Lord Kelvin's dictum on measurement - applies to finance

 

“When you can measure what you are speaking about, and express it in numbers, you know something about it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts advanced to the stage of science.”  - Lord Kelvin's dictum 

This is a good rule to follow in any financial work, yet once you are done measuring, you have to focus on what cannot be measured and make some conjectures for what is not explained.

As an aside:

Ogburn, a onetime head of the Social Sciences Division, was also responsible for perhaps the most contentious carving on campus. Curving around an oriel window facing 59th Street is a heavily edited quote from Lord Kelvin: “When you cannot measure, your knowledge is meager and unsatisfactory.” Ogburn was a hearty proponent of quantification in the social sciences, a view that some of his colleagues definitely didn’t share. In a 1939 symposium, economist Frank H. Knight Jr. (a teacher of Milton Friedman, AM’33) snarkily suggested that the quote be changed to “If you cannot measure, measure anyhow.” Fellow economist Jacob Viner chimed in with a suggested addendum: “If you can measure, your knowledge is still meager and unsatisfactory.”

"NIllius in verba" - "take nobody's word for it" especially in finance

 

The motto of the Royal Society, which is the science academy of the United Kingdom has a useful motto "Nillius in Verba" which is Latin for "take nobody's word for it". Science is not settled but is dynamic and to disprove the conjectures of the present. 

This motto is a useful guide for assessing all of the ideas and works that are done in economics and finance. Do not follow the story, follow the numbers. Live in a skeptical world when there is money involved. 

Categorize EM before running analysis

There are several ways of classifying emerging markets. JP Morgan Wealth Management has looked at a system of three key factors: economies with a large private sector which focuses on making money in a competitive environment; economies where companies generate high earnings per share; and economies with strong and growing export industries. The likelihood of success should be higher with holding country exposure in these economies. It does not guarantee success, but these are the countries which have a good environment for generating higher returns. There are five countries in this intersection. Four are in Asia and one is our southern neighbor. More focus should be spent on studying the dynamics of these countries. 

The weak link between EM returns and growth

Focusing on macro relationship and how they can be exploited in a model, we have looked at the relationship between growth and equity returns. We have been disappointed by the fact that the link has varied significantly across countries. In places like the US and Japan, equity returns have far exceeded nominal GDP over the last 15 years. In many other countries, GDP growth have exceeded equity returns. These numbers will be impacted by the percentage of companies within a country that have global business, but there is the impression or assumption that there should generally be a positive link between GDP and returns especially in the long run. Simple data does not suggest a link and deeper analysis is necessary. 

China GDP and investor returns - the big disconnect

 

The large macro disconnect in China is between its significant growth earnings, and stock returns. If we just look at China growth since 2010, we will see that the size of the economy increased by a factor over 3x. Earnings have increased, but little has changed in the last ten years. The stock market is almost flat since 2010. This is not the story that investors expected. Of course, the macro link between GDP and stock performance is far from perfect, but if you were given the growth numbers, most investors would have expected strong returns especially given the strong China export numbers. The negative view toward China is closely associated with the poor quality of this macro link.

The big rate breakout in historic context

 

There are short-term, medium, and long-term trends, but these are all usually inside a half a year for most trend-followers; nevertheless, it is good to focus on the very long-term to get a sense of the regimes that dominate the market view. If you look at trends over the last few decades, you will the great upward move of the 70’s and the 40+ year downtrend. The shorter-term cyclical credit trends show rates going up only with the market being hit with crisis which causes a reversal. Each shorter-term peak is at a lower high, but the chart is not the end of the story because we have not included the added two year period to November 2024. Look at the current level of 4.30 is way outside what anyone was thinking given the long trade. The last two years has been the great bond yield breakout and is nothing like we have seen in terms of a reversal of the bond channel. Discussion should always start with the new world bond view. 

The dollar trend is consistent with macro trends

The Fed is easing albeit less than what was expected eve three months again and the rest of the world seems to be willing to ease more than the US. The result has been a stronger dollar that is on the high end of the range for the last two years since the easing cycle began. This does not seem surprising. The US economy is stronger than expected, inflation has come down, and longer-term interest rates are more attractive to foreign investors. There is little reason for a dollar reversal even without accounting for tariffs and a new administration.

The dollar trend is consistent with macro trends with provides more confidence in this price move. 

The link between earnings, market returns, and GDP is not strong

One of the key problems with macro equity investing is that the link between earnings growth, market return and GDP growth are not often in lockstep. The chart shows that in the US earnings and market growth has been significantly higher than GDP growth, yet in many countries earnings and market growth have not been able to keep up with GDP growth. The link between GDP forecasting and market and earnings forecasting is not strong. You can be a great macro forecaster but that does not translate into making money in the equity markets.

Fractal Markets Hypothesis as an alternative to efficient markets

 

We know that the efficient markets hypothesis as originally positioned by Fama is not true. The behavioralists put a stop to the idea that markets are always rational and embed all information in prices, so good science requires an alternative hypothesis or a different way of thinking about how markets use information and generate price dynamics. We have earlier mentioned one alternative "The Discovering Markets Hypothesis - Worth a close look to add to our thinking of market dynamics" which focuses on how competing narratives impact prices. Another alternative has been developed by Edgar Peters who focuses on fractals and the fact that different investors have different time horizons that change with uncertainty. The fractal approach has merit when looking for regime shifts but may be harder to explain the day-to-day movements in price. The work of Peters has been around for some time yet has not taken hold. Neither has the work associated with Discovering markets. We will have to wait while further work is developed. 

The Fractal Markets Hypothesis of Edgar Peters states:

1. The market consists of many investors with different investment horizons.
2. The information set that is important to each investment horizon is different. The longer-term horizons are based more upon fundamental information, and shorter-term investors base their views on more technical information. As long as the market maintains this fractal structure, with no characteristic time scale, the market remains stable because each investment horizon provides liquidity to the others.
3. When long-term investors begin to question the validity of their information, their investment horizon shrinks, making the overall investment horizon of the market more uniform.
4. When the market’s investment horizon becomes uniform, the market becomes unstable because trading becomes based upon the same information set, which is interpreted in a more uniform way. So good news causes increased buying while bad news results in increased selling.
5. Liquidity dries up, causing high volatility in the markets, because most of the trading is on one side of the market.
6. Eventually the long term becomes more certain and stability returns to the market as investment horizons broaden and become more diverse.
7. During periods of low uncertainty, markets will exhibit well-behaved, finite variance statistics. In high uncertainty environments, markets will exhibit fat-tailed risks and unstable variance more associated with the stable Paretian distribution as described by Mandelbrot (1964).

"Inflation is a social phenomenon" - Not quite

"Inflation is a social phenomenon," Powell said. "If people believe that inflation will be higher, then it probably will be. And if they believe that inflation will come down, then people who make and take prices and wages, they will make sure that it does come down. So, it's absolutely critical that we be credible."

- Powell press conference 

Should we give him the benefit of the doubt or just call out the craziness of this comment. Of course, inflation is effected by expectations but where do those expectations come from? Perhaps the Fed itself as the the producer of money! 

You cannot just say that if you believe something, it will happen. Are expectations always rational? No. is a component of inflation expectations backward looking? Yes. However, if you are the head of the Fed, you have to take responsibility for your actions.  

The Discovering Markets Hypothesis - Worth a close look to add to our thinking of market dynamics

There are alternative views on how markets operate that are different from the efficient markets hypothesis which has taken a beating since the development in behavioral finance. Andrew Lo came up with the concept of Adaptive markets, but Tom Mayer and Marius Kleinheyer have developed an alternative called the Discovering Markets Hypothesis (DMH) which is based on three key points. Information held or learned by investors should be viewed as subjective not objective knowledge and this knowledge is adjusted when it compared against the behavior of others. Investors will communicate with others to cross-check their subjective knowledge. The communication of knowledge is through narrative. Narratives compete through their influence on prices. 

Facts influence subjective knowledge which is then shared with others through narratives. These narratives compete with others through their influence on prices. Prices, of course, will then provide feedback on the quality of the narrative. As subjective knowledge changes, there will be an impact on prices. Facts or new information will drive the changes in subjective knowledge. Because subjective knowledge cannot be counted or measured with certainty, there will be inherent uncertainty in markets which will cause prices to change in ways that are not always expected. 

The wild card for bond yields - the term premium

 

Treasury yield have moved higher while the Fed has lowered interest rates. This was not supped to happen. The question now is determining what is the fair value for Treasury yield out the curve. The usual method is to determine the real rate of interest which usually is about 2% plus some estimate of expected inflation which can be argued to be at level above 2%. So, if we use a real rate of 2% and an inflation rate of 2.5% we are at 4.5% as a good starting point; however, we need to add a term premium for the risk from holding these bonds out the curve. That number has been negative for an extended period but is now positive and rising. The current term premium is at the highest level in over a year; however, a longer history suggests that it can increase by a multiple of the current levels. One reason could be the lower liquidity in Treasuries, yet the recent fall is not seen in the term premium. Forecasting the term premium is now the Treasury yield forecast will card. 

Trend-following with industry groups - It works

 

In the paper, "A Century of Profitable Industry Trends" the authors explore long-only trend following for a 48 industry portfolio for just under a one hundred year period. They find that the simple trend timing strategy will lead to higher returns, lower volatility, higher Sharpe ratio and less downside risk. This strategy is easy to implement and is shown to work with sector ETFs with a smaller portfolio of 31 industries. The numbers are compelling and again show that a trend strategy can be effective. The strategy is effect with equal weighting, timing and sizing allocations. It may not work during every period, but the long run return beat the simple strategy of holding the market portfolio.

There is no equity risk premium!

There are several ways of measuring the equity risk premium. The above chart is a simple approach, and it shows the premium is at levels not seen since the dot-com bubble. Other approaches may show the premium slightly higher, but all are signaling that we are are at low levels which suggests that forward returns are likely to be lower.  

This is not saying returns will be negative in the next year nor does it say we will have a crash. It is saying that your long-term allocation to stocks is unlikely to generate returns similar to what were present over the post-COVID period. 

Replicating trend-following beta is achievable

 

Trend-following strategies have proved to add significant value to a portfolio, but there is a problem - what model or managers should I use to represent my trend exposure? This issue is discussed in the paper, "In pursuit of trend-following beta: The promise and pitfalls of replication".

Building your own trend model will have problem because here is a wide dispersion in the performance of different trend strategies. How do you pick the best strategy. However, there also is a problem if you want to pick specific managers.  There is wide dispersion across managers. The alternative is to hold an index or attempt to replicate a well-defined index like the BTOP50; however, any replication scheme has issues. One choice is to form a portfolio of managers, but there are ongoing costs with this fund of funds structure. An investor may be able to cut costs with forming a portfolio strategy replication; however, there may be skill leakage. You will not be able to capitalize on the stronger behavior of better managers.

The authors conduct a useful exercise on how to develop a replication strategy using a limited number of markets and simple OLS regression or LASSO regression. While not perfect, the cost savings with careful regression work can add value relative to a trend-following benchmark (more precisely a portfolio of CTA that are mainly trend-followers). My experience suggests that replication is not always easy. There are operational costs that can be high if there is not scale, but the idea of forming a cheaper replication of a manager bundle is useful and can add serve as an alternative to picking a bundle of managers.

VIX and corporate bonds

 

There is risk in corporate bonds and this risk can be measured through the VIX market. Equity and bond markets are linked. This should not be surprising since the corporate structure can be divided in equity - the residual value of the firm which is call option and bonds which are a short put option on the firm value. A change in volatility will lead to a change in the value of these options. If the VIX serves as a proxy for equity volatility, then there should be a link with bond spreads which are the added risk above Treasuries for holding corporate bonds.

The authors of an early draft paper, "The VIX as Stochastic Volatility for Corporate Bonds" show that adding the VIX to a time series model of corporate spreads will improve the time series model. First, the residuals of corporate bonds spreads are not Gaussian white noise; however, if you scale the residuals by the VIX to standardize, you will get an improved model. The spikes in spread are dampened when they are scaled by equity market volatility. This is a simple model and test, but it serves as an important improvement over looking at just the simple time series of spreads.

The economic of information - a history which leads to narrative information

 

The economics of information have made many advancements since the theory of market efficiency. The current direction of information economics is to link narrative economics with market sentiment and returns. This chart is from Ronnie Sadka of Boston College from his work with State Street on market narratives. There are several media-driven reservoirs that can be used to generate narrative information. There is information intensity as well as news sentiment. Once we have isolated information, we can look at dispersion, disagreement, and content. From the narrative information portfolios can be formed with narrative sensitivity. 

Ways of thinking about news narrative that can be quantified.

Trend-following with stops reduces drawdowns

 

A core question with any trading strategy is whether or not to use stops. The answer is not always clear. It is clear that having stops too close will reduce return because  many good positions are lost to reduce risk, it is often an empirical question of the value of this risk management tool. A recent paper set-up a simple model across all major assets classes to determine the value of stops. This work is not definitive and is just an example, but it does add to the discussion.  See "Cross-asset trend following algorithm".

I will not go through all of the assumptions to get these results, but the base model represents a long-term trend model based on a moving crossover model using 50 and 100 days with stops based on a multiplier using the average true range. The data includes 39 assets over a 32-year period.

For the long/short portfolio there is a slightly lower Sharpe ratio when stops are used, but there is a significant decline in the maximum drawdown. A stop-loss will not support higher returns. A review of the cumulative returns chart shows a marked difference in the return pattern.

Risk cycles and the business cycle - Form low risk comes growth but also greater credit risk

There is a business cycle, a credit cycle, and a risk cycle. These are all connected. In the paper, "The impact of risk cycles on business cycles; a historical view" the identification of the risk cycle is used to generate statement on growth, risk-taking, and the potential for crises. 

The authors show that a perceived low risk environment will encourage risk-taking which will support stronger growth, but with this growth comes greater financial vulnerabilities, that is, there will be a reach for more risk and for higher leverage. The duration of low-risk impacts growth.

Increasing financial vulnerability will lead to a reversal of growth when these risks are realized. From a low-risk cycle comes a growth upturn which creates excess credit growth. If this happens on a. global the impact on growth will be stronger because there will be grater movement in global capital flows. 

This is another way of saying that Minsky behavior can be measured through a risk cycle.

VIX and the equity markets - equities drive volatility

 

We know that there is a correlation between the VIX and SPX. A spike in volatility will be associated with lower equity returns, but the next question has not been fully explored. What is the direction of causality? A recent paper looks at this specific question, see "Which way does the wind blow between SPX futures and VIX futures?". The authors look at Granger causality tests with the method of identification through heteroskedasticity and find that the SPX futures is causally prior to the move in VIX futures. There will be a shock in new information that impacts the equity futures which then moves to the volatility futures. The authors do a good job of looking more closely at the data across some key time periods to find the correct causal relationship. 

Trend-following in high and low rate regimes

We know that trend-following can add to a portfolio mix of equity and bonds even with bonds being a diversifier; however, there is a question on whether trend-following will add value when rates are high. We know that bond volatility will be higher when rates are higher, but if you can get a higher rate, it provides a hurdle that the trend manager must overcome. For the trend-following to work it must be better than the bond rate and bond returns. The folks at Quantica Capital have another take on this issue in their piece "The Additional Benefits of Trend-following when rates are high". They find that at high rates, the correlation between stocks and bonds increase. If that is the case, there will be a good reason to give a higher allocation to the trend-following diversifier. 

The study focuses on three charts. The first chart sets the stage through showing the return, risk and correlation for stocks and bonds and shows why you should diversify over these two assets. The next figure shows trend-following return and risk in low and high-rate environments as well as the correlation between stocks, bonds and trend-following. Note that trend-following is more volatile in high-rate environments. It is also has slightly lower returns, but the correlation is very different. Trend-following is less correlated to stocks and bonds in high-rate environments, so there is greater benefit for trend-following in a portfolio. 

If rates are above average, then a simple optimizer will show that you should have on average an increase to trend-following of almost 3x versus a low-rate environment. This is easy to do and should be considered by many allocators.

Using our experiences is not always good

 

Follow our experience because as we gain more experience, we become better at making decision. Our wisdom comes from our experience. The Myth of Experience: Why we learn the wrong lessons and ways to correct them by Emre Soyer and Robin Hogarth is another take on behavioral mistakes and the problems of psychology on our decision-making. Their conclusion is that we often take-away the wrong conclusions from our experiences. Experiences that are no assess and filtered will give you the wrong answers. More experiences with the wrong assessment will make you a worse decision-maker. we use experience through linking our actions with results, but if there is not close link between the two, we will find a connection that is often wrong. The authors start with a great example. Learned people used bloodletting for centuries because they thought it worked. You bleed as a cure for a sickness and survive. It must have been the bloodletting that worked. 

We often forget or don't think about what is missing from our experiences. We do not account for the irrelevant. 

Robin Hogarth recently died, and this was one of his last books. He was one of the great researchers on decision-making and human behavior. Tversky and Kahneman have received most of the attention in this area, but Hogarth was a critical researcher in this area one the last 50 years.

Volatility is a driver for financial crises (Minsky low volatility)

Volatility is a key driver and indicator for financial crises. This volatility prediction is not what you may expect. It is known that during a financial crisis volatility will surge higher, but what is critical for determining whether there will be a crisis is the past volatility. 

What has been found is that a period of low volatility or calm markets will lead to future financial disruptions. This can be viewed as a verification of the Minsky instability hypothesis. See "Learning from History: Volatility and Financial Crises".

You could call this the "volatility paradox", low volatility will increase the chance of systemic event.  If there is prolonged low volatility, there will a higher likelihood of a banking crisis. Form a low volatility regime, there will be excessive credit build-ups and higher balance sheet leverage. You feel like there is less risk and you will then take on more leverage. This work finds that "stability is destabilizing". 

Given the long history studied and the long lag periods, it is hard to use low volatility as a trading signal for short-term shocks, but this volatility relationship is important when thinking about long-term crisis risks. Low volatility will cause investors to take bigger risks. The costs of these risks will have to be borne by someone. 

Using the TIMEMIXER approach for volatility forecasting

An application of time mixing for volatility forecasting can be an important advancement for risk management. Research has extended the work on GARCH to an extreme, but there may be other techniques in time series forecasting that can be applied to financial time series that may be very useful. A recent paper focused on TimeMixers which employs different time scales as a method to improve forecasts. See "Volatility Forecasting in Global Financial Markets Using TimeMixer".

The idea behind TimeMixers is straight-forward. There is imbedded in any times series relationship with different timeframes that can exploited. There can be long-term seasonality. There can be cycles or trends that are longer than a few days that will not be captured with daily data. Classic time series in ARMA models can handle seasonality and can identify autocorrelation at different lengths, but a more explicit breakdown of data may improve forecasts. 

I like the technique used and the author applied it to a broad set of markets, but I was disappointed that there was no testing against other types of models for volatility. This process looks interesting but it is not clear it is any better than what we already have. The MAE, MSE, and RMSE all are low especially for short-term forecasts, but the quality of technique must be balanced with the results, the ease of understanding, and the ease of implementation. This paper does not make that strong relative case for TimeMixer ML.