Sfm-three stock covariance matrix

ok i will post orignal question again.

Hi jyotsna

Pls find question in detail-

Stock               E(R)                S.d                    Variance-covariance Matrix

                                                                         A               B             C

A                      30%               16%                     256

B                       40%               20%                                    400

C                      20%                 8%                                                     64

Find out the E(rp) & SD of a portfolio comprising 70% of A and 30% of B.

plz confirm the answer ..

E(R)= 33 %

S.D of portfolio = 12.35 %

cov(x,y) = i did (30 -33)*(40-33)

what is the answer then ?

If this is the complete problem then the only way to find the SD is to assume that the correlation coefficient is 1. In which case the S.D. = 17.2%

Otherwise, we need the correlation coefficient to be give or at least the covariance between A & B to find the SD of the portofio contain 70% of A and 30% of B.

Thank you Mr. sunil for helping us.

You are right sir, as question is done by assuming correlation 1.

Otherwise, we need the correlation coefficient to be give or at least the covariance. (Thanks for the information)

 

Originally posted by : CA. Sunil Gokhale
	If this is the complete problem then the only way to find the SD is to assume that the correlation coefficient is 1. In which case the S.D. = 17.2% Otherwise, we need the correlation coefficient to be give or at least the covariance between A & B to find the SD of the portofio contain 70% of A and 30% of B.

we have assumed correlation coff. to be 1 to arrive at answer..But isn't it an inappropriate assumption?

i mean generelly its very rare that two security are perfectly positivly corelated and even data given above does not reflect this.

You are absolutely correct Jyotsna, in reality correlation of +1 or -1 are never observed. However, +1 is often taken as an assumption in the examination and you should keep that in mind. Similarly, you will find that in some cases the simple average beta of a portfolio is used instead of weighted average which is highly inappropriate.

Also you may have already solved that problem of three companies shares and bonds where market return is not given. You find the return of this portfolio and assume that to be the market return to solve the problem. This type of problems has been repeatedly asked in the exam but makes no sense at all [see Q-2(a) May 2015]. Such type of problem would be better solved by assuming market return.

You should be fully aware of this type of assumptions that are required to be made in the exams.

The Q appears as 36/37 depending upon the PM edition you have.

Visualize the problem like this: The person wants to invest Rs.4,000 out of Rs.8,000 in A this amounts to 0.5 of the total funds.  You are now trying to create portfolio Z where you know only the weight of security A and that is 0.5.

                              WA         WB           WC

Portofolio X           0.30        0.40         0.30                  (given)

Portofolio Y           0.20        0.50         0.30                  (given)
Portofolio Z           0.50           ?             ?

First we will try to find the weight of security B by taking the pairs of weights of WA & WB as minimum varinace combinations. A portfolio is a minimum variance set because of the covariance between the securities in the portfolio. From the two portfolios, X & Y, we observe that the two optimal mix combinations between security A & B are: (0.30 & 0.40) as well as (0.20 & 0.50). There must be other combinations of the mix which reduce varince but we don't know them yet like (0.50, ?). These two weights can be considered as two variables 'x' & 'y' and their combination pairs can be plotted on a graph to obtain a line which will have an equation. If we know the value of one then we can find the other using the equation of the line. Equation of a line is given by: y = mx + c. Where 'x' will be the weight of A and 'y' will be the weight of B. From the information given in the problem we see that in portfolio X the weight of B is 0.40 when the weight of A is 0.30, thus

0.40 = m(0.30) + c

Similarly, from portfolio Y

0.50 = m(0.20) + c

solving we have: m = -1 and c = 0.7

The equation of the line is thus y = -x + 0.7

If 0.5 is the weight of A we now can find the weight of B from the line of the equation.

y = -0.5 + 0.7      = 0.2

If 0.5 & 0.2 are the weights of A & B then obviously weight of C = 1 - (0.5 + 0.2) = 0.3

Thank you Sir, I really appreciated your knowledge & spending your valuable time for helping students.

Thanks alot!