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Sfm-three stock covariance matrix

Kumar Gaurav (Going...to be C.A soon...) (1624 Points)

26 June 2015

Hi experts

Please help me to solve this as i am unable to resolve it.-

STOCK	RETURN	SD	A	B	C
A	0.0427	0.1	0.01
B	0.0015	0.1044		0.0109
C	0.0285	0.1411			0.0199

How to calculate Covariance to fill blank table.

Its urgent, pls. help me out

Thanks

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20 Replies

(Guest)

R u sure tht u have copied the question correctly? Plz chk it again once.

Kumar Gaurav (Going...to be C.A soon...) (1624 Points)
Replied 26 June 2015

ok i will post orignal question again.

Kumar Gaurav (Going...to be C.A soon...) (1624 Points)
Replied 27 June 2015

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.

(Guest)

plz confirm the answer ..

E(R)= 33 %

S.D of portfolio = 12.35 %

Kumar Gaurav (Going...to be C.A soon...) (1624 Points)
Replied 28 June 2015

No dear S.d calculations are wrong. By the way how to calculate cov (xy) in this case?

(Guest)

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

what is the answer then ?

CA. Sunil Gokhale (Teacher) (1484 Points)
Replied 29 June 2015

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.

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Kumar Gaurav (Going...to be C.A soon...) (1624 Points)
Replied 29 June 2015

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)

(Guest)

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.

CA. Sunil Gokhale (Teacher) (1484 Points)
Replied 29 June 2015

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.

Kumar Gaurav (Going...to be C.A soon...) (1624 Points)
Replied 29 June 2015

Yeah, icai has taken many of the such assumptions which makes no sense at all and solved the questions accordingly.

Kumar Gaurav (Going...to be C.A soon...) (1624 Points)
Replied 29 June 2015

Pls help me to solve this one- Ques no. 37 (2nd part ) of practice manual Ques is related to minimum variance set Whre an investor wants to invest rs 4000 out of 8000 Pls explain the concept with simple language only.

CA. Sunil Gokhale (Teacher) (1484 Points)
Replied 30 June 2015

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

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