The risk free return – This is usually the return on cash, though it should be whatever rate best neutralizes your risks (e.g. for investors seeking real returns, the risk-free return is the return on inflation-indexed bonds).
q The returns from the betas – By betas, we mean the excess returns of asset classes over the risk free return. For example, if the risk free return is 2% and the expected return of equities is 7%, the expected beta of equities is 5%. So, the total return of an indexed portfolio of stocks can be broken down into the risk-free return and the beta.
q The returns from alphas – by alphas, we mean managers’ value added, which is derived from managers deviating from the betas (i.e. asset classes).

Since all returns consist of the sum of these three building blocks, and your portfolio’s return will equal the sum of these, the first step in your engineering process to achieve your 10% targeted return is to decide how much of the excess return (i.e., the return over cash) should come from the betas (i.e., the asset class returns) and how much to get from alphas (i.e. managers' value-added). This is not a question that can be answered quantitatively. It is more philosophical. That is because while betas and alphas both provide return streams, they are very different.
Betas (i.e., asset classes' excess returns) are limited in number (i.e., there are not many viable asset classes), they are typically relatively correlated with each other and their excess returns (i.e., returns above cash) are relatively low compared to their excess risks (i.e., their Sharpe ratios are typically between 0.2 to 0.3). But they are reliable - i.e., we can be confident that it will be profitable to hold them instead of cash, over long time horizons.
Alphas (managers' value-added), on the other hand, are plentiful, they are relatively uncorrelated with each other, but their returns are unreliable - i.e., their risk-adjusted returns are slightly negative on average and the range around this slightly negative average is very large, even over long time horizons.
The expected risk-adjusted returns of alpha are slightly negative because a) value-added is zero-sum - i.e., in order for one manager to add value, another one must lose - and b) there are transactions costs and fees. However, the range of risk-adjusted returns around this slight negative average is enormous because, in this zero-sum game, the smart managers take money away from the dumb ones, so some managers can produce very high return/risk ratios and others produce very bad ones. These characteristics of alpha make the rewards and penalties of a) choosing managers and b) balancing their alphas well or poorly, very large. Unlike the returns that come from beta (i.e., holding asset classes), which you can be confident will be positive over time regardless of which you choose, the returns from alpha might be negative if you do not choose wisely. But, if you select well, you can create a much better portfolio of alphas than you can of betas because you have many more, less correlated and more attractive return streams to combine in an efficient portfolio.
So:
q While the ability to create an efficient portfolio of betas is constrained by the limited number of them and their relatively high correlation, the confidence that you will eventually have a positive result, even if you choose poorly, is high; and
q While the ability to create an efficient portfolio of alphas is great because of the large number of them and their relatively low correlations, the penalties for choosing poorly are large.

In order to get a targeted return (e.g., 10%) that is higher than that which can be locked in via market pricing (e.g., 5%), one must take some risk. The question is, which risks are you most comfortable taking? So, the first decision you have to make in determining how to engineer the optimal portfolio to meet your objective (e.g., a 10%-year expected return) is how much risk do you want to take via the beta and how much risk do you want to take via the alpha.
If you are very comfortable taking beta risk and uncomfortable taking alpha risk, because you don’t feel confident about your ability to pick a portfolio of active managers that will add value, you might decide to engineer your portfolio to only have beta risk, in which case you will have to engineer the "beta portfolio" to have 100% of your targeted return (e.g., 10%. Or, if you think you can do an excellent job of picking managers who can add value, you could choose the opposite path - i.e., have no beta risk and to try to engineer your "alpha portfolio" to produce 10%/year.
Most investors have a mix that they have backed into, and it is dominated by betas (especially equities). Because the money given to an asset class typically determines the active manager chosen, the heavy commitment of assets to equities typically results in the alpha being dominated by equity managers. So, typically the portfolio that is derived through the traditional path a) has much more beta risk than alpha risk (typically about 95%/5%), b) has the beta dominated by equities (e.g. the typical pension fund is 95% correlated with equities) and c) has the alpha dominated by equity managers. It is anything but a diversified portfolio. In the PMPT approach, this mix of beta and alpha is explicitly chosen and both the beta and the alpha portfolios are much better diversified.
While there is no right mix between betas and alpha (for reasons previously mentioned), I believe that we will see, indeed we are seeing, a significant shift in the mix to increase alpha’s share. However, as mentioned, alpha is zero-sum, so choosing more alpha won’t necessarily increase returns; in fact, for about half the population, it will lower returns. I am confident that those who are smart at finding and balancing alphas will be in much demand in years ahead because there will be more demand for alphas, and because those who know how to a) find managers who can produce positive alphas and b) balance these alphas into efficient portfolios will be able to produce extremely powerful results. In any case, the disparity of results in alpha portfolios will be enormous. I also believe, for reasons explained later, that good managers' alphas will improve because investors will increasingly allow them to balance their bets better.
In the next two sections, I explain how we construct Optimal Beta and Optimal Alpha portfolios. I want to emphasize, that I am offering a menu of choices; you can pick some and reject some.

The Optimal Beta Portfolio
(i.e., Asset Allocation)
The goal of the Optimal Beta Portfolio is to create a diversified portfolio of asset classes that together have an average expected return that meets your requirements. So, suppose that you want to achieve a 10% targeted return solely through beta (i.e. without any alpha) and the risk free return is 2%, then you will need a beta portfolio that has an expected excess return of 8%, and you will want it to be highly diversified.
Chart 1 shows an example of one consultant’s expected risks and returns of various asset classes. While everyone’s is a bit different, they are all pretty similar in that riskier assets are usually expected to have higher returns. So, while asset classes have quite different expected returns and risks, they have similar risk-adjusted returns. I believe that the main reason they have similar risk-adjusted returns is because they can be made “competitive” with each other and “arbitraged” through leverage. In any case, because the expected returns and risks of asset classes look something like that which is shown in the charts, investors seeking returns that are higher than are available from the low risk assets tend to buy as much of the high returning asset classes (particularly equities) as they can stand, and then sprinkle in some of the others (mostly bonds) for diversification. In our example of trying to come up with a portfolio that has an expected return of 10%, if we follow the traditional path, we would be forced to buy assets that are in the upper right portion of chart 1, with expected returns that average about 10%/year. As a result, our portfolio would not be diversified. So, we would have an awful lot bet on one or two asset classes delivering the expected returns, with the expected risks, in the time frame that is acceptable to us. Personally, that would make me very uncomfortable.
However, we can alter the sizes of these asset class’s returns and risks to make them more suitable. Probably the investment assumption that most investors are most confident in is that asset classes will outperform cash over time. There are two reasons for this – 1) the capitalist system is based on it (i.e. the central bank creates cash and those who have good uses for it will borrow and use it to derive a higher return) and 2) investors want to be compensated for risk. Since the risk-adjusted returns of these asset classes are broadly similar (and not reliably known), and since their expected returns are greater than that of cash, the expected returns and risks of these asset classes can be made similar, and can be adjusted to deliver returns that are closer to what we are targeting (e.g. 10%) through leverage or leveraging-like techniques.
For example, by borrowing cash to leverage up lower returning asset classes (and deleveraging asset classes that are higher returning than equities) so that they have the same expected volatilities as equities, the expected returns of these asset classes can be made similar to equities. Chart 2 shows the returns of these asset classes after leveraging and deleveraging them to have the same volatility as equities. As shown, their returns are similar and all of their Sharpe ratios fall in the 0.2 to 0.3 vicinity.
The only difference between the returns shown in the first chart and those shown in the second chart is due to packaging. For example, it is a very simple task to create structured products that convert asset classes as shown in Chart 1 into asset classes as shown in Chart 2. In fact, equities are essentially a leveraged asset class in this way in that within most companies there is debt that causes equity returns and risks to be higher than they would be if these weren’t leveraged. In fact, if companies weren’t allowed to leverage, the expected returns and risks of equities would be lower than they are now. The point is, the selection of asset classes that investors can choose from can easily be altered so that a) rather than having very different expected returns and risks, they can have similar expected returns and risks and b) these expected returns and risks can be adjusted to meet investors’ objectives. Or, in our case of trying to derive a 10% expected return (let’s say, solely through beta), I could leverage all of these asset classes up so that their expected returns are all about 10%.
If investments happened to come packaged in the second form (shown in Chart 2) rather than the first (shown in Chart 1), the asset allocation mix one would choose would look very different. There would no longer be the compelling need to concentrate so much money into equities to get the high returns because the expected returns of all of the choices would be similar (in fact, they can be leveraged to be identical). So, the portfolio can be much better diversified. Further, because the expected returns can be adjusted, this diversified portfolio can have a targeted return that is consistent with your target.
This concept - i.e., that most asset classes can be levered to produce similar and higher targeted returns so that you can create a well-diversified portfolio with expected returns that are consistent with your objectives - requires you to only believe that the expected returns of the asset classes chosen are above cash. If that’s the case, then you know that the expected excess returns and risks of these asset classes can be adjusted through leverage. Once you know that you have this ability, you can then decide what you want to do with it – i.e. you do not have to accept asset classes’ returns and risks as they come pre-packaged as in Chart 1.
Once the asset classes you choose are adjusted to have returns and risks that are similar to each other, the main difference between these asset classes will be their correlations. For example, if we leverage up all the asset classes to have expected returns that are about the same as equities, a diversified portfolio of these assets will have an expected return that is about the same as equities, but with much less risk than either equities or the "typical portfolio" that is a skewed mix of equities and other investments. That is because all of the investments have the same expected return as equities, but they diversify each other much better than the "typical portfolio" (which has a lower expected return than equities because it contains lower returning assets and also has more risk because it has a high concentration in equities).
What this process has done is a) eliminated the traditional trade-off between risk and return that was conveyed in Chart 1 and that drove you to concentrate so much of your portfolio in equities, and b) allowed you to create a diversified portfolio of assets that have targeted returns that are consistent with your objectives. There are also many more benefits (e.g. substantially reduce fat tail risk) that would take more space than I have to explain in this article..
However, in summary, a traditional portfolio that combines asset classes that individually have Sharpe ratios of 0.2 to 0.3 typically yields a portfolio Sharpe ratio of about 0.4, with an expected return that is lower than equities. Typically, these traditional portfolios are also about 95% correlated to the equity markets (because most of the money is invested in equities and the volatility of equities is much larger than the volatility of the other asset classes). However, by combining the repackaged assets that still have information ratios of 0.2 to 0.3, but have expected returns equaling equities (or your targeted return), the portfolio Sharpe ratio is about 0.65 with an expected return that equals equities (or your targeted return) and that is uncorrelated with any single asset class. The increase in the portfolio’s expected Sharpe ratio from about .40 to about .65 implies about a 65% increase in the portfolio’s expected excess return, if the risk levels are kept the same. For a portfolio that has a 10% annual volatility, we estimate that this higher Sharpe ratio implies a 2.5% per year higher return than a conventional portfolio. In other words, by following the PMPT approach to asset allocation rather than the traditional MPT approach, a) one can achieve a 10% targeted return while holding a diversified portfolio of assets and b) one can substantially raise one’s returns without increasing one’s risks.
What’s the risk? Leveraging-up asset classes to have the same expected returns (as equities or as your target), and then holding a balanced portfolio of them, creates a different type of risk than holding a traditional portfolio (which has lower expected returns and more concentration in equities). Whereas the risk of the traditional portfolio is largely a function of the risk of equities, the risk of this portfolio is that other asset classes will, on average, under perform cash. We are very comfortable with this risk for the previously explained reasons, especially as it was stress-tested in the tightest money period of 1980-81. Further, the amount of leverage required to create a portfolio this way is typically very little. If investors can get used to looking at leverage in a less black and white way (e.g. “no leverage is good and any leverage is bad”), they will be able to understand that a moderately leveraged, highly diversified portfolio is considerably less risky than an unleveraged, undiversified one.

My All Weather portfolio
Following this approach, I created my own portfolio eight years ago. I did this to put my family trust money in. So it consists of that mix of return streams that I must decide on and stick with essentially forever. Because alphas require the talent of those who are doing manager selection, and I couldn't be assured of having this after my death, I wanted it to be based on 100% beta and geared to produce an equity-like return. I call the strategy “All Weather” because it is designed to perform equally well in all environments. Table 1 shows the real-time returns of that portfolio since I started investing in it.
Shown in Table 2 are the simulated historical results since 1970 of the All Weather strategy based on the asset mix that one of our pension plan clients has, with a 10%/year targeted return. We show its results in relation to those of a 60/40 S&P 500/Lehman Government-Corporate mix. As shown, the All Weather strategy calibrated at this level would have the same return as the traditional portfolio with less than 60% of the risk of the traditional portfolio, and drawdowns were far smaller than those of the standard 60%/40% asset mix over one and two-year time frames. Because the All Weather strategy has a substantially better Sharpe ratio (i.e., excess return/risk) than any of the alternatives, it could have been calibrated to deliver a) higher returns with the same, or less risk, or b) the same returns with lower risk, than any of the alternatives. Chart 3 below shows the accumulated returns above cash (US 3-month T-bill rate) over the last three years for an actual All Weather mandate with the same asset mix.
So, that is how we create “Optimal Beta”. As mentioned, the basic concepts are very straightforward. So, think about them and if they are interesting enough to pursue further, dig deeper.

The Optimal Alpha portfolio
The basic principles behind the Optimal Alpha Portfolio are the same as those that are behind the Optimal Beta Portfolio – i.e., to create a well-diversified portfolio of uncorrelated return streams that are calibrated to balance each other and to deliver a target return. The only difference is that we are applying these principles to alphas instead of betas.
There are two different ways that Optimal Alpha Portfolios can be created. The first, and currently the most popular, is via Alpha Overlay; the other is to create a total portfolio of all alphas, regardless of the asset classes that they are generated in. In both cases the alpha chosen is independent from the beta and is overlaid on the beta.
For example, in Bridgewater’s providing alpha overlay, each client chooses their benchmark/beta (we now manage to 26 different benchmarks), which we replicate, and then we overlay our “Pure Alpha” on top of it. The client specifies the targeted tracking error (risk) at which we should run the alpha. When following the second approach, to creating an Optimal Alpha Portfolio, all managers’ alphas are looked at as return streams and combined into one alpha portfolio. While we think that the second approach is best, both approaches lead to significant improvements from what is conventionally done. In either case, most of the basic concepts are the same, so let's get into them.
The total return of a portfolio equals the return of the asset classes invested in, plus the managers’ alpha. That is equally true if the alpha produced is in the same markets as the asset class or in other markets. As a result, a portfolio constructed by independently choosing the asset class (beta) and the alpha is no more risky than one managed by following the traditional approach (i.e. with alphas coming from the same markets as the betas). However, by being able to choose alphas from wherever they are best obtained, and by being able to create a much more diversified portfolio of alphas, much better risk-adjusted alphas can be produced through a properly executed alpha overlay strategy.
The traditional approach to investing typically leads to an undiversified portfolio of relatively poor alphas because the alphas are tied to the betas, rather than being chosen on the basis of what is best. For example, because most traditional investors have the most amount of money invested in domestic equities they have the most amount of alpha coming from domestic equities. Not only is the alpha portfolio undiversified because too much of the alpha is coming from domestic equities, but domestic equities is one of the toughest markets to generate alpha in, so the alpha is smaller than it would be if alphas were chosen on their merits, without the link to the asset class.
Picking the best alphas and creating a diversified portfolio of them, whether that is achieved by allowing each manager to diversify his alphas or by using many managers’ alphas to create a well-diversified total portfolio of alphas, will yield radically better results than the traditional portfolio. To convey the concepts, compare the results of Alpha Portfolio 1 and Alpha Portfolio 2 in chart 4. Each pie represents 100% of the opportunity set and each slice of the pie represents one alpha sources as a percent of all of the alpha sources. In our example, the average information ratio of each slice of both pies is 0.35. So, the alphas in Alpha Portfolio 1 and Alpha Portfolio 2 are equally good. However, because there are more alpha sources that are better balanced and less correlated in Portfolio 2, the information ratio of the second portfolio is about 2.5 times as good as the first one.
In other words, the greater diversification that arises from being able to have more sources of lower correlated alphas (that are balanced better) can lead to a much higher return per unit of risk. Since alphas can be calibrated, you can choose whether to use this improved ratio to derive a higher expected return with comparable risk, or a lower risk with a comparable return. This principle is equally applicable in allowing a) each manager to create his diversified portfolio of alphas over a single benchmark/beta in the first type of alpha overlay or b) creating a portfolio of manager alphas (i.e., the second type of overlay). In the case of the alpha overlay manager (i.e., the first type), the manager’s ability to create a well-diversified portfolio of his alphas is greater (because he is free to get them from many places and to balance them well), which gives him a tremendous leg up on the traditional manager who cannot diversify and balance his alphas as well. In the case of creating a total portfolio of many different managers’ alphas (i.e., the second type), the investor’s ability to choose good managers’ alphas and to balance them well is enhanced (because of not being confined to having them tied to the betas), which provides a comparable leg up on the traditional investor who forces them to be tied together.
We have found that by following this general approach to generating Optimal Alpha, portfolios’ information ratios have been able to increase by factors of two to four times. So, in summary, we believe that by a) being able to better balance the amounts of returns that come from alpha and beta, b) creating more diversified beta portfolios that are calibrated to one’s targeted returns and c) creating better and more diversified alpha portfolios that are also calibrated to one’s targeted returns, investors can radically improve their portfolio’s results.

The Future of Investment Management
We believe in the inevitability of evolution, and we believe that this PMPT approach to structuring portfolio is substantially better to the more traditional MPT approach. So, we believe that the investment management industry will quickly evolve toward having two broad types of investment managers – those who efficiently create betas and those who are alpha generators. Many of the alpha generators will replicate the betas and throw them in free of charge (as we do now). Alpha generators will produce their alphas in the best ways that they can, unconstrained by not having to link them to betas, though they will be more constrained by sensible controls (e.g. controls that limit their concentration risks or their VaRs). These alpha managers will also adjust the sizes of their alphas to suit the client’s tastes – e.g., one client might choose a 3% tracking error while another might choose 6%. And all alpha managers will compete with each other, without regard for the betas. For example, rather than “equity managers” competing with other “equity managers” in the investor’s equity piece of the pie, all alpha generators will compete with each other for the whole enchilada.
Hedge funds are making progress along these lines (because they have the most freedom to properly engineer their alphas), and they are helping to foster change throughout the investment industry (because investors are having to ask themselves if they should let their traditional managers operate by rules that are similar to their hedge fund managers’ rules), but they will change too. In this new paradigm, investors will realize that there is no such thing as a hedge fund asset class. When one makes an allocation to hedge funds, one is really investing into a bouillabaisse of different betas and alphas, but mostly alphas. These alphas can be overlaid on top of just about any asset class. For example, an investor can compare the alternative of having his domestic equities (e.g. benchmarked against the S&P 500) managed by a) a domestic equity manager who has a tracking error of 4% or b) buying S&P 500 futures and investing 50% of his money in a hedge fund-of-funds that has a tracking error of 8%. So, traditional managers, hedge fund managers, and alpha overlay managers will all compete to be the ones who produce the best alphas.
I believe that these changes will happen very fast and profoundly change investing and the investment management business.

Ray Dalio is chief executive of Bridgewater Associates, based in Westport, CT.


Table 1: The performance history provided above is based on the returns of the Bridgewater “All Weather” strategy implemented for Bridgewater's principals. The performance provided is gross of fees and includes the reinvestment of all interest, gains, and losses. Returns will be reduced by investment advisory fees and any other expenses that may be incurred in the management of any portfolio. No representation is being made that any account will or is likely to achieve returns similar to those shown. Trading in futures is risky and can result in losses as well as profits. PAST PERFORMANCE IS NOT NECESSARILY INDICATIVE OF FUTURE RESULTS


Table 2: HYPOTHETICAL OR SIMULATED PERFORMANCE RESULTS HAVE CERTAIN INHERENT LIMITATIONS. UNLIKE AN ACTUAL PERFORMANCE RECORD, SIMULATED RESULTS DO NOT REPRESENT ACTUAL TRADING. ALSO, SINCE THE TRADES HAVE NOT ACTUALLY BEEN EXECUTED, THE RESULTS MAY HAVE UNDER - OR OVER-COMPENSATED FOR THE IMPACT, IF ANY, OF CERTAIN MARKET FACTORS, SUCH AS LACK OF LIQUIDITY. SIMULATED TRADING PROGRAMS IN GENERAL ARE ALSO SUBJECT TO THE FACT THAT THEY ARE DESIGNED WITH THE BENEFIT OF HINDSIGHT. The performance provided is gross of fees and includes the reinvestment of all interest, gains, and losses. Returns will be reduced by investment advisory fees and any other expenses that may be incurred in the management of any portfolio. No representation is being made that any account will or is likely to achieve profits or losses similar to those shown. Trading in futures is risky and can result in losses as well as profits. PAST PERFORMANCE IS NOT NECESSARILY INDICATIVE OF FUTURE RESULTS.


Chart 3: The performance history provided above is based on the returns of the Bridgewater "All Weather" strategy implemented for Bridgewater's principals. The performance provided is gross of fees and includes the reinvestment of all interest, gains, and losses. Returns will be reduced by investment advisory fees and any other expenses that may be incurred in the management of any portfolio. No representation is being made that any account will or is likely to achieve returns similar to those shown. Trading in futures is risky and can result in losses as well as profits. PAST PERFORMANCE IS NOT NECESSARILY INDICATIVE OF FUTURE RESULTS