Can the "smart fund" smart beta strategy make big money?

Since 2000, the stock market has experienced two big bear markets, and now it shows signs of weakening. Not surprisingly, pension funds, insurance companies and endowment funds are looking for new sources of returns. "smart-beta" is the latest term in the fund management industry.

"Alpha" is the skill of choosing a single basic asset to surpass the market.

"Beta" is the relative return of a portfolio relative to the overall market (such as index funds).

The traditional "market value weighting" method is a way for investors to buy stocks or bonds in proportion to market value.

"smart beta" is an investment method, which tries to track a large class of assets and adjust the weight of component securities to obtain enhanced returns.

[Smart Beta]

As we all know, beta measures the risk premium in CAPM model relative to holding the whole market. The whole market is usually represented by a market portfolio or a market index fund. The market index is usually weighted by market value. If the market index is changed into a non-market value-weighted index or portfolio, the beta obtained is smart beta, also called alternative beta or exotic beta. The reason is that the weights of these new indexes are obtained through some quantitative algorithms, which seem to be more "smart" than the most common and simple market value weights.

Now the more popular algorithms are:

Equal weight, EW):

Risk parity can be regarded as equal rights after adjusting volatility.

Equal risk contribution (ERC) can be regarded as risk parity after considering the covariance between asset returns.

Minimum variance weighted (mv)

Maximum diversification weight

As shown in the figure below, from left to right, the parameters required by these weighting methods gradually increase. ERC, MV and MD all belong to "robust risk parity" because they consider covariance. The most classical mean-variance optimization method needs to know the expected return, variance and covariance, because this optimization method maximizes the expected return while minimizing the risk. However, it involves FAP(Factor Alignment Problem), which will be mentioned below. Smart beta strategies only consider volatility and covariance, so we regard them as strategies based on risk, not expected returns.

[random discount coefficient, SDF]

In fact, CAPM model is a famous special case of asset pricing model, because the generalized random discount factor (SDF) is represented by the narrow market portfolio in CAPM.

According to the definition of asset pricing model: p = E(mx), the price of any asset is the expected income after discount, where X is the future income of the asset and M is the random discount factor SDF. Using the definition of covariance, we get

Therefore, the price of any asset is equal to the income expectation discounted with risk-free interest rate plus a risk premium, which is the covariance of SDF and future income.

John Cochrane, an economics professor at the University of Chicago, believes that investors have "good times" and "bad times". The' bad' state generally refers to the reduction of personal wealth, which can be too much personal debt or a decrease in income. And SDF is an indicator when the state is defined as' bad'. The worse the state, the higher the index. This covariance is usually negative because most assets have high returns in a "good" state. More importantly, if the return of an asset has nothing to do with personal identity, that is, SDF (risk neutrality), then its price can only be determined by the risk-free rate (covariance is zero).

It will be more intuitive to write the above formula in the form of expected income.

The "beta expression" of expected return on assets is further derived.

In other words, people can only make profits by taking systemic risks (related to SDF). If you take a special risk, there is no benefit.

Therefore, the self-defense forces play an important role, but it only exists in theory. People try their best to find substitutes in the real world, which is the so-called risk factor. Therefore, we can also think that the greater the (systemic) risk people take (especially when the state is' bad'), the greater the factor risk premium as compensation (especially when the state is' good'). High-risk assets must have a high enough expected rate of return, that is, a low enough price to attract people to buy and hold.

[Multi-factor model]

Because we assume in CAPM that SDF is only related to market portfolio's income, market portfolio is the only factor in CAPM. On this basis, we can further assume that SDF is linearly related to many factors.

A multi-factor model is obtained. Different factors have different definitions of' bad' investor status, so the risk exposure and premium will be different. Fama-French three-factor model is a classic representative of multi-factor model. Gene Fama, the Nobel Prize winner, and Professor Ken French of Dartmouth University screened out some * * * identical features from a large number of stocks, and got two new factors: size and value (HML, SMB), forming a three-factor model. The model can accurately explain the expected return of stocks. Later, momentum factor was added to the model to form a four-factor model. Structurally, this is similar to the arbitrage pricing theory put forward by stephen ross. The only difference is that APT directly starts from the statistical level and assumes that the return on assets can be expressed by a series of factors.

[Factor-based asset allocation strategy]

Having said so much in the past, I just want to emphasize the importance of factors. It should be pointed out that the generalized asset pricing model and risk factors mentioned above are not limited to the stock market, but are applicable to any asset and capital market. It can be said that the risk factor is the root cause of the linkage between assets, and asset allocation is actually the allocation of elements.

We can compare various assets to various foods and compare various factors to various nutrients, such as vitamins. Theoretically, we can get different vitamins by eating different foods, or we can get the needed nutrition by taking vitamins directly. For example, in order to treat beriberi, people can eat more foods rich in vitamin B 1, such as cereals, kiwis and blueberries, or take vitamin B 1 tablet directly.

Just as a food contains multiple nutrients, buying and holding an asset may bring different factors of risk exposure. For example, Baidu, which is listed on NASDAQ in the United States, has a share price that includes risks in the technology sector and small and medium-sized sectors. In addition, as the company is headquartered in China, it also includes the risks of economic development in China. Of course, it may also include some other unknown risks. This is also the essence of performance evaluation in multi-factor model.

Similarly, if we only want a single risk, such as vitamin B 1 pill, we must choose assets skillfully to achieve this goal. In the Fama-French three-factor model mentioned above, Fama and French show us how to screen a large number of stocks, combine multiple stocks with * * *, and construct the required factors to imitate the portfolio. People choose different factors according to different risk preferences, so as to obtain different factor risk exposure and earn different factor risk premiums, such as momentum factor and fundamental index.

How to find new and useful risk factors is beyond the scope of this post. However, the following figure shows that the development process of asset allocation strategy is inseparable from the discovery of new risk factors. These new factors have been widely used in investment by the public.

In 1970s, people began to use portfolio in active investment management.

In the 1980s, the popularity of market index funds made it easier and cheaper for people to invest in the whole market, because CAPM model made them realize that only by taking systematic risks can they get benefits, and risks and benefits are measured by beta. And these market excess returns are measured by alpha.

In the 1990s, people were no longer confined to the single factor of the market. APT and Barra multi-factor models expand the range of factors people choose, including national and regional factors, industry factors, macro factors and so on.

After 2000, people's understanding of factors has expanded to new areas: style factors and strategy factors. For example, the scale, value and momentum in Fama-French three-factor model and Carhart four-factor model. New factors, such as arbitrage, low volatility, liquidity, fundamental factors, and the smart beta strategy introduced in this paper. More importantly, people realize that what they think of as alpha is largely unconventional beta. Industry insiders sell these beta as alpha (see "Alternative Investment" below).

With the popularity of ETF, people can more and more easily come into contact with different factors and directly apply them to investment, especially passive investment. Compared with hedge funds, mutual funds and futures, ETF has the advantages of more transparency, lower cost and lower market entry threshold. Some popular factor ETFs or smart beta ETF include: RSP (Standard & Poor's 500 Equivalent ETF), SPLV (Standard & Poor's 500 Low Volatility ETF), FNDB (Schwab American Fundamental Index ETF) and so on.

[All-weather portfolio]

When the macro factors are mentioned above, we have to mention the relevant asset allocation strategy: all-weather portfolio. This strategy is the result of long-term research by Ray Dalio, the head of Bridgewater, a well-known American hedge fund. Its core point is to combine the macro factors, economic scenarios and equal risk parity mentioned above.

The correlation between macro factors and asset returns is very low, especially in the short term, but the application of economic scenarios can make up for this deficiency of long-term investment. In addition, because ordinary investors don't like to borrow money to invest, the weight of high-risk assets such as stocks in the portfolio is higher than the theoretical optimal value. Using equal risk weights can correct this deviation.

Here, macro factors mainly examine economic growth and inflation, and thus define four economic scenarios:

(1) Economic growth rises and inflation rises.

(2) Economic growth rises and inflation falls.

(3) Economic growth declines and inflation rises.

(4) Economic growth and inflation decline.

Then, find out the relationship between the change of asset price and these economic scenarios from the historical data, so as to determine the investable assets and the corresponding weights, so that the risks allocated by the portfolio in each economic scenario are equal (as shown in the following figure). In this way, with the passage of time, the portfolio can resist the impact of various macro risks, hence the name "all-weather"

However, the all-weather combination encountered some minor problems on 20 13. With the Standard & Poor's 500 index rising by 30%, the return rate of all-weather funds in Ray Dalio is -3.9%. So the concept of all-weather investment has also been questioned. But I think one of the important functions of asset allocation is to help protect investors' wealth and guard against risks. Therefore, its advantage of risk diversification can only be shown in long-term investment, and people should not pay too much attention to short-term losses, as will be mentioned below.

[Yale model]

Yale Endowment has always been regarded as a model of asset allocation industry because of its long-term outstanding investment performance among peers, referred to as Yale model or Ivy League portfolio. The reason why the Yale model can achieve good returns is mainly because of its high allocation in alternative investments, including various private equity funds, hedge funds, venture capital, real estate and so on. In recent years, it accounts for 60% of the total investment portfolio. Yale Fund has been investing in mysterious private equity funds and hedge funds since 1990s. These funds are characterized by lack of interest and high investment entry threshold, so their income can be said to come from value factors and low liquidity factors.

Although these factors have brought considerable returns to Yale Fund, in the financial crisis of 2008, due to people's panic selling, the fund was hit hard by illiquid assets. Theoretically, this is in line with the characteristics of factor investment mentioned above, that is, the greater the (systemic) risk people take (especially when the state is' bad'), the greater the factor risk premium as compensation (especially when the state is' good').

However, after the financial crisis in 2008, the assets of Yale Fund never exceeded the highest point in 2008, although the Standard & Poor's 500 Index hit a record high. A very important reason is that the successful model of Yale Fund has been imitated by many pension institutions and small-scale university endowment funds, which has greatly reduced the risk premium of alternative investment. The Yale Foundation also acknowledged this in its annual report. However, in recent years, it can still maintain a weak advantage over peers in investment performance. The key to its success lies in finding the best fund manager to manage investment, which is also mentioned in its annual report. Unfortunately, most of these best fund managers have stopped accepting new funds. Therefore, this key to success only applies to Yale itself, and others cannot copy it.

It can be seen that Yale Fund may continue to lead the industry in the foreseeable future, but as a well-known investment model, it is impossible to rebuild its glory in the short term.

[Alternative investment is not alternative]

With the success of Yale Fund, those previously unknown alternative investments have also unveiled their mystery. Take hedge fund as an example, its high returns and low correlation attract people to study it.

The results show that the return of hedge funds can provide very limited alpha, and a large part of it comes from various beta. I have a post devoted to this phenomenon. Except for a few star funds, an important reason why most hedge funds can get returns is not because they can provide protection against downside risks. On the contrary, when the market falls, their returns are bad enough, that is, they have a large tail risk exposure. This is not the same as our previous cognition, but it conforms to the characteristics of factor investment.

Everyone may know the ten-year bet between Warren Buffett and Protege Partners, an alternative investment company. Buffett made a bet with the other party in early 2008 that "an index fund will beat a hedge fund in ten years". What's the result so far (20 14)? People with "good things" compared the two and found that Buffett's suggested investment was temporarily ahead (see the figure below)

Further research found that if we reduce the leverage of index funds and charge fees, we will actually get the same income as hedge funds! (see the picture below)

On the other hand, if you want to get the return of private equity funds, you can only increase leverage and charge fees. It can be seen that the alternative investment industry often promotes the known beta as alpha. However, with the deepening of factor research, people's understanding of alternative investment is becoming more and more profound. Alternative investment is no longer alternative.

[Re-examine Smart Beta]

After understanding the relationship between factors and assets, let's re-examine Smart Beta strategies to see if they are special. The answer is no.

Studies have shown that these clever β strategies are actually a combination of some factors. For example, the equal weight method tends to be proportional factor. This is easy to understand, because this weighting method gives small-cap stocks and large-cap stocks the same weight. For another example, the minimum variance weighting method is biased towards low beta factor and low volatility factor. However, equal risk weight method and equal risk contribution weight method are more inclined to low beta factor and scale factor.

As shown in the figure below, Smart Beta strategy and other factor strategies mentioned above all belong to a mean-variance framework, but as mentioned above, Smart Beta strategy focuses on risks, while other factor strategies focus on expected returns (risk-based and return-based). But in the end, the effect is similar, and some factors are tilted.

What is even more unexpected is that just the strategy of operating in the opposite direction with Smart Beta can actually make money. The reason is that these reverse strategies are still biased towards scale and value factors. Even a random portfolio ("gorilla throwing darts to pick stocks" mentioned many times in the famous Walking Wall Street) has a similar factor tilt (as shown in the figure below). Therefore, it is not surprising that smart beta strategies can outperform the broader market, because they bear certain factor risks.

Now that we have discussed the mean-variance optimization framework, I would like to mention the factor alignment problem by the way. This problem arises because the expected return, risk and optimization constraints in the mean-variance optimization method sometimes focus on different factors. For example, factors used to predict expected returns may not be used in the risk model. When we use the optimization algorithm, this problem is even more serious, because we may underestimate the risks of those factors, and thus overestimate the expected returns of those factors that have nothing to do with the risk model in the process of maximizing the expected returns. Fortunately, Smart Beta strategy and other factor strategies only focus on a part of the mean-variance optimization method, thus avoiding this problem.

Although the Smart Beta strategy is just a common element configuration, there are reasons why it is so popular. I think the main reasons are as follows:

(1) QE of the Federal Reserve greatly reduces the income of fixed-income assets, which makes investors have to find other investment doorways to increase their income.

(2) The panic in the financial crisis in 2008 and the subsequent QE of the Federal Reserve affected the real pricing function of the market for various assets, and the original relationship between assets was weakened. On the contrary, most assets dance with the Fed's monetary policy. The "risk on/off" mode makes the traditional asset diversification fail.

(3) Investors still remember the sharp decline in wealth during the financial crisis in 2008, so they pay more attention to risk control and prefer strategies that can control risks rather than expected return on assets.

(4) After the financial crisis in 2008, investors hope to reduce the factors of artificial manipulation in investment and prefer investment products with high transparency and simple principles.

(5) The rule-based investment strategy generated according to some algorithm or rule can greatly reduce the loss caused by people's behavioral deviation.

(6) The high fees of traditional hedge funds and mutual funds have been criticized.

Therefore, these Smart Beta strategies with clear themes, low cost and seemingly able to control risks have been quickly sought after by the public after careful packaging. At present, pension funds, university endowment funds, asset management companies, insurance companies and other institutional investors holding most of the funds in the financial market are developing in this direction, and this trend has had a far-reaching impact on people's investment philosophy.

[Market and factor risk premium]

Although factor investment has various advantages, we don't have any theory to guarantee that a certain factor strategy can always outperform the market.

In fact, what we often see is that a certain strategy or asset stays ahead of the whole market for a certain period of time, and ordinary investors immediately flock to the market through media reports and the packaging of industry professionals. Therefore, the corresponding asset prices in these strategies are driven up and the expected returns are greatly reduced until the bubble bursts and returns to the long-term moving average. Examples abound, such as growth stock strategy in the 1990s, emerging market strategy before the financial crisis in 2008, post-crisis gold, low volatility strategy, high dividend strategy and so on.

When investors hold assets, they will get a risk premium to compensate for certain systemic risks they bear. We know that the risk premium changes with time, and we don't know when it will be compensated. This is why Warren Buffett constantly encourages people not to care about temporary gains and losses, not to change their investment style at will, and to make long-term investments. Only in this way can we get premium compensation, which is a high probability event. Buffett himself proved the correctness of this idea with his experience for most of his life. If we build a multi-factor portfolio, we can make use of their advantages of stability and low correlation to diversify our investments and avoid the loss of the above-mentioned single-factor strategy. AQR, a famous American hedge fund, skillfully used these advantages to build a portfolio and achieved sustained and good returns.

The market is a zero-sum game. Any investment different from the market must have corresponding reverse investment, and in the long run, they will all return to the dynamic equilibrium point of the market. Any investment strategy (including factor strategy, timing strategy, etc. ) Trying to beat the market only applies to some people, because it requires others to operate in the opposite direction to support it. If most people in the market adopt the same strategy, then a new market equilibrium point will be formed and the investment strategy will lose its meaning. This is why alternative investments, including hedge funds, have lost their former aura after being well known by the public.

Some people worry that if a large amount of funds flow to index funds and passive investment strategies, the reduction of active investment transactions will make the market lose its function of discovering the true value of assets. I don't think so, because from the analysis of this post, we know that only a portfolio that holds the whole market for a long time is a real passive investment. In addition, other strategies or indexes different from market weight are all active investments, because they are biased by some factors. In order to keep these factors exposed, people should take the initiative to rebalance regularly (that is, always hold the assets with the strongest bias to a certain factor and discard the assets with the weakest bias). However, the control of active investment does not lie with investors, but with index or ETF management companies. In any case, active investment still accounts for the majority in the market.

On the other hand, traditional active investment (including mutual funds and hedge funds) will not disappear in the long run. Although the performance of active investment is not satisfactory, the fees are also high. As shown in the figure below, the index HFRX, which represents the overall level of hedge funds, has underperformed the simple portfolio composed of stocks and bonds for ten consecutive years.

However, investors hope to choose a better fund manager to outperform passive investment in the future. The fewer participants who actively invest, the greater the probability of winning. Therefore, despite the decline, investors still adhere to a positive investment stance. This seemingly stupid decision of investors is actually made after rational thinking.

This is the dialectical relationship between active investment and passive investment. Assuming that in extreme cases, the price of assets reflects all the information, then people have no incentive to actively seek new information. Everyone passively accepts information, and as a result, there is no information in the whole market. Then, at this time, actively looking for new information can take the lead. This relationship can be regarded as an interpretation of the Efficient Market Hypothesis (EMH). Therefore, a completely efficient market is an unstable equilibrium point that will never be reached. The market is always in a state of semi-information and semi-unity, and the number of people in the two depends on the information cost and the structure of the market itself. For example, in an immature market like China, for various reasons, the cost of obtaining information is higher, which makes it easier for active investors to obtain higher returns. However, with the continuous improvement of the market and the reduction of the cost of information acquisition, more and more investors will join the passive investment camp.

[Conclusion]

In a word, risk factor is the root cause of the relationship between assets, which describes some common characteristics between assets. The essence of asset allocation is factor allocation. It is difficult for large-scale asset allocation investment not to involve the exposure of some factors, and the characteristics of factor investment will constantly inspire people to explore new factors. With the continuous development of asset pricing theory, there will be less and less beta we don't know.