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What determines assets prices?

research 9 January 2017 455   

Price formula

Let’s have a look on shares, currency or gold. These assets are classified into one category, only because their storage does not cost anything, and therefore does not impose on the owner additional restrictions. In such a way, whole variety of factors that really affect their quotes, can be summarized in to three conditionally independent variables. This is – sentiment (social mood), money supply (aggregate reserves) and factor that responsible for the amount of asset:

What determines assets prices?
where C – asset price; K - dimensional coefficient;
S – social mood; MR – money supply; E – amount of asset.

Investor’s sentiment is the driving force of the market. This sentiment shows how expensive or cheap particular asset, that’s why wave-analysts interested in sentiment, but not in price of asset. Short period time frames of stock prices completely repeat investor’s sentiment trajectory, this fact significantly simplified task and reduce it to analysis of price chart. Long-term timeframes are different; in order to do analysis, it is necessary to get rid all extraneous factors.

It's hard to argue that $ 1 today is noticeably different from the dollar in the 2000 year. For the last 16 years purchasing capability of the US currency fell by almost half, and the monetary aggregate M2 in the US grew by 2,6 times, not included excess reserves on Federal Reserve accounts. US stock indexes during this period rose slightly, in such a way in constant dollars, US stock indexes remain in a corrective phase. However, we are unlikely to find an analyst who willingly admits it.

The idea of price cleaning from extraneous factors is not new. For instance, Robert Prechter in his book, “Elliot wave principle. Key to market behaviour”, provide 2 diagrams in constant dollars - the US market chart since the end of the 18th century (Figure 1) and chart of correctional wave from 1966 to the 1982nd years, when US inflation was especially strong. Unfortunately, Prechter does not develop this approach and did not answer the question, which chart have to be considered as correct for marking - regular price, in constant dollars, or some another one.

What determines assets prices?
Figure 1 – US stock market in constant dollars.

Aggregate reserves

Let’s consider person whose take into account personal finances as a bank. Such a person has an assets (house, cash, and shares) and liabilities, not just loans, but also future expenses (wellbeing in later life, education for children). This person also participant of the market, which has not just risk appetite, but also keep own reserve requirements. Reserves are cash and deposits, according to the rules, they are liquid and protected from market risks.

Bank reserves are in the treasury or regulator accounts. They should not fall below the required standards, but often exceed them, if the bankers do not want to invest or prepare for write-off. In all other things being equal, the more bank assets, the more it needs free reserves. The converse is also true – the more bank reserve, the more risky assets can be handled on balance.

Such an approach used by all market participants, include private investors, corporations and banks. In such a way, all this assets and liabilities can be sum up together, in order to obtain enclosed system which, in contrast to the particular bank, not able to manage nor any amount of assets on its balance E, nor the size of free reserves MR. The system regulates only the price and, as a consequence, the aggregate value of the assets of a particular class.

As mentioned, the main requirements to reserves: liquidity and lack of market risk. The accounts and deposits in foreign currency, as well as corporate and government bonds cannot be considered, except for securities with very short duration. In simplest version, MR formula is the sum of bank reserves, M2 aggregate, and investments in money market funds made by individuals and non-credit institutions:

What determines assets prices?
where M2 – money aggregate M2;
M0 – cash outside of banking system;
A – total amount of issued coins and banknotes;
F – investments in money market funds.

In present days, of era of infinite QE, the simplest value of MR not suitable. As part of this value must be considered excess reserves, which were formed as a result of the repurchase of assets, but do not need to take into account the money received in repo transactions by banks, swaps and other types of loans:

What determines assets prices?
where D – banks deposits on regulator accounts;
R - reverse repurchase agreements (if present);
L - repurchase agreements and other types of loans.

It should be noted that calculation methods of monetary aggregates differ by country, but it's a small problem. Within the large cycle, sentiment on currency pairs change up to 7 times, so the components, that provide in total no more than 20%, can be easily ignored, if their weight in the total mass is relatively stable. Detailed calculations have to be performed only for US, because dollar is major world currency and all exchange rates calculates against dollar.

Everywhere except the United States, don’t need to take into consideration reverse repurchase transactions, everywhere except the United States and the Eurozone cannot be taken into account money market funds and loan L, instead, net value D can be taken; instead of M2 in some cases, can be considered M3 or M4 aggregates, if regulator traditionally calculate it. For the US, the M2 calculation should be performed by component - this is the only way not to lose sight of the large deposits of more than 100 thousand dollars that Federal Reserve does not considered as part of M2.

In addition, reasonable attention should be given to data connectivity. It is often, when changes in method lead to situation when numerical row splits into two parts (before and after) where is hike between each other in 20 or even 40%, however within each part, money supply growth rates represented correctly. If it happens, simply multiply the older data on raising (or lowering) coefficient, in such a way that gap was filled.

Determination of sentiment

During the process of definition of main formula, there are few steps ahead has been made. It is clear that monetary supply boost lead to growth of stock indexes and gold, while increase in the number of assets drop the prices. What degree of these values should be used, also, why analysis based on money aggregate and inflation does not taken in consideration?

In order to answer such an awkward question it is necessary to address to the nature of social mood. As long as sentiment is the main active force, when it remains constant, any flow of capital from one market to another impeded, and therefore the share of the aggregate wealth U, invested in a particular asset class remains largely unchanged, namely:

What determines assets prices?

There are enough examples in market history, when stocks, bonds and commodities rose or fell simultaneously. Sentiment on them moved in one direction, but where were taken fresh money, if their number never change so rapidly? The answer is obvious – the picture of the world do not have a buffer that accumulates all unrealized sentiment (Figure 2). It can be called "inactive money".
What determines assets prices?
Figure 2 – model inactive money.

The aggregate wealth is full market energy - kinetic and potential. Sleeping money do not have physical cost, but able to obtain it if the global sentiment will begin to improve. The limit case, is when sleeping money are zero and aggregate wealth is the value of all risky assets, which are on the balance of the system. In such a way, the aggregate wealth is directly proportional to the volume of reserves MR:

What determines assets prices?

Now, in order to prove formula (1), it is enough to have just two assumptions. Firstly, the MR and E value do not depend on the perception of risk inside the system, which is obvious. Second, the sentiment S and C price linked by simple linear dependence. Otherwise it is necessary to call into question all the methods of technical analysis.

Fortunately, not necessary to calculate the absolute value of the sentiment that is impossible to do, because of the K coefficient. As wave-analyst it is interested in chart models, it can be obtained by implementation relative values in comparison with any past value. In order to implement this approach, it is necessary to select a reference point and put it S = 1. In all other points:

What determines assets prices?
where C₀ – price of the asset at the reference point;
MR₀ – money supply at the reference point;
E₀ – amount of asset at the reference point.

It needs to be noted that reference point can be chosen arbitrarily, but it is much more convenient to attach it to the deepest bottom, for example, considered OIL it is low of 98-year.

Currency pairs

For national currency amount of the asset E will be size of GDP. Actually, the more economy produce, the more it needs the money supply. At the same time it is critical to use the GDP at purchasing power parity (GDP PPP), nominated in US dollars. The official GDP can grow only because of inflation and do not reflect the real situation. The GDP PPP got rid from this disadvantage, it will timely indicate about overvaluation of national currency and need for devaluation. The formula of sentiment for national currency looks like this:

What determines assets prices?
where C and C₀ - dollar rate (units of currency per dollar);
MR and MR₀ - money supply in national currency;
G and G₀ - GDP PPC in US dollars.

In the formula (6) the numerator and denominator have been swapped. In such a way, sentiment improvement leads to strengthening of the national currency (dollar falls), formula implements principle of currency for asset, but not vice versa, as it can be done with gold or stock indexes. In case if all zero values will be removed, than it can be obtained monetization of GDP at purchasing power parity; it is the physical meaning of sentiment for the national currency. For the US dollar it is logical to accept C = C0.

It should be noted, that in real market, not separately taken currency traded, but its ration to any other currency. If in the Unites States increase GDP monetization, it is on the principle of communicating vessels will be reflected in all other countries and in all other things being equal, it will result in a similar increase in the monetization of their GDP. Sentiment for exchange rate is equal to sentiment ratio of included in that rate national currencies:

What determines assets prices?

Foreign markets it is another story. On the one hand, cross-border operations are demonstration of sentiment, which is move the exchange rates; on the other hand - it is an effective way to change not only the quantity of assets, but the amount of the reserves, when it comes to panic cash and deposits transfer in foreign currency. As a part of its model, changes of this values do not taken in consideration, assuming them insignificant.

Stock indexes

For stock markets, formula (6) applied in its pure form, but it doesn’t make analysis easier. As it mentioned, the sentiment is responsible for part of aggregate wealth that invested in all assets of one class, so that does not allow to pick from the total weight any single company or it is conglomerate that compose stock index. The only chance is to use the total market capitalization of the MC (the product of E and C), provided that the share of public companies does not change much from year to year.

Let’s give an example. During the period from 1900 to 1920 years, capitalization of the US market has grown 4.5 times, while the value of the SP composite index calculated by Robert Shiller, almost did not change - grew by a modest 12%. In the modern world, dominated by corporations, the broad market index is much more effective, so on a comparatively small historical term (within 20 years), consider to use assumption E = E0.

What determines assets prices?
Figure 3 - ratio of the market capitalization of the US (in trillion dollars) to the index SP composite.

In contrast to stock market indexes, capitalization data are insufficient. In open sources, it can be found only World Bank statistics, which is calculate MC value once a year since 1975. In order to cover larger historical period, it is necessary to look for correlation between this value and index value, by take into consideration that ratio. The research process of correlation, clearly demonstrate Figure 3.

The blue line on the right is the ratio, built by the World Bank for the United States market. Fourth years of available statistics is enough to identify long-term upward trend, which is caused by the emergence of new companies and grow of economy securitization. The physical meaning of the ratio points directly to its correlation with the logistic function (red line):

What determines assets prices?

In order to define curve, it is enough to determine value in its three points. Two values from modern period, third one have to find in books focused on the Great Depression - {f(28)=2.4, f(80)=9.2, f(114)=12.8}. The justification of theory is ration based on data from Lyndon Moore for the period from 1900 till 1925th years (blue line on the left). As it can be seen, its match pretty well, this fact provides analyst with freedom.

Of course, the actual curve differs from the theoretical. In fact, companies developed unevenly, one of the natural tendency to perform the listing only in a favourable conjuncture provide the error of 20%. In ancient history, it is permissible, in the modern period it is better to use a broad market index, or do specified calculation, synchronized it with the data on capitalization:

What determines assets prices?
where f(x) – spline-function created by ratios of capitalization to index in base points.

Exception, when stock index or capitalization of the whole market nominated in foreign currencies, strictly in US dollars. In this case, have to proceed similarly as with currency pair and represent S formula as the product of sentiment on index in national currency and sentiment at national currency in the pair with the US dollar. After necessary changes, the formula will looks like:

What determines assets prices?
where C and C₀ - value of index in US dollars;
G and G₀ - national GDP PPC in US dollars;
Susd – sentiment on the US dollar.

Now, sentiment does not depend on changes in country monetary aggregates. The dynamics completely hidden in quotes C, and place of aggregate wealth took by national GDP in purchasing power parity. In such a way, stock index, calculated in US dollars completely free from extraneous factors that raised due to exchange rate. The stock and currency markets are now equivalent in quality.

Precious metals

Gold is the only asset that does not associated with any particular country, except the United States, in whose currency calculated quotes. Investments in gold performed around the world, and the whole world is a closed system, where assets can be folded together, as in the case of banks, corporations and individuals. In particular country formula for gold similar to formula for index in foreign currency; Worldwide formula is:

What determines assets prices?
where C and C₀ - quotes in US dollars per ounce;
G and G₀ - world GDP PPP in US dollars;
E and E₀ - accumulated amount of investments in ounces;
Susd – sentiment on the US dollar.

In fact, short time-frame quotes of gold are closely correlated with the US dollar, in such a way dynamics of the American currency has been taken into account long time ago in the value of C and cannot participate in the evaluation of aggregate wealth. World GDP at purchasing power parity is the only option to assess. Product of GDP and sentiment on the dollar is the equivalent of the global money supply MR, which is purified from the sentiment of individual currencies.

The E value is the accumulated volume of private investments in gold, include coins and bars. This does not include the reserves of central banks, art objects and jewellery. These reserves stay long without actions, and year after year, do not participate in the formation of sentiment. From the perspective of private investors, all these reserves slightly differ from the reserves hidden in the ground.

Silver has two-faced nature, which means it can be considered as goods and money. Silver produced and consumed, but possession does not cost anything. Silver almost all the time traded similar with gold, but its investment reserves E is too small, to be considered this volume independent from quote C. It can be stated, that formula (12) can be applied to second precious metal, however proportions on chart unlikely will be perfect.


According to the principle of pricing, commodities significantly different from those assets that have been studied earlier. Commodities storage costs money, and its reserves are small compared with the annual production and consumption. As a result, sentiment on commodities does not depends on the money supply and the amount of E asset. From all extraneous factors, commodities quotes affected only by inflation.

What determines assets prices?
where C and C₀ - commodity quote in US dollars;
p and p₀ - consumer price index.

As can be seen, the trajectory of sentiment completely repeats the cost of an asset in constant dollars, but only if mining costs or production increase in proportion accepted to measure of inflation, which in fact is not usually performed. For example, oil and other mineral resources, steadily become expensive relative to the constant dollar, while food, on the other hand, become cheaper on a long-term trend.

It should be noted that in the formula (13) there was no place for the balance of supply and demand, which is entirely accounted in sentiment. There is a reasonable alternative to any type of commodities can be found, and car buyer, exactly the same bull on oil, as trader with a long position. They are both are guided by the subjective view of the world.

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