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Bond Valuation

  0 Downloads   |   2 Pages 364 Words   |   Published Date: 18/05/2017

Questions:

Consider shares in two companies, JAY and KAY, as follows:

 

Expected Return

E(R)

Standard Deviation

s

Correlation Coefficient

r

Share JAY

12%

18%

– 0.3

Share KAY

24%

32%

a) Calculate the covariance between Share JAY and KAY returns.

b) What is the expected return and standard deviation of returns on a portfolio comprising 35% in Share JAY and 65% in Share KAY?

c) If you wanted to create a portfolio consisting only of these two shares, how much would you need to invest (weights) in each share so that your portfolio return would be equal to 15.6%? Note: do not round.

d) Using the weights calculated in part c); calculate the variance and standard deviation of your portfolio. 

 

Answers:

(a).

Covariance between Share JAY and KAY returns: - To calculate the Covariance between Share JAY and KAY returns following formula is used:-

= Standard Deviation of JAY * Standard Deviation of KAY *(Correlation Coefficient)

= 18 *32 *(0.3)

= 172.6

Hence, Covariance between Share JAY and KAY returns is 172.6

(b). 

(i) Expected Return: - Expected return means that the return the investor can expect in the future. It is not the accurate return but only expected return. 

Expected Return = Weight of JAY *(Expected Return) + Weight of KAY * (Expected Return)

Expected Return = 0.35*(12) + 0.65 * (24)

Expected Return = 19.8%

Hence, the Expected Return is 19.8%

(ii)  Standard Deviation

√(WA2σa)+ (WB2σB)+2 (σA*WA*Σb *WB)* Correlation Coefficient

√(0.35*0.35*18*18)+(0.65*0.65*32*32)+2(18* 0.35*32*0.65*-0.3)

√39.69+32.64 -78.624

√393.706

σ = 19.84

(c). 

If a portfolio is to create consisting only of these two shares, and to make the portfolio return equal to 15.6% then  the investment is to be made of :-

Let assume the weight of JAY is W, then the Weight of KAY WILL BE 1-W

Desired Portfolio Return = 15.6%

15.6% = W*12%+ (1-W)* 24%

0.156 = 0.12W +0.24- 0.14 W

0.156 -0.24 =-0.12W

0.084 = 0.12W

0.084 / 0.12 = W

0.7 =W

Expected weight which is earned is 15.6%

Then weight of JAY (W) will be 70%

Weight of KAY (1-W) will be 30%.

(d). 

(i) Basis on the above calculation revised Standard Deviation is:-

 

New Weight

Standard Deviation

JAY

70%

18

KAY

30%

32


σ   = √ (0.70 * 0.70 *18 *18) + (0.30 * 0.30 * 32 * 32) + 2 (0.70 *18*0.30 *32 *- 0.3)

σ = √158.76 + 92.16 -36.288

σ= √214.632

σ = 14.65  

 

(ii) Variance is the square of standard deviation

Variance = (σ) 2

= (14.65) 2

Variance = 214.62.

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