How to beat stock market manipulators

The term 'stock market crash' has a striking similarity with the popularity of a celebrity. A celebrated figure such as an actor or actress comes into our notice when we see him/her in the big screen and likewise a stock market crash comes to our notice only when the crash is a reality. This is a dilemma that haunts professionals and academics. And the people in general start asking: why can't anybody warn before the crash that it is going to happen? So was the 2010 stock market crash: we rarely heard any forebodings not only from academics but also from active investors and professionals. When notorious manipulators and the greedy investors pauperised the gullible, we came to realise that a crash had happened and somebody had played the trick.
A lot of debates are going on how to stabilise the market through enforcing a strong regulatory framework. Those who believe that strong regulatory framework would ensure a stable stock market should at least remember that stock market crash can come in different ways, and the next crash, if and when comes, will not come in the same way as it came in the past. Besides, manipulators will always be there to look for any opportunity to manipulate the market and hoodwink the investors. Faced with these problems we have two feasible solutions at hand. First, beating the manipulators through strong regulatory framework and second, beating the manipulators through investment strategy by investors. We discuss below the second option.
In an article titled The art of investing in stock Market published in the Financial Express on September 15, 2014, we suggested that investors should gamble in the stock market using the money they gain from current trading and not using past profit or fresh capital. We will formally show how this simple strategy makes the stock market crash impossible even if manipulators try to manipulate the market. We assume the following situation: There is a representative group of stock market investors called X. They maintain a stock portfolio in which there is a stock called Z. We also assume that there is a group of manipulators called Y who are deliberately manipulating the price of the stock Z. The X don't completely know who are manipulating the price but at least know that they are playing a gamble on the price of the stock Z. In playing the gamble, X will invest in Z stock only using the money gathered from most recent gains from the stock market. To simplify the matter, we assume that X sell Z and use the gains from Z stock to repurchase a new lot of Z. On the other hand, Y increases the price of Z to encourage investors to invest in Z stock. But as the price of Z increases, the trading volume of Z decreases since X use gains from Z stock to repurchase a new lot of Z. Or we say more clearly as:

Now if we graph the above two functions, we find the following picture:

In the figure I, the price of Z stock (pZ) is measured on the horizontal axis and the total trade volume (TZ) and investment in Z stock (IZ) are measured on the vertical axis. The PQ downward sloping curve shows that as the manipulated price of Z stock increases, the total trade volume TZ decreases. The reason is that investors reinvest the gains in Z stock made from selling of Z stock and as the price increases trade volume must decrease since gains from Z stock and the manipulated price of Z stock must be inversely related. On the other hand, upward rising RS curve shows that as the manipulated price of Z increase, investors increase the investment in Z stock. But the investment IZ can be composed of two components. One is the immediate gains from stock market and the other is the fresh capital either borrowed or equity capital invested in the Z stock. As long as the curve RS remains inside the PQ curve all investment in Z stock will be carried by investing immediate gains from the stock market or the immediate gains from Z stock. When PQ and RS intersect, the equilibrium amount of trading at which no stock market crash happens is determined. This is short-term equilibrium in the stock market with short-term fluctuations. However, when RS crosses PQ and goes above it, the total investment in Z stock includes both immediate gains and fresh capital. When this happens, the stock market crash will happen. The figure shows that at p1, the total investment in Z stock exceeds the equilibrium trade volume of Z stock indicated by PQ curve.
In the figure II, RS is an upward rising curve that has positive second derivative. But the downward sloping curve RS indicates that investors invest only the immediate gains in the Z stock. This implies that RS curve must not have positive second derivative. In other words, the investment in Z stock will increase over time but at a decreasing rate with the increase of manipulated price of the Z stock. So, we have:

In the figure II, the upward rising ST curve shows that over time investment in Z stock increases with the increase in manipulated price but at a decreasing rate since investors invest only the recent gains in Z. And at any point of time, gains represent a small fraction of total capital invested in the stock market. As for the gains in Z stock, the total gain is a small fraction of the total capital invested in Z. So, investment in Z must rise at a decreasing rate over time. Over time ST will approach the equilibrium trade volume of Z at which stock market crash is impossible even if manipulators manipulate the market price of Z stock.  From the graph, we also see that trade volume of Z is same for any price level after p0 price. So, even if manipulators try to manipulate the market price of Z, they will be forced to leave the market since they can't increase the trade volume of Z increasing the manipulated price of Z stock. Therefore, after price p0, manipulators will give up and will be forced to leave the market; their incentive to raise the market price through unwanted manipulation is totally destroyed by the above investment strategy of stock market investors embodied into the ST curve. That means ST curve frustrates manipulators and ultimately beats them. Hence, manipulators are left with no choice but to leave the market with whatever they can grab, and market will not collapse due to their small grabbing.
The above analysis gives answer to most common questions. First, gambling in the stock market will not necessarily cause any significant crash if investors know how to gamble. Since the opportunities for gambling will always exist, there is little use asking investors to resist themselves from gambling. Rather, the more realistic approach is to know how to gamble. The above-mentioned investment strategy embodied into ST curve - gambling in stocks using most recent gains from the stock market - says an investor would never suffer significant loss due to gambling, and the stock market will never crash. Secondly, manipulator can't manipulate the market as to cause significant crash. This is also embodied into the ST curve. If an investor invests following ST curve, he will come out victorious beating manipulators no matter how smart and cunning manipulators are.  
On a practical note, this explanation implies that curbing manipulation through strict rules is in most of the cases a futile attempt because manipulation comes in different forms and shape. Just to mention some examples, when the dot.com bubble burst everybody came to know that bubble had burst. That was a big lesson for investors. But the puzzling fact is how did investors become the victim of housing bubble? The answer is: who knows? How did regulators become so blind in the face of such impending danger? Why couldn't they act before the burst and why did they remain dormant until the bubble burst? The reason is that every circumstance has unique characteristics and due to this feature people often delude themselves in thinking that this is not like in the past. Therefore, they wait, knowingly or unknowingly, until the bubble bursts. This is why regulators - how smart they are - fail to foresee or prevent a crash.

The contributor writes from the University of Denver, USA.   
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