Risk and Return for CFP-4
Posted by Prashant Shah on February 8, 2013
Risk of a Portfolio:
|
Systematic Risk |
Unsystematic Risk |
|
Non-diversifiable risk / market risk |
Diversifiable risk / firm specific risk / residual risk |
|
|
|
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
PVS (Prashant V Shah) 
Manish said
Dear prashant sir,
i have one query regarding the usage of “alpha” term and facing a little bit of problem while interpreting it.As far as i know it is a risk adjusted return on an investment and it is a excess return on the stock over the benchmark,but somewhere else i read that it is the security propensity to move independent of the market.for ex there is one question with me in which we need to calculate the characterestic line:- expected return on security x is 2.079, market return= -0.247,cov(i,m)=41.930,variance of market returns=28.578,beta=1.467 and alpha works out to be 2.44.My question is what does 2.44 indicates in the equation?.
jasbir singh said
Dear manish,
Ur answer is included in the question, when you say that ” it is a risk adjusted return on an investment and it is a excess return on the stock over the benchmark”… 2. The abnormal rate of return on a security or portfolio in excess of what would be predicted by an equilibrium model like the capital asset pricing model (CAPM) required rate.
now let us understand this statement with the formula of alpha which is a=ybar-(b*xbar)…. now we know that the measure for systematic risk is beta.. here in formula ybar is expected return on stock while xbar is expected return of market, now by multiplying xbar with beta we will get required rate of return, which will be deducted from expected rate of returns of security(ybar)…. thus excess of ybar over required rate is obtained which is ‘alpha’
jasbir singh said
here 2.44 indicates the excess of 2.44% over required rate of returns which is calculated by CAPM