The relationship between trading profitibility and forecasting accuracy is forecasting accuracy and trading profitability related? 
How to explain the existence of the relationship? 
Thank you. 
 A: This answer addresses the second question by explaining how greater forecasting accuracy could lead to higher profitability.  I present a model with the minimum of elements needed to demonstrate a  connection between forecasting accuracy and profitability.  It could be developed in many ways to correspond more closely to real situations.
Forecasting accuracy can be relevant to profitability in two broad circumstances: pure trading (eg share dealing); or trading as a business producing a good or service.  I describe the model in terms of the latter, although it could be adapted to the former by re-interpreting ‘cost’ as ‘opening price’ and ‘revenue’ as ‘closing price’.  
The essential elements of a relevant model are these:


*

*The business environment must be assumed to include a variable,
relevant to profitability, that is not known with certainty.

*The business must be assumed to make forecasts of that variable, and
there must be a way of quantifying or ranking the accuracy of the
forecasting.

*The business must be assumed to adjust its behaviour on the basis of its forecasts.

*There must be an assumption about how improved forecasting accuracy affects business costs (via the cost of the resources used in preparing forecasts).


Considering these elements in turn, my ‘minimal’ model assumes the following:


*

*The only relevant variable that is not known with certainty is the
demand for the good produced by the business, measured as a number
of units. Demand in any period is either 0 or 1 units. There is
independence between demand in any two periods.  An unsold unit
cannot be sold in a later period.

*The business forecasts demand in each period as either 0 or 1 units, and the probability that its forecast for any one period is correct is $p$.

*The business produces in each period the number of units for which it forecasts demand in that period.  This can be supported by a broader assumption that the businesses maximises its expected profit, based on what it knows or forecasts.  

*The costs of the business do not change with forecasting accuracy, in other words, the extra resources used in improving forecasting accuracy are negligible.  


To illustrate the working of the model, it is assumed that the ex ante probability in each period of demand being 0 or 1 is 0.5 each, revenue is 100 per unit sold and costs are 60 per unit produced.
Expected profitability $E[\Pi]$ in any period can then be calculated by considering in turn the four combinations of actual demand ($D_A$) and forecast demand ($D_F$):
$D_A = 1; D_F = 1$: Profit ($\Pi$) = Revenue – Cost = $100 - 60 = 40$.  Probability ($P$) $= 0.5p$.
$D_A = 1; D_F = 0$: $\Pi = 0 - 0 = 0$.  $P = 0.5(1-p)$.
$D_A = 0; D_F = 1$: $\Pi = 0 - 60 = -60$ (a loss).  $P = 0.5(1-p)$.
$D_A = 0; D_F = 0$: $\Pi = 0 - 0 = 0$.  $P = 0.5p$.
Hence expected profitability is:
$$E[\Pi]  =  0.5p(40) + 0.5(1-p)(0) + 0.5(1-p)(-60) + 0.5p(0)  =  50p – 30$$
Thus expected profitability is an increasing function of forecasting accuracy.  Break even (zero expected profitability) is achieved when forecasting accuracy is $0.6$.  Perfect accuracy $(p = 1)$ implies expected profitability of $20$ per period. 
It is not claimed that the model is realistic: obviously it isn’t.  What is claimed is that it demonstrates a connection between forecasting accuracy and profitability that can plausibly be expected to be present, albeit with modification, in many real situations.  
