Measuring Risk from Discrete distribution


We are familiar with the fact that  Political and economic uncertainty affect stock market risk.  Let’s understand it by example Indian we can’t forget the date of 8 November 2016 when demonetization held. Currencies of 500 and thousand rupees announce invalid and unworthy they returned document. Seen this market way,  if investor knew that the demonetization was what to hold in the currencies a power to ban,  he or she could take some steps, which can affect their return or risk.

 At the risk of oversimplification,  this outcome represented three different pictures for the market, and with each scenario having a different market return.

 Possible distribution for discrete outcomes

 Possibilities and probabilities are considered as a chance that an event will occur.  Like there 40% chance that India will win the match and 60% chance to lose it if all possible events considered and listed and if we give the probability to eat each event then the listing is called a probability distribution. And we all know probability 1 considered as 100% chance.

 Now consider an investor is facing a situation like a demonetization and there are three possible scenarios:

1.  Most positive case, 30% probability that the market would grow by 32%.

2.  Most likely case,  50%   e probability e that market would grow by 25%

3.   Worst case, a 20% probability that the market would go down by 43%.

Risk and return

Possible Rate of Return for Discrete Distribution

With the help of the payoff matrix, which you can see in the input section.  we can find out the weighted average of outcomes and a weighted average is the expected date of Return, ” r-hat”.

Here is the equation to calculate the expected Rate of return.

Discrete Return


 calculating stand-alone risk in discrete distribution:-

in a simple distribution, it’s easy to assess by looking at the dispersions of possible results, and distribution with widely dispersed possible outcomes is riskier and one with the narrowly dispersed outcomes.  On the contrary, when there are many possible outcomes that can occur, it became impossible to assess risk by just looking at the distribution.  We need a quantitative measure of the tightness of the probability distribution.  Standard deviations for work here, a symbol of standard deviation is sigma denoted as”σ”. 

Discrete Distribution

There are majorly two types of deviations first one is a large deviation which means that possible result are dispersed widely division refers that possible outcomes is tightly clustered around the expected value.

here is the following step to find the standard deviation-;

1.  Calculate the expected value of the rate of return

2.  Now deduct the expected value of the rate of return from all possible outcomes (ri)  to find a set of divisions.


3.   Now, square each deviation from the expected return and then multiply the square deviation to the possible cases.

4.   After getting the product of all squared deviations and possible cases we need to add them to get variances.


Continious Distribution

Normally investors prefer the scenario approach during special events such as the debt ceiling crisis European Bond crisis, oil supply issues, and Bank stress, in this scenario investor, would estimate more than three outcomes.  So here we can say that investor doesn’t estimate distorted outcome in the normal economic situation.


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