Risk of a Portfolio:
Systematic Risk
|
Unsystematic Risk
|
Non-diversifiable risk / market risk
|
Diversifiable risk / firm specific risk / residual risk
|
- Unpredictability of monsoon
- Changes in economic policy, inflation
- War & other calamities
- Increase or decrease in inflation rates
|
- Company strike
- Bankruptcy of a major supplier
- Death of a key company officer
- Unexpected entry of a new competitor
|
Total risk (δ ) = Systematic risk + Unsystematic risk
|

- This traditional chart clearly states for equal weighted portfolio that, as you increase the number of securities, the unsystematic risk declines but at decreasing rate while systematic risk remains constant
- The benefit of diversification tends to decline with increase in the number of securities
Risk Classification Mathematically:

Beta: A measure of Systematic Risk
- Beta explains the sensitivity of security return with respect to market return
- Market return is an independent variable and stock return dependent variable.
- There can be ex-post (Historical) and ex-ante (Estimated) beta
- Mathematically it is derived from the relationship between market return and stock return
- Based on this a regression line is formulated
- Regression line is also known as characteristic line [Y = a + βX]
- The slope of this line is beta, which shows the changes in stock return given the change in the market return

Interpretation of Beta
- β >1 : aggressive security (β =1.2, 10% change in market will have 12% change in stock)
- β <1 : defensive security (β =0.8, 10% change in market will have only 8% changes in stock)
- β =0 : Risk-free security (No change)
- β =1 : Market Portfolio (Portfolio replicating market index) (Same Change)
Exercise
Probability
|
Stock Price (exp)
|
Sensex (exp)
|
0.3
|
10
|
4370
|
0.4
|
11
|
4750
|
0.3
|
12
|
5130
|
Current price of the stock is Rs.10. Expected dividend is Rs.1 per share and current sensex value is 3800. Calculate Beta of the stock.
Note:
- We require returns to solve the question
- Answer: 1
Beta of the portfolio is the weighted average of the beta of the securities. Based on the same concept FPSB has asked a few question.
Mr. A’s portfolio consists of two stocks A and B in which he has invested Rs. 75,000 and Rs. 67,000, respectively. Stock A has beta of 1.4 and stock B has beta of 0.80. The return expected from the market in current scenario is 12% while the return on Treasury bonds is 7%. What is the expected return from the portfolio?
Answer: 12.58%
Hint:
- Find the weighted beta of the portfolio. [(75000/142000)*1.4]+](67000/142000)*0.80]
- Put the beta value in the CAPM equation.(we are yet to study the same.)
Your manage a Rs. 10,00,000 portfolio. You are expecting to receive an additional Rs. 6,50,000 from a new client. The existing portfolio has a required return of 10.25 percent. The risk-free rate is 5 percent and the return on the market is 9.5 percent. If you want required return on the new portfolio to be 11 percent, what should be the average beta for the new stocks added to the portfolio?
Answer: 1.59