Measuring Risks

Meaning of Risk

The term 'risk' can be defined as the probability of something bad happening. In other words, it is an actual outcome or investment's return that differ from expected outcome or return. It includes the possibility of losing all or some of an original investment. Mathematically,

Risk = Sum [Actual Return - Expected Return] i.e. Risk = Sum [R- R Bar]

Risk is a condition in which there is a possibility of an adverse deviation from a desired outcome that is expected or hoped for- Emmet J. Vaughan and Theres Vaughan

In finance, it is generally representing by sigma i.e. standard deviation of various outcomes.

Types of Risk

There are various kinds of risk that can be categorized into the following basis:

1. Based on Chance of Occurrence: Pure and Speculative
2. Based on Flexibility: Static and Dynamic
3. Based on Measurability: Financial and Non-Financial
4. Based on Coverage: Fundamental and Particular
5. Based on Behavior: Subjective and Objective
6. Based on Diversification: Systematic and Unsystematic
   

Here, we'll focus on the category of Diversification Based Risk that are basically divided the total risk into two parts described as bellows:

1. Systematic Risk: It is also known as un-diversifiable/market/rewardable risk. It is associated with market. These risk includes market risk, interest rate risk and inflation rate risk. It can be calculated by multiplying the beta coefficient of the company or stock with variance of market.
   

2. Unsystematic Risk: It is also known as diversification risk/firm-specific risk/non-rewardable risk. It is associated with company or industry. These risk includes business risk and financial risk. It is the remaining part of total risk after deducting the systematic risk from total risk. It cannot be calculated.
   

• Total Risk: It can be calculated by calculating the variance of any stock or company. In other words, it is sum of systematic risk and unsystematic risk.
  

Forms or Measures Risk

There are various types of measures that represent the risk in the investment project. The following are the most measures that are used to calculate the risk as:

• Standard Deviation: A standard deviation (or σ) is a measure that shows how dispersed the data is in relation to the mean or average. The following formula is to calculate the standard deviation as:

Fig: Formula of Standard Deviation

• Beta Coefficient: The beta coefficient is the tool for measuring the systematic risk. It measures the sensitivity (volatility) of a particulars security return in response to market return.

The beta coefficient of market is always considered as 1. The beta coefficient for any assets can be calculated as:

Fig: Formula of Beta Coefficient  

Nature of Stocks by Beta Coefficient

Basically there could be three conditions raised mentioned as bellows:

1. If B>1 : High Volatility- An Aggressive security assets

2. If B<1 : Low Volatility- A Defensive security assets

3. If B=1 : Neutral - An Average security assets  

Now, which security stock can be purchased for investment purposes that vary from person to person because every person has its own unique risk taking capacity or risk profile. In general, higher the risk higher the return philosophy has been found.

Note: Standard Deviation and Beta have only discussed because others are not required here.  

Parameters for Portfolio risk

Basically there are three parameters that are essentials or required for calculating the portfolio risk mentioned as bellows:

• Risk of each individual assets or company 

• Weight of Investment amount 

• Covariance or correlation coefficient between the assets

According to Hery Markowitz, he has given a formula for calculating the risk presented as bellows:

  OR

 where, COA of AB = (Sum [Ra- Ra Bar] [Rb- Rb Bar]) / n- 1 

            Correl of AB = COV of AB / (Sigma A * Sigma B)

Note 1: If there are more than 2 assets the number of COV will also be increased and it can be calculated as :

No. of COV = n * (n-1). For example for 3 assets the number of COV will be: 3 * (3-1) = 3* 2 = 6 and so on.

Note 2: The correlation studies the relationship strength between two variables. The correlation coefficient value lies between -1 to +1. If the correlation coefficient value will become exactly 0 then it means there is no correlation between or among the assets. If the correlation coefficient value will become exactly +1 then it means there is perfectly positive correlation between or among the assets similarly, if the correlation coefficient value will become exactly -1 then it means there is perfectly negative correlation between or among the assets.

Note 3: Covariance shows the direction of the linear relationship between two variables. The covariance values is measured by comparing with 0 numeric value. It could be COVab>0 or COVab<0 or COVab=0. If the COVab value is greater than 0 then it is called upward linear relationship. Similarly, if the COVab value is less than 0 then it is called downward linear relationship otherwise it will say as  zero linear relationship between the variables.

Conclusion

The term 'risk' can be defined as the probability of something bad happening. It is an actual outcome or investment's return that differ from expected outcome or return. The total risk can be divided broadly into two parts as systematic risk and unsystematic risk. The most measures that are used to calculate the risk such as standard deviation, beta coefficient, value at risk and conditional value at risk. A standard deviation (or σ) is a measure that shows how dispersed the data is in relation to the mean or average. The beta coefficient is the tool for measuring the systematic risk. The beta coefficient of market is always considered as 1. Basically there are three parameters that are essentials or required for calculating the portfolio risk include risk of each individual assets, weight of Investment amount and covariance or correlation coefficient between the assets. The correlation coefficient value lies between -1 to +1. If the correlation coefficient value will become exactly 0 then it means there is no correlation between or among the assets.

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