Risk and Return Analysis in Financial Management

Risk and return analysis in Financial Management is related with the number of different uncorrelated investments in the form of portfolio. It is an overall risk and return of the portfolio.

Portfolio

The collection of multiple investments is referred to as portfolio. Mostly large size organizations maintains portfolio of their different investments and hence the risk and return is considered as the entire portfolio risk and return. Portfolio may be composed of 2 or more bonds, stocks, securities and investments or combination of all.

Risk is Relative:

The risk associated with the investments in stocks of Company XYZ generally decreases as more and more investment is made in different stocks of other uncorrelated companies. It is clear from an example in which a person is running a particular business that provides him return of $200,000 per month. Another business is also run by the same person that gives him $ 400,000 loss. Then that person will look onto both of his businesses in order to calculate overall rate of return for his investments. Similarly if different investments are made in stocks and bonds, then all of these are considered in calculating the overall portfolio risk & return. If a person has portfolio of different uncorrelated investments then risk of additional investment in particular Company XYZ will be changed. This means that when a person (organization) keeps portfolio having large number of different investments than further investing in particular share of Company XYZ will be different.

Diversification:

The risk of additional investment in certain share of Company XYZ will be different after maintaining portfolio of many uncorrelated different investments. In fact the risk is reduced by investing in different shares & bonds of different companies & in different countries. Diversified investments result in lowering of risk. With the increase in the size of portfolio, the level of risk generally reduces.

Portfolio Risk & Return

Portfolio of investments has overall Risk & Return which is considered. When additional investment in certain stock or bond is made, then the incremental effect of that additional investment on the entire portfolio is viewed.

Investment Rule:

The investor will struggle to minimize the portfolio risk and maximize the portfolio return on his investments. The investor will not be willing to take on additional portfolio risk unless additional portfolio return is provided to him.

Kinds of Risks for a Stock:

Following are the kinds of risks related with stocks that create uncertainty in the future possible returns and cash flows.

Total Risk of Stock = Diversifiable Risk + Market Risk

Diversifiable Risk:

Diversifiable risk is Company Specific or Non Systematic and is connected with the random events of respective Company whose stocks are being purchased. Examples of random events include successful marketing campaign, winning major contract, losing a charismatic CEO and losing court case etc. Diversification can reduce diversifiable risk. The good random events influencing one stock will be cancel out by the bad random events that influence another stock of the portfolio.

Market Risk:

Market risk is also called Beta Risk or Non-Diversifiable Risk and is connected with Socio-political & Macroeconomic events that occur on global basis. The stock investments in every stock market of the country are systematically influenced by these global events i.e. Macro Market Interest Rates, Inflation, War and Recession etc. Market risk is never reduced through diversification.

 

Portfolio’s Expected Rate of Return (rP):

The weighted average of expected returns of every single investment in the portfolio is referred to as portfolio’s expected rate of return. Following is its formula which is similar to the expected return for single investment but its interpretation is quite different.

rP* = r1 x 1 + r2 x 2 + r3 x 3 + . . . + rn x n

In case there are “n” no of various investments in the portfolio then r1 corresponds to the expected return (in % age) on investment no.1 and x1 corresponds to the weight of investment no.1 (fraction of the Rupee value of total portfolio represented by investment no.1).

Example:

Suppose an investor have portfolio of the following 2 stock investments.

Stocks:           Value of Investment ($)         Expected Return

Stock A:                    40                                                   15

Stock B:                    60                                                    20

Total Value = 100

Now the expected rate of return of above portfolio is calculated by the following formula

rP* = rA x A + rB x B

rP* = 20% x (40/100) + 15% x (60/100)

rP* = 8% + 9%

rP* = 17%

Portfolio Risk of 2 Stock Investments:

The portfolio risk is not the weighted average risk of the singles investments and more specifically it is less than weighted average risk of single investments. Following is formula of portfolio risk of 2 stocks.

p =     X_A² σ_A² + X_B² σ_B² + 2 (X_A X_B σ_A σ_{B      AB}

The investment A’s weight in total value of portfolio is represented by X_A and investment A’s single risk (Standard deviation) is represented by σ_A.       _AB represents correlation coefficient called covariance term which evaluates the correlation in the returns of two investments.

Example:

Following is the data of portfolio of two stocks

Stock:              Value        Expected Return        Risk (Std.dv)

Stock A:              40                        20                      20%

Stock B:              60                         15                     10% 

Total Value = 100         Correlation coefficient = +0.6

Portfolio risk is calculated by using following formula

p =     X_A² σ_A² + X_B² σ_B² + 2 (X_A X_B σ_A σ_{B      AB}

p = {(40/100)² (20%)² + (60/100)² (15%)² + 2 [(40/100)(60/100)(20%)(15%)(0.6)]}^0.5

p = {(0.16) (0.04) + (0.36) (0.0025) + 2 [(0.4) (0.6) (0.2) (0.15) (0.6)]}^0.5

p = {(0.0073) + 2 [(0.00432)]}^0.5

p = {0.01594}^0.5

p = 0.1262 or 1.26%