Tenth letter to Malaysian PM

The reason behind this letter is that I would like to address a concern about the December 1999 peak - nothing to panic about. I will digress quite a bit before coming to the point in order to get the ideas across.

I read NST 6th May 1999, Business, page 27, article "Malaysia's recovery 'phenomenal'". It got me thinking and gave me a clue. I believe that it is because of the swift implementation of recovery measures on the climb of the economic wave that resonance is taking place. This helps accelerate recovery.

Having said that let me say.

A lot of economic theory such as sales, marketing, demand and supply can be modelled with Probability Theory. The stock markets and a few other business phenomena can be modelled with Wave Theory. I have managed to develop a model that comprehends this change in behaviour from Probability Theory model to Wave Theory model.

The reason for bringing this topic up will become clearer when I discuss speculation and resonance and how to control excessive speculation. Lets make the assumption that all financial systems obey the law of demand and supply. Hence we can use probability theory to model the Demand and Supply curves for any product if empirical data is provided. But I'm using Wave theory to model the stock markets but stock markets too, must obey the law of Demand and Supply. So in order to make Probability Theory interchangeable with Wave theory, the Probability Theory model must converge to a Wave Theory model under certain constraints. In order to determine this constraining condition Probability theory models have to rewritten to be functions of time (t). This I have done, but without going into the details, here is the general reasoning, please bear with me a little further as I will switch from human language descriptions to mathematical descriptions.

The probability of sale of a product is described by

If one examines eqn. (1) and let p approach 1 in value, the final sales probability is indeterminate, because of 0/0 (a zero divided by a zero term). This gives us a clue that the system is oscillatory.

If we attempt to determine the final value at which eqn. (1) converges for values of p less than one, we let n ? ? hence pn ? 0. Hence

In order to examine stability, we need to convert this equation to z state space i.e. take the Z transforms.

just to double check that this conversion is on the right track lets determine the final value of this function using the Final Value Theorem.

Examination of Eqn. (4) above indicates that there is one pole, ( z + p ), that indicates that the system response will be oscillatory. When p=1, that is the probability of a sale is 100% the market becomes oscillatory or astable i.e. never settles. The market response is that of an oscillation of constant amplitude.

When p < 1 in magnitude the market exhibits a damped oscillatory behaviour before settling to a final value, the stock or market eventually dies.

There are systems where value of p can be larger than 1 i.e. p > 1. When this occurs the response is unstable that is oscillations with ever larger and larger amplitudes. But I'll be called a heretic to say that the probability of a sale can be greater than 1 i.e. greater than 100% as this goes against conventional thinking - the probability of an event occurring is always less than or equal one or 100%. But I would like to state that, in financial systems p can be greater than 1. For example when p > 1 the stock market exhibits excessive speculative behaviour resulting in very sharp climbs followed by very large drop in share prices.

The graph below shows what the three general oscillatory characteristics look like. In an actual stock market response there would be the added effect of inflation which would slant the curves slightly upwards. Resonance can result in either a an astable response or an unstable response. Heavy speculation can result in an unstable response where subsequent highs are higher and subsequent lows are lower.

For the stock market to be active and attract investors it needs to have generally, an astable response. In reality, it will be possible to find all three types of oscillatory behaviour among stocks in a large stock market. An astable response will ensure that there is plenty of trading activity and hence will make it much easier for companies to raise funds on the stock market.

Recent past experience, Asian currency crisis - a result of highly speculative attacks, has shown that the oscillatory behaviour that we need to avoid is sustained unstable response or highly speculative behaviour as higher market highs will be followed by lower market lows. That is the market boom and bust cycle will get more and more severe.

When I began this theoretical analysis to figure out what was the relationship between probability theory and wave theory, I had no idea that it would lead to solutions to stabilising the stock markets. Any way, the derivation of solutions is as below.

The response of this system can be modified by the use of a compensator. The conditions we need to modify are

1. The order of the numerator should be of a lower then the denominator
   
2. cancellation of (z + p) term and introduction of very much smaller probability of sale, d.
   
3. a further option would be lowering the Gain of the system.
   

The effect of this compensation would be to cancel out the oscillatory effect of (z + p) with a much smaller one, (z + d).

This equation show that it is possible to stabilise the stock market response by

1. Reducing the gain of the system with G.
   
2. Introducing a delay into the system response.
   
3. Shifting the value of the probability of sale to a smaller value p -> d.
   

1. limit the number of lots trade per transaction to smaller amounts. I believe a similar effect is carried out with capital controls where there is a limit as to how much a Malaysian can take out of the country. As for share trading this is covered in item (iii).

2. Introduction of a delay was carried by the KLSE before. They had between 5 minutes to 15 minutes delay between actual traded values and when public received the share prices information.

3. Cancellation or replacement of very high probability of trading (p>=1) with a much lower probability of trading. In other words make it more difficult to complete all trades for that particular stock. For example, what the maths suggest here is not complete suspension of the stock but a "partial suspension" (d << p). The key concept here is that of making trading difficult and for this to be effective it has to make trading difficult, for those with huge amount of funds to speculate, when heavy short selling or excessive speculation is in progress.

Partial suspension is explained as follows. Let us say that during normal trading activity (historically) a stock had a daily trading volume of 20 lots. During a highly speculative period, this volume traded has shot up to 200 lots traded per day. Partial suspension would mean that after first 20 lots are traded the stock cannot be traded until the next day.

This would allow the stock to move with the long term trends of the market but prevent speculative attacks from succeeding. As if market players are speculating based on T+5 period, implementation of partial suspension for T+6 or longer will reduce speculative activity as successful speculative activity requires, or is dependant upon, a buy order and a sell order (two transactions) over a very short period of time before actual shares (short selling) or money (speculation) changes hands. Hence once this D(z) compensator is activated there is no guarantee for the prospective speculator that he can complete both buy and sell orders within a short period of time as he has to compete with every one else (thousands of other speculators) for a limited number of trades per day. For example, using the example above, if 200 lots were bought by speculators at the beginning of the T+5 period after which the D(z) compensator was activated, subsequent trading days would only allow 20 lots traded per day. Therefore it would take a minimum of 10 days for the sell off to occur and 50% of the speculators would need to pay up by T+5.

Longer term investments will show a lower probability of transactions as there is only one transaction, a buy order or a sell order over a short period of time.

It is important to note that the partial suspension of stocks needs to be carried with the delayed release of share price movement for that particular stock.

Personally, I don't think taxation (eg. Tobin Tax) would be effective in neutralising excessive speculation as it does not discriminate between genuine & long term investors and short term speculators. Neither does it discriminate between healthy short term speculation and excessive short term speculation and we do need some degree of short term speculation to keep the markets volatile. But the D(z) compensator does not address the problem of rapid out flow of funds. For the D(z) compensator to be effective, the market has to be internalised, as in the case of the Ringgit and cessation of CLOB which is what the Malaysian authorities have implemented. This is because the two necessary conditions for effective compensation is Observabilty and Controllability. That is if the authorities cannot observe what is happening to the market they will be unable to compensate for trends, like wise if they do not have the legal or sovereign right to compensate the trends then they cannot do so.

The other advantages of the D(z) compensator is that it would cause funds to move to other stocks, that is, cause a better spread of funds across the market during highly speculative periods. But the D(z) compensator should not be used during normal periods otherwise it will kill off the market.

When to activate the D(z) compensator? The KLSE already has a rule - 30% increase in share price within a trading day, my guess is that this will be good enough a guide for activation under normal conditions. But when the mood turns ugly and the speculators are attacking for the fun of it, 30% change in prices per day may be too late. I do not know what would be good rule for activation during short selling.

Unlike stock markets which require healthy speculation for volatility, currencies need to exhibit little or no low frequency oscillations (small day to day oscillations - higher frequency oscillations, of low amplitude that do not affect the long term trends are O.K.). That is the transient response should die out as fast as possible to a final value. This is because stock markets and currencies have different functions or roles to play in a healthy global economy. Stock markets are used to raise funds but currencies are used for the transfer of funds, goods and services. When currencies change rapidly we would expect the global economy to shut down as international trade would oscillate unstablely, resulting in periods of excessive trading followed by periods of no trade. These periods of no trade will affect domestic economies of most countries, especially those involved in international trade (creating local recessions). Is this what the international community wants? Hence the probability of trading in currencies should be closer to zero. That is what Malaysian limited exchange controls have done.

I do hope that this information will help prevent a runaway peak in December 1999.

This article on the 10th letter to PM was reproduced here by Dr. Peter Achutha - 24 December 2017.