The March 2020 equity market crash has created an unprecedented situation. In an already low bond yield environment, the Federal Reserve lowered the T-bond yield even more (temporarily) and in an attempt to re-launch the economy the money stock index was increased by 26% in 2020. As result of this, the equity market recovered fairly quickly but at the same time inflation also increased as result of the increase in money stock. With higher inflation the real bond yield turned negative thus becoming an unattractive asset to invest in.
How can now the US debt be financed? Increasing the money stock even more can create a run-away effect. This is because increasing the money stock will increase inflation that will make the real bond yield even more negative (assuming the nominal value does not change) thus in any subsequent step the money stock should increase even faster together with the inflation.
If on one hand it might seem that there is no way out from the current spiral, on the other hand in this article, I’ll examine a path forward that might bring to a way out from this cycle. The analysis will look into the most appropriate increase of T-bond yield to contain the inflation between 2-4% per year and the most appropriate increase in monthly money stock to avoid an equity market pull-back as result of the increase in bond yields.
Remember: T-bond yield and the money stock index are levers. What happens to the equity market and inflation is a consequence of moving these two levers. This is not an obvious path forward. As result models have been built to analytically provide guidance on the most appropriate way forward out of this increase in inflation and equity market overvaluation.
Before digging into the analysis, let’s look at some historical data.
Figure 1 shows the money stock index variation on monthly basis between 2006 and 2021. In the chart, it can be noted that this parameter spikes during economic downturn. This is usually done as a way to sustain the economy during periods of downturn. During the 2007-2009 economic crises, the money stock reached a peak value just above 2%. Nothing compares to what happened in 2020 when it spiked to 6.5%. In this period its mean value has been calculated to be 0.49% while its median value 0.62%.
Figure 1: Money stock index variation month over month
The nominal 10Y T-bond yield is shown in Figure 2. It can be noticed that it has steadily decreased in value since 2006. Occasionally it has sharply dipped for a few months as result of temporary economic downturns. In 2020, the T-bond has experienced its lowest historical value well below 1%.
Figure 2: Nominal 10Y T-bond yield as function of time
In Figure 3 it is presented the annualized monthly inflation calculated from the consumer price index. Usually this number spikes during economic downturns. It reached a peak value of ca. 12.5% during the 2007-2009 economic crises and the 2020 COVID pandemic. Its median value has been calculated to be 2.32%. The black line in the chart represents the real 10Y T-bond yield; i.e. the nominal value compensated with the inflation. As result of the increase in inflation, this number has been in the negative territory from 2020 onward. This is somewhat unprecedented when compared with the historical data preceding 2020. Its long term median value was computed to be 0.25%.
Figure 3: Annualized monthly inflation and real 10Y T-bond yield as function of time
The US industrial production as function of time is shown in Figure 4. It can be noticed that it dips during downturns (as expected) and it has not reached new peaks after 2007. This is highlighting that the growth of the equity market is predominantly due to an increase in money supply.
Figure 4: Industrial production as function of time
To perform this analysis, it was necessary to build two models to evaluate the consumer price index (CPI) and equity market valuation (S&P500). These two models are an improved version of what it was presented in [S&P500 Mode Reference], [CPI Model Reference]. These two models now take also as input the nominal 10 year T bond yield. More specifically, the CPI was modeled as function of: money stock, velocity of money, unemployment rate, industrial output and 10Y nominal T-bond yield. The S&P500 was modeled as a function of: money stock, velocity of money, unemployment rate, industrial output, 10Y nominal T-bond yield, consumer price index and gross domestic product.
I am going with the assumption that the nominal bond yield has to increase to contain the inflation while the money stock has to increase to avoid an equity market pull back. I am also assuming that it is targeted real T-bond yield to be in the positive territory; 0.25 to 0.75%. This is an important assumption. When the real bond yield is positive then they become an interesting asset for the investors to purchase thus effectively ending the vicious cycle of the Federal Reserve steadily increasing the monthly increase percentage in money stock.
Some other relevant assumptions have been made to run the models and generate the charts presented below. More specifically, it is assumed that: unemployment, M2V and industrial output will stay at the same level at the time, the article was written. This decision was taken to focus on the most important parameters of the analysis and avoid going on the tangent. When it comes to GDP, it is assumed that its nominal value varies at the same rate of the CPI month over month variation. The just mentioned CPI is the one calculated using the model.
Figure 5 shows the nominal bond yield as function of time predicted with the simulation. The three numbers in the legend should be interpreted as follow. The first number represents the monthly increase of the money stock index. The second number represents the quarterly basis points increase of the 10Y T-bond yield. The third number represents the targeted 10Y real bond yield. In the simulation, it was assumed that when the calculated real 10Y yield reaches its targeted value then the nominal one does not increase. In the figure, it can be observed that in order to keep the inflation between 2 to 4% while reaching a positive real yield value, it can be expected for the nominal T-bond yield to increase from the current 1.52% to a value between 2.5 & 7.5%.
Figure 5: Modeled nominal 10Y Treasury yields as function of elapsed months
In Figure 6, it is shown the value of the S&P500 calculated in the simulations relative to the September 2021 market price. The numbers in the legend follow the same logic as Figure 5. The way to read this chart is the following. Currently the market seems to be 18% higher in value than its fair price. With the parameters set in the simulations in terms of money stock and nominal yield, it will take between 25 and 75 months for the fair value of the S&P500 to reach the current value.
We must keep in mind that this is a simulation that does not take into account the equity market dynamic. It is not unlikely that in the next 25 to 75 months, the market will experience a pullback followed by some uptrends as result of investors’ behaviors. The message I am trying to convey is that the current valuation is “fair” only if in the next 25 to 75 months the money stock increases between 0.5 to 0.75% per month and the Treasury yield increases between 0.25 and 0.75% points every quarter.
Figure 6: Ratio of the modeled S&P500 and the September 2021 value as function of elapsed months
In conclusion to this article. Many people might think that we are going to experience a period of stagflanation as result of the generous fiscal stimulus and very low T-bond yield. If on one hand this might be correct looking at the situation as it is now, on the other hand in this article it is shown that by carefully increasing the bond yield and simultaneously the money stock index, it is then possible to simultaneously control the inflation to 2-4% per year without creating the conditions of a major pullback of the stock market. In the article it is indicated that 28 to 80 months might be required to stabilize the situation while having the money stock monthly increase and the bond yield to ca. 2006 levels.
If you are a quant investor or a wanna be one, the first thing you do is to define an investment strategy, backtest it and eventually launch it live.
How many times have happened that the strategy has not performed on a real or demo account? If the answer is nearly always, let me explain you why it has happened and let me suggest you what I think is the best way to perform a backtest prior launching your new strategy live.
There might be four main reasons why your backtest did not work in real life:
Assuming you have not done any mistake in setting up the equations and you are patient enough, most likely, your strategy did not work in real life because your model is over-fitted.
With the term “over-fit” I mean that the model knows quite well how to behave if the past would exactly represent itself while it would partially/total fail if future events are not exactly the same as past ones.
Let me illustrate this with an example.
Imagine you have figured out the importance of rotating your investments among uncorrelated asset classes depending on the market conditions, now what you will try to do is to define some rules that will tell you in which asset class to be invested in. It is 2021, so you decide to use Machine Learning and more specifically you define a classification problem. Typically a classification problem tells you what to select depending on a given set of input variables. Input variables that in the case of investing could be: market volatility, return of a given asset, volatility of a given asset,… You then take your Python or Matlab software, build your model, train your data and… you are astonished by the outstanding performances of your strategy. I did the exercise and I have assumed that the strategy rotates among three asset classes: US T-bond, gold and US equities. I have then assumed that my holding period is between one week and one month. The result:
You’ll then get super exited because when you look at the backtested data, you know that in no time you’ll be rich and you are confident enough that the strategy is robust enough to survive a market crash because your model was also trained with data including bad years like 2007, 2008 and 2020.
What next? You go to your brokerage account, start implement the strategy, the first month does not go as expected, so you say that it was a one-off. Then eventually there is an equity market downturn and your drawdown is higher than 15%, you lose money and you: in the best case ask yourself what has happened and in the worst case you blame the rigged market.
What went wrong?
Long story short: your model is over fitted and this is not the way you run a back test.
The way I personally run a backtest is to mirror exactly what I would do in real life. If I have to take an investment decision in e.g. March 2016, the data I would have in real life to train my model are the ones available up to March 2016 and not September 2021. The way that a backtest should be structured is to iteratively train your model within the backtest. By doing so, your model is still over fitted (assuming we are still dealing with the previous example) but the outcome of using it is closer to what would happen in real life. The differences would be due to e.g. fees, orders slippage,…
By running a backtest in this way, the performances of the strategy are now:
A huge difference is not it?
In my opinion, this is the most appropriate way to backtest a strategy and provide a very good idea on how your investment would perform in real life without losing money while implementing a possibly over fitted investment strategy.
I hope you find it useful and you have learned something new, to the next time!
In 2021 the S&P500 has grown 14.10% (06/25/2021). Fear as result of Treasury bond yield and inflation increase has led many to believe that the equity market is heading downward. We share the same opinion. We have developed 24 different possible scenarios for the next 6 months. All of them are expecting the S&P500 to drop at least 19% and at most 23% by the end of 2021.
The fair value of the S&P500 was estimated using our proprietary model described in more details in here. We have then estimated the year end value of the macroeconomic parameters used to feed the model under different assumptions. The model inputs and their expected values under different scenarios are described below.
US Gross Domestic Product (GDP):
M2 US Money Stock:
BAA Corporate Bond Yield Relative to Yield on 10-Year Constant Maturity (BAA-10Y):
US Consumer Price Index (CPI):
A full factorial combination of the different estimates of the parameters used to feed the model resulted in 24 different scenarios to estimate the S&P500 value by the end of the year. In Table 1 it is reported the value of each parameter used in each scenario and the estimated fair value of the S&P500 by the end of 2021. The upper and lower estimated have been calculated assuming plus/minus 2 standard deviation.
Table 1: Expected value of the S&P500 by the end of 2021 under different scenarios.
In conclusion: given the current economic environment and the expected macroeconomic trends, according to our model, it is expected that the S&P500 might close 2021 between 3,050 and 3,462.
The question is: is this going to happen? We need to keep in mind that there is a difference between fair price and actual price. As long as there are buyers, prices can stay where they are or even go higher. This can be noted during the Dotcom bubble in which there has been a large discrepancy between actual and fair value of the S&P500; see Figure 1. But… if there is an event that will trigger a sell-off then we know where the index might land.
Figure 1: Actual and modeled S&P500 index; reference here.
The first quarter of 2021 has been quite eventful. One of the situations that has somewhat shaken the equity market has been the rise in bond yields. More precisely the 10 year bond yield has been raised from 0.93% to 1.64%. There have been a large number of interviews in which it was stated that a rise in yield would have spelled the end of a rise of the equity market.
Is this really true?
Not in my opinion. The 10 years Treasury bond yields are loosely correlated with the equity market. Between 1960 and 2020, this correlation has been 5.35%. This loose correlation is more evident in Figure 1. In some years there is a positive strong correlation while in some others, the opposite happens.
Figure 1: 5 years rolling correlation between the S&P500 and the 10Y Treasury bond yields.
What should we really fear when it comes to yields?
According to our S&P500 model (link to the article here), problems might start when the corporate bond yield increases much faster than the 10 years Treasury bond yield. All being equal, 1% point increase in spread between corporate and Treasury bond yield results in a 2.48% decrease in value of the S&P500; see Figure 2. Personally, I would rather track the evolution of this spread rather than the actual value of the Treasury bond yields.
Investing in bonds could be convenient only if the yield is higher than the long term return of the S&P500; ca. 10%. From 1960 to today, this only happened between 1979 and 1985; link in here.
Figure 2: Relationship between the S&P500 and the corporate-Treasury bond yield spread. It is assumed that all the other macro-economic factors are constant.
The second and not least important hot topic of 2020 and 2021 has been the money supply. 40% of all US dollars were printed in the last 12 months.
What does that mean for the equity market?
According to our S&P500 model, increasing the money supply (M1) results in an increase in value of the S&P500. For each 1 trillion dollar of additional money printed, all the rest been equal, we can expect a 6.96% increase of the S&P500; see Figure 3. This is assuming that the money that were printed will end up in the hands of business owners.
Figure 3: S&P500 variation as a function of the money supply (M1) increase.
The situation could be somewhat different if the new money would reach the general public rather than business owners. This can lead to an increase in inflation. For each 1 trillion dollar of additional money printed, all the rest been equal, the consumer price index can be expected to rise by 7.45%; see Figure 4. With this happening, the S&P500 might experience and increase of 3.88% for each additional trillion of dollar printed. The increase in equity market value will not compensate for the increase in inflation. Even the money invested into the financial market will not be spared by inflation.
Figure 4: CPI variation as a function of the money supply (M1) increase.
What is the tipping point?
If the tipping point is defined as the percentage of money given to the general public when the increase in inflation is equal to the increase of the S&P500 then the tipping point is ca. 60%; see Figure 5.
Figure 5: Spread between S&P500 and CPI as a function of the money supply increase and money provided to the general public.
We now might have a better understanding of the influence of yield spread and money supply on the equity market and consumer price index.
There are lot of news out there that might induce fear and urge to change asset allocation. My advice is: take a step back, look at the situation as objectively as possible, filter the noise, look at similar past events and with the best analytical approach, take decisions as objectively as you can.
When it comes about protecting the portfolio during downturns, I often I read about diversification either using a combination of uncorrelated asset classes or through equities ETFs that cover different regions of the World.
Does it really work?
When sell-offs start and the fear gauge (VIX, the volatility index) spikes, all of a sudden loosely correlated equities ETFs become correlated; see Figure 1. This means that if the broad market goes down and the correlation is nearly 100% then all the rest goes down. Diversifying through equities ETFs that cover different regions of the World is not really helping when we need it the most. The same is true when diversification is done across different sectors.
Figure 1: 1 month rolling correlation between the S&P500 and three others equities ETFs.
How about diversifying using different asset classes?
If we thing about investing in gold, medium term bonds (e.g. IEF) and equities (e.g. SPY) and allocate capital based on the risk parity methodology, definitely the maximum drawdown is reduced during downturns. For instance when in 2020 Q1, the S&P500 went down by nearly 35%, this allocation would have experienced a maximum drawdown lower than 7%. Unfortunately everything has a cost and this strategy has the drawback of very low annualized return: 3.36% vs. the 15.52% of the S&P500 (2009-2021).
What to do about this? Can we break the trade-off between annualized return and the maximum drawdown?
VXX, the VIX short term future ETN, might do the trick and help out our portfolio. By the way it was designed, VXX decays over time. Buying and Holding this ETN is a financial suicide; see Figure 2. The good news is that when the market crashes, this ETN spikes in value. For instance between February and March 2020, in the panic of the pandemic, VXX increased by 436% while the S&P500 dropped by 35%.
Figure 2: Buying and holding VXX.
How to take advantage of these spikes?
The first thing to do is to understand when to enter a long position in VXX. To do that we must look at the VIX term structure. This chart can be found on vixcentral.com and is shown in Figure 3. Each dot represents a VIX future value while the dashed line represents the VIX spot price. If all the future contracts values are pointing upwards and the spot VIX is below the futures then no major sell-off can be expected. Troubles can be expected when the first front two months are ca. 10% below the VIX spot value. If this happens, it is highly probable that a major sell-off is underway and it will continue even stronger in the next few days. When this happens then the VXX ETN spikes quite rapidly. For the sake of brevity, lot of information on how to read the VIX term structure have been omitted.
Figure 3: The VIX term structure on March the 29th 2021.
By knowing that the VXX spikes when the first two front months are ca. 10% below the VIX spot price, assuming our portfolio is made 100% of equities, then we can think of taking part of it and allocating it to a long volatility position.
Table 1 shows the CAGR and maximum drawdown as function of the percentage of the portfolio allocated to a long volatility position. It is assumed that the investor sells all the equities positions as soon as the first two front futures are 10% below the spot price. In this example, it is assumed that the equities are represented by the S&P500.
Table 1: annualized return of investment and maximum drawdown as function of the portfolio allocation to a long volatility trade.
By allocating 30% of the portfolio to a long volatility trade is effective in maximizing the annualized return while minimizing the drawdown. In the same period, buying and holding the S&P500 would have resulted in an annualized return of 15.3% and a maximum drawdown of 34%. The backtest of this optimal case is shown in Figure 4.
Figure 4: Equities portfolio hedged with a long VXX position versus buying and holding equities.
In conclusion, diversification is not protecting our portfolio when we need it the most. Equities become all correlated when the market goes down. Diversifying using different asset classes can reduce the drawdown but the long term return is penalized. By wisely opening long volatility positions when the equity market sinks can provide an effective hedge to reduce the maximum drawdown while improving the annualized returns.
In this article we propose a methodology to pick-up stocks. The method consists in creating a portfolio of 10 stocks. The stocks can be taken from the components of the S&P500 or Nasdaq 100. The securities are selected based on their return of investment over a certain number of months. Six months if the stocks come from the S&P500 components while three months if they are from the Nasdaq 100. The stocks are then hold 10 days if they are selected from the S&P500 constituents or six months if they are taken from the Nasdaq 100’s basket.
Selecting stocks can be a very complex and time consuming task. Even when automatized, valuing a company can be a challenge and the return of investment on a company can be heavily influenced by the sentiment of the market. GameStop can be a textbook example of this situation. In this article we propose a methodology in which a portfolio of stocks is selected based on their past returns. The method is made of three parameters that have to be optimized in order to maximize the portfolio return with an acceptable maximum drawdown. These variables are:
Selecting Stocks Using the S&P500 Components
In Figure 1 the return of investment as function of the maximum drawdown is presented. The lowest maximum drawdown is ca. 46-47% which is not substantially lower than buying and holding the S&P500; ca. 57% in the last 20 years. The return on investment can be highly amplified using this stock picking methodology. In the best case, the highest annualized return of investment with a maximum drawdown not exceeding 50%, is 33.32% vs. 8.77% of the S&P500.
Figure 1: Return of investment as function of the maximum drawdown for all the runs using the S&P500 components.
Increasing the CAGR by 3.8 times can be done with:
Table 1: key statistics of the proposed stock picking approach and the S&P500.
Figure 2: Annualized returns of the proposed stock picking approach and the S&P500.
Selecting Stocks Using the Nasdaq 100 Components
Figure 3 shows the return of investment as function of the maximum drawdown. The lowest maximum drawdown is ca. 35% which is lower than buying and holding the Nasdaq 100; ca. 56% in the last 20 years. Assuming we try to maximize the return of investment with a maximum drawdown lower than 50% then this methodology allows achieving an annualized return of 41.79% vs. the 12.97% of the Nasdaq 100.
Figure 3: Return of investment as function of the maximum drawdown for all the runs using the Nasdaq 100 components.
Increasing the CAGR by 3.2 times can be done with:
Table 2: key statistics of the proposed stock picking approach and the Nasdaq 100.
Figure 4: Annualized returns of the proposed stock picking approach and the Nasdaq 100.
Comparing to Berkshire Hathaway
One of the greatest stock pickers of all the time is Warren Buffet, how would this methodology compare to the returns of Berkshire Hathaway? The answer is provided in Table 3 and Figure 5. Despite this strategy hypothetically behaves better than the performances of Berkshire Hathaway, it is important to keep in mind that these conclusions were drawn assuming that there is no bottle neck with this strategy in the ability to purchasing whatever stock.
Table 3: key statistics of the proposed stock picking approaches, Berkshire Hathaway and the reference indexes.
Figure 5: Annualized returns of the proposed stock picking approaches, Berkshire Hathaway and the reference indexes.
Stock picking can be a very complex and tedious work to perform. In this article, it was proposed a methodology to select stocks based on the company momentum. The optimal number of stocks and holding duration was also discussed. The methodology allows increasing the annualized returns by 3.2-3.8 times versus the benchmark indexes while keeping the maximum drawdown below 50%.
Cash is trash. Considering all the money that has been printed by the Federal Reserve in 2020, this strong statement made by Ray Dalio in 2020 is more than justified. The questions are: what rate of inflation should we expect? Is there anything we can do about it to protect our hard earned money?
In this article we will:
Inflation is not just about money printing, there are three more factors affecting its value. CPI could be thought as a function of: money stock index (M1), velocity of the money stock (M2V) (i.e. how fast money changes hands), unemployment rate and industrial output. Increasing these four independent variables increases the inflation. A simple linear regression model was built using these parameters. The model has an accuracy of 99% (R2) and a P-value below 0.05 for all the regression coefficients. Two times the average error between modeled and actual data has been calculated to be 7.18%. The actual and modeled CPI is shown in Figure 1.
Figure 1: Actual and modeled consumer price index.
Where is the inflation heading?
To answer to this question, we need to understand the value of all the variables affecting the inflation by the end of 2021. It is estimated that M1 might reach a level of 8.2 trillion dollars. The estimation is based both on the current trend as well as the stimulus package announced by the Government. Due to the current restrictions and “normal” life not expected to be back before 2022/2023, it is estimated that M2V will not increase in value and stays relatively flat at 1.13 throughout 2021. The unemployment level has been drastically decreasing in the last few months. If the trend continues, it will not be unlikely that it might reach 5.7% by the end of 2021. The unemployment will not reach the pre-COVID levels because, due to the current and projected restrictions, several sectors will not be able to operate again at full speed. The industrial output is expected to increase by 3.5%, reaching a value of 107.23 point. For the same reasons mentioned so far, not a full recovery from its peak value of 110.11 points . Given these assumptions, using the above mentioned model, it is estimated that by the end of 2021, the CPI might reach 353 point: 35% higher than the current level (261.78).
If the prices would increase by 35% by the end of 2021 (or even a fraction of this estimate), this would mean that the cash in our bank accounts might lose its purchasing power. To make an example, imagine you have $50,000 in your saving account in 2020. By the end of 2021, the purchasing power of this $50,000 would be equivalent to $32,500 ($50,000 * 35%). By now the statement “cash is trash” should make more sense.
What to do about it?
Bond yields are currently very low; ca.1.25%. It would roughly take 35 years to recover this inflation loss while assuming there will not be any inflation increase in the future. Not the best way to go.
How about investing in an index fund that follows the S&P500? To do that we have estimated the value of the S&P500 based on: gross domestic product (GDP), medium term Treasury bond yield, CPI, M1, M2V, unemployment rate and industrial output. This linear regression model is an updated version of the model we have presented in this article; link here. Assuming that the GDP will rise by 1.0% in 2021 while the bond yield will stay at 1.25% then it is estimated that by the end of 2021, the S&P500 should be valued: 3,488 points plus/minus 12.52%. The current market value of the S&P500 is 3,901 points. This means that the equity market might not be the most suited place where to put your hard saved money.
What is left? Bitcoin and gold.
I’ll focus on the yellow metal since my competencies on crypto currencies are limited. Our linear regression gold model takes as independent variables: the S&P500 value, M1 and CPI. More details on the model can be found in here. With the numbers estimated so far, gold might reach by the end of the year 3,857 USD/oz plus/minus 279 USD/oz. Currently gold is at 1,844 USD/oz meaning that there is an upside potential of 209%. The number is high enough thus offering an effective protection mechanism against the damage that a potential increase in inflation might create.
Because the current conclusion is based on several assumptions, a sensitivity analysis has been done on the assumptions that have been made. Table 1 shows the sensitivity boundary values of each of the six variables. A total of 729 combinations were created and analyzed. In Figure 1 and Figure 2, it is shown the estimated value of the S&P500 and gold as a function of the estimated value of the CPI at the end of 2021. These three parameters have been normalized relative to their current levels. Figure 2 shows that the CPI might increase between 15 and 45%, unfortunately in the vast majority of the cases the S&P500 would have a negative return in 2021; at worst -20%. Gold, Figure 3, shows that might experience an increase in value between 60 and 120%. The sensitivity analysis still support the main finding: inflation might increase and gold should be the best asset to invest in and avoid that our money will lose their value.
Figure 2: Estimated CPI vs. estimated S&P500 value both relative to current valuation. Scatter plot of the sensitivity analysis.
Figure 3: Estimated CPI vs. estimated gold price both relative to current valuation. Scatter plot of the sensitivity analysis.
Table 1: Sensitivity analysis boundary values for the variables used to estimate: CPI, S&P500 value and gold price.
In conclusion, in this work we have presented that is possible to model the consumer price index. The model indicates that by the end of the year the inflation might substantially increase as result of the money that has been printed, industrial output and unemployment. To avoid losing the value of the money, investing in bonds or the S&P500 will not provide a hedge. It is projected that the S&P500 might lose ground in 2021. Gold offers an effective hedge against the projected rise in inflation. The estimated increase in gold value should more than balance the decrease in value of the cash due to the rise in inflation; it will actually result in a value increase of the invested capital.
I was born in 1981 and my first year of college was 1999. What if my parents would have decided to invest 25 $/month from the time I was born to the time I started university? For sure they would have experienced the dot-com bubble. The Dollar Cost Averaging (DCA) approach would not have survived well: the market dropped by ca.50%, the recovery took ca. 7 years and exactly the same would have happened to my saving account; see light green line in the first image below.
Why did it happen? Sure, the market has its cycles but basically there are a few things that could have been done to mitigate what happened during the dot-com bubble and the house market bubble crises.
First: the amount of money that is injected in every DCA should constantly increase over time. Let’s say our parents are generous and they get a few promotions over the years, we can then assume that they would increase the amount of money they donate by 7.5% per year. By doing so, they would have managed to reduce the drawdown duration by 1.5 years (5.5. years in total) while, unfortunately, the drawdown would have stayed at ca. 50%; see dark blue line in the first image below.
The second thing that they could have done, it would have been not to put all the eggs in the same basket and diversify the asset allocation. In this example I have chosen 60% equities (S&P500) and 40% medium term T-bonds. Surprise, surprise, they would have now been able to experience 22.5% max drawdown during the dot-com bubble for a duration of 3 years. Much better right? Moving forward in time and we get the house market bubble. This time we get a steeper drawdown (35%) while a recovery time of 1.4 years. In comparison, it took ca.5 years to the S&P500 to get back to the previous high.
What did we learn so far? DCA is not a magic bullet to navigate through difficult times. The market goes through cycles and when they happen, it is better to be prepared. Preparation means: implement DCA, diversify your assets and steadily increase the amount of money you place each month in the brokerage account. Lastly and most importantly make a few calculations to verify that your plan is solid. Yes, the S&P500 returns an annualized 10% but do not forget that there are market cycles. These cycles might take several years to recover and we definitely do not want to lose capital when we need it the most.
If we now want to improve our drawdown even more, there are ways to do that. Somewhat complex and counterintuitive but worth. What are these tricks? First the split between equities and bonds can be adjusted over time. When we are infants we do not need money so our parents can invest in riskier assets e.g. 100 equities. As we grow up, we slowly start investing more and more in bonds. In this new example 40% after 40 years. To further improve the performances of the account, it is beneficial to add more money when the market goes down and less when it goes up. By doing that our return on investment is very similar to the 60-40 case but this time, the maximum drawdown is 24% while its duration 1.2 years. See dark blue line below. Better, is not it?
I am very tempted to talk about NEXT-alpha and make a case study around it but today I’ll skip it. It does not sound fair for the equity market. But it is important to keep in mind that there might be better strategies out there other than the traditional equities-bond allocation.
This article was written after opening a brokerage account for my 3 years old toddler and make him benefit of everything I have learned in the last decade.
Would not be awesome to double your return of investment while decreasing drawdown and the volatility of the portfolio? I bet everybody would like doing that. So let me share a lesson I learned a bit late in life. Never too late to learn and if applied at younger age, well… later in life you might find yourself with some good money in your brokerage account.
Imagine you have $5,000 and you want to make this money grow in the market. Depending on your risk tolerance you might choose to allocate a part of this money to equities and the remaining part to bonds. How much can you make? Let’s look at the CAGR of the first table below. In the upper row, the first number represents the percentage of medium term treasury bonds (ETF = IEF) while the second, the percentage of equities (S&P500, ETF = SPY). 100% equities would give you an annualized return of 9.12% (good) with a max drawdown of 52% (bad). 100% bonds would give an annualized return of 2.17% (bad) with a max drawdown of 11% (OK-ish). If looking for stability, we might want to allocate 60% to equities and 40% to bonds. How much my $5,000 would be worth in 15 years? $11,755. Sooo much waiting to add a mere $6,755 in 15 years.
Do not you want to do better? Actually, there is a way to do it while still investing in the same instruments with exactly the same investment methodology. The trick is: add a little bit of money each month to your investments. In technical terms this is called Dollar Cost Averaging. Many of you might be familiar with this practice, despite, first: let’s quantify its potential, second: let’s see how to do this even better.
Going back to the previous example. Let’s start investing $5,000, 60% in equities and 40% in bonds. This time, we add $250 per month to the brokerage account. Our annualized growth now increases from 5.86% to 117.79% with a maximum drawdown of 12%; see table below. After 15 years, the original $5,000 would have grown into $106,229.Better than $11,755, right? Yes! Of course this is not only thanks to the market. By adding $250 per month, you have actually contributed $45,000 ($250*12*15). The difference this time is: by combining the effect of the market and your ability to save money each month, you manage to create an actual growth of $56,229 (106,229-45,000-5,000). Definitely much better than the previous $6,755!
Can we do better than this? I bet we can! The way I do it is by investing in an actively managed strategy. NEXT-alpha is the flagship strategy of Alpha Growth Capital. The strategy returned an annualized 24.74% in its more than three years of life. By investing $5,000 in NEXT-alpha, without dollar cost averaging, after 15 years, the AUM would be worth $137,696. If we now add $250 per month, at the end of the 15 years, the account would be worth $1,123,211. Much better is not it?
Concluding: definitely getting rich over night with the stock market might be tough but… today we have learned that if we leverage the compounding potential of the market, combined with the ability to save and invest some money each month, by having enough patience, we can grow a small amount of money into something much bigger.
I do it, why can not you? 😊
Traditionally the vast majority of market players focus their investment efforts in trading equities and bonds. This is because equities might enable high returns while bonds might protect the portfolio during bear markets. Alpha Growth Capital has traditionally focused in using predictive analytics to trade equities in its flagship strategy NEXT-alpha (https://www.alphagrowthcapital.co/next-alpha.html). In the quest to reduce the strategy volatility while possibly leaving the annualized returns unchanged, Alpha Growth Capital has explored the viability of investing in asset classes other than equities.
In this article, we will explore the viability of trading commodities. Corn was taken as case study and the historical data from the Teucrium Corn Fund (CORN) were used to evaluate different trading methodologies. The results were finally compared to buy & hold the S&P500 using different risk matrixes. The following trading strategies were investigated:
A commercial software (Matlab) was used to perform a parametric optimization of all the three strategies to find the optimal value of each parameter for each indicator. The optimization was targeting the maximization of the return of investment. Trading fees and ask-bid price spreads were neglected in the optimization.
In regards to the entry and exit signals:
Trading Methodology 1: the position is entered when the ratio between the conversion line period and the baseline period exceeds a threshold level. The position is close when the ratio is below the threshold level. Entries and exits signals are evaluated just before the market closes.
Trading Methodology 2: the position is entered when the Commodity Channel Index is above and given value and vice-versa. Entries and exits signals are evaluated just before the market closes.
Trading Methodology 3: this is a proprietary methodology developed by Alpha Growth Capital for its core strategy NEXT-alpha. With this methodology, the price action is expressed as function of the volatility of the equity market (VIX) instead of time. Depending on the volatility level of the market: different intraday exit price levels are established for the position opened at the previous end of trading day, position size is selected and intraday limit and stop orders are set at a pre-determined price.
Because of the contango/backwardation effect, buying and holding CORN from mid-2011 to December 2020 would have resulted in an annualized loss of 10.66%. When the conversion line is set at 8 days while the baseline line at 11 days, using a ratio threshold of 1%, the Trading Methodology 1 would have led to an annualized return of 5.04% with a maximum drawdown of 10.35%. With the second trading methodology, the Commodity Channel Indicator period was set at 3 while its threshold entry/exit level at 125. In this case the annualized return was 2.01% while the maximum drawdown 10.61%. The proprietary Trading Methodology 3 provided the best results. The annualized return was 16.62% while the maximum drawdown 17.55%. The risk adjusted return was the highest among the three strategies. An overview of the results is presented in Table 1. The simulated optimized price evolution for the three strategies is presented in Figure 1.
Table 1: Comparison of the three optimized trading methodologies. B&H = Buy & Hold. CAGR = Compounded Annual Growth Rate. STD = Standard Deviation.
Figure 1: Simulated price evolution of the three optimized trading strategies.
The Trading Methodology 3 has emerged to be the winner. The question now is how it would compare to buying and holding the S&P500 (SPY). From mid-2011 to end of December 2020, the S&P500 has returned an annualized 10.48%, 33.92% as maximum drawdown and a Sharpe ratio of 0.60. In comparison this optimized strategy has delivered an annualized return of 16.62%, 17.55% as maximum drawdown and a SharperRatio of 0.46%. As compared to the S&P500, the optimized strategy improves both the return and the drawdown while the Sharpe ratio slightly deteriorates.
As compared to NEXT-alpha, the Trading Methodology 3 shows both lower returns (29% vs. 17%) and lower drawdown (26% vs. 18%). If on one hand trading CORN might offer diversification on the other hand its implementation into the portfolio would lower the annualized returns of NEXT-alpha.
In conclusion, this article has evaluated three different trading strategies to trade CORN. Trading based on the Ichimoku and the Commodity Channel Index indicators can result in positive returns vs. buying and holding CORN. Looking at the price action in the volatility domain and define appropriate entry & exit levels as function of the market volatility can provide even better results than the above mentioned two indicators. The optimized strategy enables to achieve 16.62% annualized returns while trading based on the Ichimoku and Commodity Channel Index indicators: 5.04 and 2.01% respectively. The optimized strategy also delivers better returns versus buying and holding the S&P500 over the same time frame.
All of us are very familiar with the concept of time because this is something we experience on daily basis since the time we were born. As result when we deal with financial time series and we try to optimize them to reach our targeted CAGR, maximum drawdown,… we do that in the time domain. We download data from e.g. Yahoo Finance, we get our nice spreadsheet which is basically a series of data sampled on daily basis and then we work on it.
With this article I would to show that there is a better way to optimize financial time series. I’ll do that with a case study about optimizing the daily stop loss value of the Nasdaq 100. In this example I have used the ETF QQQ.
First: forget looking at the price action in the time domain. Second: start looking at the price action in the volatility domain. When I talk of volatility, I am referring to the S&P500 volatility which is typically measured with the CBOE Volatility Index (VIX).
Let’s start with the case study. The research question is: what is the best stop loss to maximize the CAGR of the Nasdaq 100 (QQQ)? What most of the people would do is to find a single stop loss (SL) value to maximize the CAGR of the time series. When doing so, I get 0% as the most appropriate SL. This means that as soon as the daily price variation becomes negative or the market opens below the previous close then the strategy is in cash until the position is re-opened at the end of the trading day. With this approach, the CAGR increases from 8.53% to 10.23% while the maximum drawdown is reduced from 83 to 60%. Not too bad. Let me tell you that there is a better way to do that. This is by looking at the price action in the volatility domain.
We can think of dividing the VIX in three equally spaced ranges; low, medium and high. For each of these ranges there is a daily price action associated with the Nasdaq. We can now think of optimizing the SL value for each of the volatility range. It might get somewhat complicated in Excel but it is worth the effort. If we do that, the optimal SL values are: 2, 1 and 0% for the low, medium and high volatility range respectively. The optimized time series will now have a CAGR of 11.67% while a drawdown of 66%. The CAGR increase by 3.14% points vs. the baseline case. This might not seem much but over a 20 years investment period this means to nearly double the returns at the end of this 20 years’ time.
The key statistics and time series for these three different investment approaches are presented in Table 1 and Figure 1 respectively.
Figure 1: time series for the three different investment approaches.
Table 1: key statistics for the three different investment approaches.
It is clearly advantageous to look at the price action in the volatility domain. Optimizations can take place in several shapes like e.g. looking at minimizing the max drawdown or finding the highest CAGR for a targeted max drawdown or splicing time series depending on the volatility level. In this article for simplicity we just looked into maximization of the CAGR but I ensure you that there is much more that can be done.
Large and small investors are quite often faced with the question: where is the equity market heading? Generally speaking nobody knows what will happen tomorrow or in a year from now. I am confident that any of the reader did not come across the idea of world lockdown prior this COVID pandemic.
What we know is that the market is influenced by factors like GDP, treasury rates, inflation and so on. For instance, it is given that when the GDP grows, all other factors being equal, then the equity market goes up. The question then becomes: how much?
In this article, I am showing that the S&P500 can be modeled as function of the main macroeconomic parameters of the USA economy. These factors are: gross domestic product (GDP), money stock index (M1), BAA corporate bond yield relative to 10 year Treasury bond (BAA-10Y) and consumer price index (CPI).
In Figure 1, the actual and modeled S&P500 index is presented. The model uses monthly data tracing back to the 1960’s. The model has an accuracy of 95.72%; R2. The 2 standard deviation of the error has been calculated to be 10.48%. The error is defined as the relative difference between actual and modeled value.
Figure 1: Actual and modeled S&P500 index.
In Figure 2, it is shown how these four macro-economic variables are affecting the value of the S&P500. The variables were varied one at the time ±20% from their reference value. The reference value was assumed to be the one available on fred.stlouisfed.org at the end of November 2020.
If an analyst and/or an investor are interested in understand where the market is heading in e.g. one year from now, this model can be used to create outlooks based on estimations of future values of: GDP, M1, BAA-10Y and CPI.
The next question that might come to mind is whether the predictions are robust. To answer this question we need to keep two things in mind. First, the prediction is heavily dependent on the guess of the future value of the variable. If the guess is off then the prediction will be off. Second, this is a neutral model. Geopolitical events and buyers/sellers momentum are not accounted. If for any reason the GDP goes down and investors keep on heavily buying equities then the market will trend higher instead of going down as the model would have estimated.
Figure 2: Calculated S&P500 as function of macro-economic variables variations from their end of November 2020 values.
How to include geopolitical and market sentiment? The approach that was used in this work has been to calculate the coefficients of the model recursively. Figure 3 shows the accuracy of the model as a function of the rolling sample size. Each sample is equivalent to one month. As it can be observed, by having a smaller rolling training period the accuracy of the model improves. 733 samples (the entire time series) has an accuracy of 10.48%, with 120 samples (10 years), the accuracy is as low as 1%. This latest case is shown in Figure 4. With an improved in accuracy, such approach can be used to assess whether the market is fairly valued both based on fundamentals as well as other factors such as investor sentiment. Based on such information investors might decide whether to take a direction bet. Alternatively, as in the previous case, it can be used for short term outlooks.
Figure 3: Model error as function of the number of samples used to train the model.
Figure 4: Actual and modeled S&P500 index. The modeled S&P500 was created using a rolling regressive approach with 120 samples (10 years).
Concluding, the two models presented in this article are able to fairly well reproduce the trend of the S&P500. The second one does a better job since it also takes into account the market dynamic on top of macro-economic factors. The models can not predict where the market is heading, the future is not written. Despite they might be able to provide insights on how far off is the fair value of the market in relation to its actual value or alternatively they might be able to indicate where the market might head based on short term estimations of the economy.
The growth of your wealth is essentially made by three parts: what you earn, what you spend and potentially the returns from your investments.
A multitude of people in my network talk about getting rich. Most of them focus on increasing their wealth by increasing the earnings. Which, it can work if expenses do not increase as fast as the salary. Many of us are working for corporations. We all know how hard it can be to get a rise in salary. We over perform our team members and then at the end of the year we hear from our manager: You did a great job but the company has not been as profitable as forecasted, this year the increase is kept at 0.75%, next year it will be better. The next year comes and here we are with a new reason not to have a rise or promotion. Can you relate to this?
Probably yes and even if not, let me share with you a few things you can do to grow your wealth.
Increasing your net worth by increasing your salary while working from somebody else, it is probably the hardest thing to do. Why? Because you have no control over the business you work for. So my first recommendation is to grow your wealth by acting on things you have direct control of: expenses, side hustles and investments. Let’s tackle one of them at the time. As average people spend $1,700 a month in personal consumption. Despite the fact you can afford it, have you thought of: cutting on daily coffee, prepare your own lunch, cook your meals, one night less per month eating out, less junk food, useless subscriptions,…? If you do then you can save as much as $750/month. Moving on: the side hustle. Have you thought of renting your home parking lot when you go to work? Rent the room you do not use to a student or people on vacation? Instead of watching TV, how about spending one to two hours per day providing consultancy work on websites like www.freelancer.com? Realistically, it is likely you can make an additional $500 per month. Third and last point to act on: consistently investing savings. Treasury bonds: 2.5% p.a., option trading: 10.2% p.a., passive index 9.8% p.a., managed strategy 15%p.a.,… Saving account: 0% (negative in some parts of Europe!).
Recapping: thinking how to spend money and having a side hustle can give you an additional $1,250 month while investing an average of 12%. The numbers might not look exceptional and this is because people tend to focus on the present moment or days. Rarely people have a long term perspective: weeks, months, years and in some cases decades.
Let’s make a little effort to look at things in the long term perspective and let’s look at two case studies: the Traditional Way and the Exponential Game. Both cases have the same starting point (salary & savings) but the first does not cut on expenses, does not invest,… while the second applies everything we have discussed so far. The result? After 10 years: the first case is worth $246,400 while the second $724,657 (+194%). After 30 years: the first case is worth $738,400 while the second $10,185,923 (+1279%).
By Year 12, The Exponential Game case can be millionaire without even having a single $ rise in salary. This is not magic, it is reality!
Successful investors and traders use a variety of investing techniques. Some are more profitable than others but the line in between succeeding and failing is the decision making process. All the successful traders and investors have one thing in common: they know when to enter and exit each single trade.
One of the investing techniques that several people are using is price arbitrage. With this approach, the investor estimates the fair price of equities, commodities or you name it and if there is a large enough gap between the fair estimated value and the spot price then a position is entered. Position are opened either long or short depending whether the fair value is above or below the spot price.
In the past I have built a couple of these models: the first to estimate the value of the S&P500 while the second the fair price of gold (here). In this article, I’ll present the work that was done in modeling the oil price of the West Texas Intermediate; WTI in short.
Crude oil is a commodity and as such it follows the law of supply, demand and inventories. At constant demand, increasing the supply, the inventories go up and the price goes down. With lower supply the opposite happens. When the supply is constant and the demand decreases (what happened in early 2020 due to the COVID-19), the inventories tend to build up and the price goes down. With higher demand, the opposite happens. The WTI model that was built was based solely on the law of supply and demand.
The simulated WTI price follows quite well the actual price with an accuracy of 82% and a proxy of two standard deviations of 18%. Sudden market movements due to excessive market buying or selling sentiment are not well captured; e.g. 2007-2009 and 2014-2015.
The next question that might come to mind is: how do I use it?
Let me start with how I do not use it. When I see a large enough gap between the fair and spot price, I never buy or short sell any future contract or ETPs. This is because I do not know when the two prices will converge and whether the market is gona rally in the opposite direction of the fair price. Few macro firms went bankrupt while following this approach.
The way I use the model is to guide my decisions when deciding what option strategy to use. With small to non-existent price gap I tend to use neutral strategies. When the fair price is above the spot, I go with a bullish strategy while bearish in the opposite case. It goes without saying that the choice of the strategy should be made together with the current volatility rank of the WTI while properly selecting the position size and keep enough money in the account in the eventuality the option contract is assigned.
If you have enjoyed the article, leave your comment below. If you find the model useful and you would like to use it, then click the link.
Before you read any further, I would like you to focus on the image below and think for a minute or two if there is a pattern in what you see.
Like me, probably you have not. But… I ensure you that these lines were drawn by a mechanism that follows a given set of laws of physic: the double pendulum
If you know the geometry of this pendulum and the forces acting on it then, with the right background, you will be probably able to have a given set of equations to describe its motion and its apparent randomness.
In my opinion, the financial market is as random as a double pendulum. Meaning: it is not; or better not fully. I wrote a couple of articles in the past on how the value of Gold and the S&P500 can be modeled knowing the fundamental blocks of the American economy. Without sudden external forces or changes, the direction of the movement of the pendulum, market value and gold can be forecasted with a good degree of accuracy.
Going back to finance.
If you like investing in stocks and you are good at picking them up then probably in the very long run you will be able to generate an annualized 18% (this is what Buffet did in the last 32 years). You would have nearly over performed the S&P500 by a factor of 2! The index returned 9.8% in the same timeframe. 18% might not seem that much but investing $10,000 for 32 years the Buffett's way, you now would have nearly 2 million USD.
Many of us (myself included) do not know, have no interest or have no time to go through financial statements of companies to choose which ones have high growth potential. Despite some of us are able to figure out patterns from something that in appearance looks like a chaotic system. In my opinion the most successful person at mastering this skill is the American mathematician Jim Simons. In one of his rare interviews, he claimed that he has no interest in reading financial company statements but he saw patterns in the prices of commodities. This gave him the idea to start trading and profit from the knowledge of these patterns. The result? 40% annualized return (net of fees, 66% gross) with only one single negative year. In perspective, investing the same $10,000 with Renaissance, after 32 years, the money would be worth north of 474 million USD.
Comparing investing and trading:
This brings me to my last point. Truly understanding the mechanism of how stuff works can create a major competitive advantage. A mathematician (very intelligent) managed to solve the market using mathematics rather than financial statements.
If he did it, we can do it too. Key being: patience, time, knowledge and smart work.
According to Benjamin Graham: “The investor’s chief problem—and even his worst enemy—is likely to be himself.”
The underlying reason is that the vast majority of investors are irrational. We all have biases that can lead us to take the wrong decision. There is not much we can do about it because we are not machines but… acknowledging that there biases and understanding them, next time we face one, we might be able to spot it, do something about it and probably take a better decision.
In the investment process, investors often experience the “roller coaster of emotions”. Does this look or feel familiar?
If so, you’re not alone. After all, the cyclical investment process is full of psychological pitfalls. However, only by becoming aware of and actively avoiding behavioral biases can lead investors to take better and hopefully impartial decisions.
Bias does not always have a negative connotation. They can help us in our day to day lives but when it comes to investing, they might have the opposite effect. There are two categories of bias: cognitive and emotional. In the first case we might misinterpret information and data and/or wrong memories. In the second case, people act based on feeling and emotions instead of facts.
When it comes to investor’s biases, we can identify four of them.
Investor overconfidence can lead to excessive or active trading, which can cause underperformance. In a 1999 study, the least active traders had annual portfolio return of 18.5%, versus the 11.4% return that the most active traders experienced.
Fear of loss. When asked to choose between receiving $900 or taking a 90% chance of winning $1000, most people avoid the risk and take the $900. This is despite the fact that the expected outcome is the same in both cases. However, if choosing between losing $900 and take a 90% chance of losing $1000, most people would prefer the second option (with the 90% chance of losing $1000).
The "disposition effect" is the tendency of investors to sell winning positions and hold onto losing positions. This effect directly contradicts the famous investing rule, “Cut your losses short and let your winners run.”
Portfolio Construction and Diversification
Familiarity Bias. Investors prefer to invest in "familiar" investments of their own country, region, state, or company.
Misuse of Information
Gambler’s Fallacy. When asked to choose which is more likely to occur when a coin is tossed—HHHTTT or HTHTTH—most people erroneously believe that the second sequence is more likely. The human mind seeks patterns and is quick to perceive causality in events.
Attention Bias. A 2006 study posits that individual investors are more likely to buy rather than sell those stocks that catch their attention. For example, when Maria Bartiromo mentions a stock during the Midday Call on CNBC, volume in the stock increases nearly fivefold minutes after the mention.
Investing money is a strategic process. Learn your blind spots, develop a systematic strategy and be part of that 20-30% that can make money in the financial market.
Source: this article was a re-edit of Why Investors Are Irrational, According to Behavioral Finance from Melissa Lin
I was born in the 1980’s in a coastal town in the south of Italy and life was great in that decade. Great, mostly for the Baby Boomers and the Silent Generation. If your parents were high school teachers in their forties, they could afford a house or two paid cash. A family of medical doctors could afford a new FIAT every month and still put food on the table. If you were 60 years old, you could retire with a lavish pension enjoying: the beach, the sun, the wine and the food. So basically my generation, the Millennial, grew up with that stereotype of life in mind. Graduate, get a decent job, make a family and enjoy life. Thirty years later and it is hard to debate that the Western World is a totally different place nowadays.
I am a hard coded engineer and by nature, we (engineers) think of the worst while hope of the best. During the 2008 financial crisis, I had few recurring scary thoughts. Jobs opportunities are limited and do not pay much, how am I gona afford the same lifestyle as my parents did? People live longer, there are less newborns, governments are on the hedge of bankruptcy, who will pay my pension?
It was and it is, still today, an uncertain time for generations like the Millenials and Gen Z. Being sad and nagging definitely it is not gona help. Like Caecus used to say: Homo faber suae quisque fortunae ("Every man is the artifex of his destiny"). If we really want, we can take control of our future and mold it the way we want it to be. Actions must be taken because life is not like the book of Rhonda Byrne (“The Secret”, the law of attraction stuff).
Actions, what can we do?
Back again in 2008, I remember I received a notification from my bank stating to cash in some money that was left in some kind of financial instrument by my mom 20 years earlier. I was happy and at the same time surprise. Why surprised? The sum received was 10 to 15 times what was invested 20 years earlier. I did not give much importance and thoughts to this until five years ago when I became passionate by finance.
Compounding: how beautiful this concept is. 10 to 15 times the return of investment in 20 years is equivalent to annualized gains of 12 to 15%. Essentially, not too far from what it can be made by investing in a passive index fund tracking the S&P500 (9.8% in the last 90 years or a total return of 451,000%).
I wish I would have learned this basic skill in my younger age together with everything else I have learned at school.
Let’s assumed that my parents were so generous to donate me $1,000 at my birth and invest them in the S&P500. By the age of 15, my account would have been worth $4,065. With a great school system, teaching students about passive investments and compounding (i.e. the Financial Literacy class that, in my opinion, everybody should be thought), I would have decided to take $20 per month from my allowance or afterschool job, and put it in the saving account that my parents created 15 years earlier. By the age of 25, my account would be worth $14,513. I am 25 with a decent job and now I can save $100 per month. Guess what, at the age of 33, the account would have been worth $49,180. I get a better job with higher salary and cutting few expenses (weekends, eating out,…), I can save $300/month until the age of 65. By that time, my account would be worth $1,583,586.
Impressive, is not it? Compounding, patience (lot of it), investing in a passive index, saving money here and there, can do the trick.
Think of Warren Buffet. At 14, he had $5,000 and at 83, he had $83.58 billion. If you do the math, this is equivalent to an annualized return of 26.6%. It is impressive and well above the S&P500 but not impossible to realized similar annualized returns.
What if we start later in life?
Compounding can still do the trick. Of course this is not enough because we need to invest in something better than a passive index like the S&P500. Smartly rotating uncorrelated assets (equities, bonds and gold) can do the trick. An annualized 20% is within reach without taking excessive risks. The result? Investing $25,000 at the age of 35 and adding $300 per month then by the age of 65, the account should be worth $10,185,581. Not too bad, is not it?
Bottom line: it does not matter when you were born or how uncertain the future might look like, financial literacy can help you in making each sweat earned $ to work for you, helping building a solid future. Patience is the key.
The short answer is: nobody knows not even artificial intelligence.
Lot of people have tried to predict the future and it does not take a lot before you stumble on somebody on YouTube or Google that ensures you to double your money each year because they know what the market will do the next day. Thinking a bit in perspective, let’s say that some money manager would have found this holy grail, it would not take more than 10 years for a fund to go from 100M$ to 102T$. Wait a bit longer and the fund will take over all the money in the market. Unlikely, right?
Nowadays, Artificial Intelligence is a quite popular field that is gaining traction in everything that surrounds us. Why then not to use AI to make predictions on how the market will move the next day? Let’s try and see what we get.
To do the job, I believe that the most suited AI architecture is the long short-term memory (LSTM). LSTM networks are well-suited to classifying, processing and making predictions based on time series data. It has the ability to encapsulate the notion of forgetting part of its previously stored knowledge, as well as to add part of the new information. Personally I found that the highest level of accuracy is achieved when LSTM algorithm remembers only what happened in the previous 5 days.
LSTM was applied to predict the next day price of the XIV (short selling VXX). To be honest when the simulation was completed, I thought I discovered the holy grail of investing. Simply look at the image below, the two curves are matching.
My enthusiasm was short lived because looking closely at the two lines, there was a gap. The gap might not seem much but if we are thinking whether to short the VXX or being in cash based on this predicted value then this difference will play a major role.
I then ran a backtest in which the strategy was in cash if the expected next day return was negative and short VXX if positive.
What happened? It did not go well: poor performances and lot of drawdown. This means that the gap in value between the estimation and the actual value even if in appearance it looks small then it is not as negligible as one might think.
There are some techniques that can improve the results. I’ll illustrate them in the next post but in either cases…
The bottom line is: tomorrow can not be predicted with high enough accuracy, neither by humans nor by machines. Which in perspective is quite nice because otherwise life would be totally boring and dull.
Looking at the past
Historically gold coinage was widely used as currency. When paper money was introduced, it typically was a receipt redeemable for gold coin or bullion. In a monetary system known as the gold standard, a certain weight of gold was given the name of a unit of currency. For a long period, the United States government set the value of the US dollar so that one troy ounce was equal to $20.67, but in 1934 the dollar was devalued to $35.00 per troy ounce. On 17 March 1968, economic circumstances caused the collapse of the gold pool, and a two-tiered pricing scheme was established whereby gold was still used to settle international accounts at the old $35.00 per troy ounce but the price of gold on the private market was allowed to fluctuate; this two-tiered pricing system was abandoned in 1975 when the price of gold was left to find its free-market level. After 15 August 1971 Nixon shock, the price began to greatly increase, and between 1968 and 2000 the price of gold ranged widely. In late 2009, gold markets experienced renewed momentum upwards due to increased demand and a weakening US dollar. Gold further rallied hitting new highs in May 2010 after the European Union debt crisis prompted further purchase of gold as a safe asset [edited from: https://en.wikipedia.org/wiki/Gold#Price].
Why to value gold?
Gold is perceived as a safe asset to protect capital during: equities market downturns, periods of inflation and periods of stagflation. Understanding how its price might move in relationship to the equity market and inflation might help the investor to identify opportunities.
Modeling the gold price
Traditionally commodities prices depend on the law of supply, demand and inventories. Too much supply and the price will go down and vice versa. When it comes to gold, the situation is somewhat different. Because gold is perceived as safe heaven against inflation and bad economy, its price is mostly affected by the valuation of the equity market, consumer price index and money in circulation (the last two directly proportional to the level of inflation).
Regression was used to model the fair value of gold. Three inputs were used: S&P500 value, USA money stock and USA consumer price index. Regressing these three factors against monthly gold price, using more than 20 years of data, yields to a fairly good fit (i.e. 0.77 R2).
Like in the case of the S&P500 fair value model, we must keep in mind that these models are not predictive. An action must take place (i.e. actual value of the three inputs) for a reaction to happen (i.e. gold price).
The next question that comes to mind is: where is the gold price heading?
Because the gold price is affected by the equity market valuation, first we need to understand where the equity market might head. To do that, the model of the S&P500 presented in one of the Alpha Growth Capital previous articles is used.
From a fundamental perspective (GDP, CPI, money stock and corporate-treasure yield spread), the S&P500 looks to be overvalued between 14 and 28% (as per September the 1st). 28% assuming that the current USA GDP is the same as the one reported in 20Q2 while 14% assuming the GDP being the same of 19Q4 (i.e. all the time high).
Given that now we have an overview of where the market might be heading, the gold price can be estimated for three different scenarios. Using the current value of the S&P500 (September the 1st), according to this model, gold is somewhat overpriced by ca. 6%. In the eventuality, the market would move lower to its estimated value, the yellow metal might reach 2081-2255 USD/oz (ca. 5 to 12% higher than the current value).
I hope the reader enjoyed the article. I would like to remind that this article is not an investment advice and there are no certainties that in the future the gold and S&P500 values will move as indicated by the models and presented in this post.
Diversification: does it really protect your money when you need it the most?
If I am writing this article, it is because the short answer is: not quite, but…
Let’s start explaining the concept of diversification and why we need it. Diversify your portfolio means to take uncorrelated assets and combine them together in such a way to be protected from excess drawdowns during equity market downturn while generating alpha in the long run. Typical long term uncorrelated assets from the S&P500 (SPY) are: emerging market equities (EEM), gold (GLD), bonds (TLT), agricultural commodities (DBA), energy (XLE),… There are several techniques to select the appropriate allocation; one of the simplest way to do it is the Risk Parity methodology.
In theory this approach makes sense but what we must keep in mind is that the financial market is a very dynamic environment. As the chart below shows, the correlation coefficient (between different asset classes and the S&P500 dynamically calculated over a period of one month) substantially changes with the volatility of the market (VIX). In periods of lower volatility, the asset classes are somewhat uncorrelated from one another. When the volatility starts to spike (often associated with sudden pullback of the equity market), then most of the assets start to move in the same direction of the market (positive correlation). The only exceptions are: treasury bonds that move in the opposite direction (negative correlation) while gold is somewhat all over the place.
What does that mean for the portfolio? Let’s say that the portfolio is statically diversified over the six different asset classes, as soon as the volatility starts to spike (market moving down), five assets out of six will also move down thus limiting the downside protection risk. The only savior is treasury bonds.
If bonds are the only way to protect the portfolio when the market goes south, while keeping in mind that over the long run equities have the best return, then diversification can be heavily simplified by investing solely in equities and bonds.
There is a “but” to this: the splicing of the portfolio must be dynamic. In particular:
Moreover, if the profits should be maximized as much as possible:
Putting all this knowledge / steps together, we then get the dark blue time series. The light blue being the risk parity approach to the six different asset classes while the gray line is the benchmark.
Compared to the benchmark, dynamically diversifying between equities and bonds allows: increase the overall return by 26% while reducing the max drawdown from 56 to 15%. Dynamic diversification of truly uncorrelated assets creates the real hedge against market downturns. The risk parity methodology applied to the six statically uncorrelated asset classes would have resulted in 12% lower return than the benchmark and 33% maximum drawdown.
I hope you enjoy reading it and find the content useful.
Leave a comment if you would like to read more of these type of posts!
By Andrew White, CFA and Alpha Growth Capital LLC
FYI - Article was written on June 1, 2020, so is now out of date. Despite the market gaining about +5% in the week following, article conclusions still largely hold.
How to Value the Market Amid Economic Wipe-out?
In normal times, measures such as P/E ratio, dividend yield, or other traditional metrics are widely used to value the stock market. In abnormal times – such as the ongoing global pandemic resulting in the effective shutdown of huge parts of the national economy – traditional measures fall short. For how can you value stocks normally when there is no way to reliably estimate earnings and share dilution?
Over last 60 years though, one method stood the test of time that does not depend on traditional inputs: regression. It too requires inputs, but they are sometimes more discernible than traditional measures. To wit, just four inputs rationally predict S&P 500 fair value: Gross Domestic Product (GDP), Money Stock (M1), corporate bond spread, and CPI. And we think markets discount earnings?
Regressing these four factors against the monthly level of S&P 500 since 1959 (i.e. 60 years of data) yields a model with exceptional fit (i.e. 0.96 R2), credibility across factors/model itself (i.e. high t-stats and F-factor significance), and correlation/coefficient alignment. In other words, it is not coincidence and includes a range measure capturing most history (i.e. proxy for 3x standard deviation of residuals):
Given strong factor causation implied in the model above, it is natural to extrapolate the model forward to the end of 2020/beginning of 2021 amid the global lockdown to determine potential fair value level for the S&P 500. Amazingly, S&P 500 May-close value IS basically fair value re model (assumptions: -5% GDP, $6tn M1, 3% corp bond spread, -4% CPI over next 12 months). How? Federal intervention.
Where does the market go from here then? To determine market trajectory, consider the future of Federal stimulus, given it was responsible for providing the bridge over 2020 valley. Considering a range of estimates for GDP, CPI, and corporate bond spread, it is possible to estimate how much money the Federal government must pump into the market/economy to obtain market highs (current M1 = $5tn):
Scenario: V Economic Recovery
The US economic machine effectively came to a near full stop for two months, now begins to re-open in a bumpy fashion, and the Federal Reserve does “what it takes” to permanently re-start the engine. Specifically, the following assumptions are made:
·12-month GDP change: -10% over next 12 months
·12-month Corporate - 10Y T-bond spread: 2.8% (long-term average + 1 standard deviation)
·12-month CPI change: -4% (maximum decline in 2008/09 economic contraction)
·12-month M1 level: $7.5tn (+$2.5tn more stimulus that translates down to M1 level)
The question in this scenario is how much the federal government reacts, but react it is already clear they will. Exact level estimated is best left up to the stock market to predict. However, in this “V” scenario, the S&P500 is actually now 5% UNDER fair value (i.e. 3,200). If melt-up exuberance begins in earnest (i.e. valuation rises to proxy level for 3x standard deviation), S&P 500 has 20% upside to 3,600.
Scenario: U or W Economic Recovery
The economic recovery turns out to be deeper and more “U” or “W” as consumer spending does not return as fast as currently expected due to persistent unemployment and/or COVID 2nd wave. Thus, the Federal government and Federal Reserve inject vastly more stimulus. Specifically, the following assumptions are made:
· 12-month GDP change: -15% over next 12 months
· 12-month Corporate - 10Y T-bond spread: 4.4% (long-term average + 3 standard deviations)
· 12-month CPI change: -8% (twice the maximum decline in 2008/09 economic contraction)
·12-month M1 level: $10tn (+$5tn more stimulus that translates down to M1 level)
In short, bad - even horrific news - IS now a material positive for the S&P 500 as it effectively calls the federal government’s hand – in 2020 at least. In this “U or W” scenario then, the S&P500 is currently 10% UNDER fair value (i.e. 3,400). If a melt-up exuberance begins in earnest (i.e. valuation rises to proxy level for 3x standard deviation), S&P 500 has 30% upside to 4,000.
Not a Question of Whether to Buy Right Now. Question is How Fast?
According to our long-term regressed model for the S&P500, the S&P 500 incredibly is currently fairly valued. In an economic V recovery scenario, the market has potential for +5% to +20% upside all the way to 3,600. If an economic U or W recovery were to manifest, the S&P500 has potential for +10% to +30% upside all the way to 4,000. All…depending…on…the…federal…government.
S&P 500 has risks: e.g. re-openings, earnings, China trade, COVID-19 2nd wave, election, and what comes after. Market valuation (currently or post-additional federal stimulus) though is NOT one. Indeed, material upside remains before valuation even becomes a concern, according to our regressed model. Little backstopped downside; meaningful future stimulus upside; wall of worry. Place your bets.
The short answer I can give you is: I have no idea.
My investments so far have been systematic and macro based. The market moves in a certain direction and the macro points towards the asset that is more likely to generate the highest return within the next 30 days.
Despite, lot of folks have been talking about recession for at least the last couple of years. When the stock market reaches the all the time high, quite often we read of doomsday predictions right around the corner. A recession is defined by the GDP falling two consecutive quarters. Nothing in life or in the nature is coincidental. There is always some sort of cause-effect behind everything. The same applies to recession.
Now if you want to get a better insights on how the economy machine works, I would recommend to watch this video from Ray Dalio; https://www.youtube.com/watch?v=PHe0bXAIuk0&t=1097s.
The video is 30 minutes long and it provides a good overview of the bolts and nuts behind the economic machines. So it does about recession. If causes and effects can be clearly quantified, we can then think of creating a model and try to predict the next recession. I have tried to do that using a large part of the mechanics shown in the video. It was not easy and has you can see the model captures most of the recessions from 1929 to modern days, it misses the ones of 1945/48/53/60 and sometimes it predicts recession when (according to the standard definition) the GDP still goes up.
Let’s imagine that this model would been available to us back in 1928 (use lot of imagination) and then we would have bought the S&P500 when the probability of a recession is below 50% while going cash when the probability is above 50%. By now we should have managed to achieve a CAGR of 7.47% with a max drawdown of 51%. Buying & holding the S&P 500, we would have made 6.81% with a max drawdown of 86%. 0.66% might not seem much but if you would have invested $1 in 1928 by now it would have grown to $433 vs. the $129 of the buy & hold approach. Every drop counts.
Going back to the original question: is a recession around the corner? No, according to the model.
It has been a while since I wrote my last article. There has been hectic time with: work, Xmas break and developing AI based strategies applied to commodities and volatility products.
As I am getting better and better in understanding advanced forms of AI and their potential, I told to myself why not to share with the community what it is and how I am applying it to our preferred strategy: NEXT-alpha.
What is it?
In computer science, artificial intelligence (AI), sometimes called machine intelligence, is intelligence demonstrated by machines, in contrast to the natural intelligence displayed by humans. Leading AI textbooks define it as any device that perceives its environment and takes actions that maximize its chance of successfully achieving its goals. Colloquially, the term "artificial intelligence" is often used to describe machines (or computers) that mimic "cognitive" functions that humans associate with the human mind, such as "learning" and "problem solving".
A typical AI analyzes its environment and takes actions that maximize its chance of success. An AI's intended goal can be as simple as: 1 if the AI wins a game, 0 otherwise, or complex such as repeat actions that have been successful in the past. AI often revolves around the use of algorithms. An algorithm is a set of unambiguous instructions that a mechanical computer can execute. Many AI algorithms are capable of learning from data; they can enhance themselves by learning new strategies, or "rules of thumb", that have worked well in the past. Alternatively in the most complex cases: they can themselves write other algorithms.
Intelligent but not as human mind can do
The cognitive capabilities of current architectures are very limited, using only a simplified version of what intelligence is really capable of. For instance, the human mind has come up with ways to reason beyond measure and logical explanations to different occurrences in life. In simpler words: humans can innovate and move beyond the status quo, machines can only move on a straight line and hardly make evolutionary innovations that goes beyond the current status of the world we live in.
Does AI learn?
Yes, it does. It does it continually and thus constantly improving its ability to take decisions and successfully execute a task. The computer algorithms automatically constantly improve based on what they learn on daily basis!
How to apply this to finance?
The equity market has existed for centuries, the future market for millennial (Yes! From the time of ancient Greece). Like Ray Dalio says understanding the mechanisms behind long and short term cyclicality of the market in its broader sense (stocks, bonds, metals,…) can help to forecast the most likely event to take place in the future.
Now, once a mechanism is well understood, because it is a set of consecutive logical instructions, it can then be transformed in an algorithm, and once we have it in our hands we can then train it using a multitude of historical data that in some cases are tracing back to the beginning of 1900.
With NEXT-alpha this is exactly what we are doing. We have used historical data to train our AI model to understand the most likely asset that is able to generate money in the next 1 to 3 months. Algorithms keep on evolving over time and so it was for NEXT-alpha. It went through some adjustments since it is inception back in 2017. The core principles are still there, the percentage of positive months and magnitude of returns keeps getting better and better.
note: part of the article has been a re-edit from Wikipedia
The short answer is yes (!) and of course there are some “but”. If on one hand, we do not need to be financial geniuses to do that on the other hand we need: discipline, planning and start as soon as we are born (parents need to do some planning as well).
How to do that? Let’s start from the high level requirements. We are teens or less, we have not much money, let’s put this money to work in a passive managed index e.g. the S&P500. We have a bad crisis, money go down by 50-60%, we might not care much: all our life is in front of us, in absolute terms we are not losing much capital and we do not need this money right away. On the opposite side, let’s say we are 70 years old and we have just retired and we have to live out of our savings and we want our savings keep making money for us. Best place to invest them: short term bonds with a pay off of 2.1% per year and a max drawdown of 0.4%. In between these two extreme cases, we can think of allocating more and more money as we grow into bonds and less into e.g. the S&P500.
Let’s now get down to some details and let’s do that in chronological order i.e. from when we are born until we are 100 years old.
We are born and we get 1,000 USD and every year until we graduate from college at 25 y.o. we get in our saving account $500. We (our parents until we are 18 y.o.) take the money and invest them in the financial market, at the beginning 100% in the S&P500 and by age 25, 30% in bond and 70% in the S&P500. We then start working until we are 70. Because we are wise and we understand the importance of compounding, every year we incrementally add in our broker account some of our savings until the age of 70 in which we can comfortably put the equivalent of 2019 $12,000/year. By 2089, this should be 48,000 USD assuming 2% inflation per year. The money that we put on the broker account each year are invested in a combination of bonds and stocks as e.g. indicated in the table below according to a given age range. By 2089, we should have made $3.6M ($870,000 in 2019 money purchasing power).
What next? We start enjoying our well deserved retirement spending 3-4,000 USD/month (2019 value) while investing all the remaining part in bonds giving us a steady 2%/year.
It is not complicated to be a millionaire, it just requires some planning and discipline.
This is what it can be achieved by using the S&P500 and simple bonds, we can then thinking of moving (wisely) to more sophisticated investment instruments and then we get the real deal!
After having written about FOMO and the importance of an entry/exit strategy, it is now time to talk about how to build a portfolio.
We all know that our portfolio should be diversified, but why?
Fundamentally all of us are looking after maximizing the earnings while minimizing the risks. This can be effectively done by holding stocks, commodities and bonds. Easy, right? Yes, not a braniac. The question then become how much to allocate to each of the asset or strategy. We are now entering a trickier territory in which as investors we have to face the trade-off between risk and reward. We all want the strategy that in the long run gives the highest return (even knowing a priory the risk involved) but then in real life when we experience too much drawdown or a bad year we might rush into bad decisions such as revising our approach and thus ineffectively try to chase the tail.
When it comes to portfolio optimization, I personally use two approaches: risk parity and the Markowitz approach. I ll spare the post from the mathematical details, if you want to know more either ask or Wikipedia has good enough info. I find the approaches complementary mostly because the risk parity might not always give the risk-reward profile we are after (despite being very easy to compute, not quite the same for the Markowitz).
In the table below you can see how these two models are applied to a portfolio consisting of stocks (S&P500), gold and bonds (US medium term). The risk parity approach gives returns in between holding solely bonds or equities/gold while having low drawdown, higher Sharpe ratio and low correlation with the market. Using the Markowitz approach, while maximizing the Sharpe, the returns are as equities/gold while the maximum drawdown roughly half of what it is experienced in the last 15 years with these two assets. If on the other hand the drawdown is minimized then the results are very similar to the risk parity theory.
Two approaches and three different answers: up to our risk appetite to decide what to follow.