Question

Ebenezer Scrooge has invested 65% of his money in share A and the remainder in share B. He assesses their prospects as follows:

	A		B
Expected return (%)	15		19
Standard deviation (%)	21		21
Correlation between returns		0.5

a. What are the expected return and standard deviation of returns on his portfolio? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

b. How would your answer change if the correlation coefficient were 0 or –0.50? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

c. Is Mr. Scrooge’s portfolio better or worse than one invested entirely in share A, or is it not possible to say?

• Better

• Worse

• Not possible to say

Answer 1

Portfolio Return:
Portfolio ret is weighted avg return of Individual securities in portfolio.

Portfolio SD:

It is nothing but volataility of Portfolio. It is calculated based on three factors. They are
a. weights of Individual assets in portfolio
b. Volatality of individual assets in portfolio
c. Correlation betwen individual assets in portfolio.
If correlation = +1, portfolio SD is weighted avg of individual Asset's SD in portfolio. We can't reduce the SD through diversification.
If Correlation = -1, we casn reduce the SD to Sero, by investing at propoer weights.
If correlation > -1 but <1, We can reduce the SD, n=but it will not become Zero.

Wa = Weight of A
Wb = Weigh of B
SDa = SD of A
SDb = SD of B

Part A:

Portfolio Ret :

Stock	Weight	Ret	WTd Ret
A	0.6500	15.00%	9.75%
B	0.3500	19.00%	6.65%
Portfolio Ret Return			16.40%

Portfolio SD :

Particulars	Amount
Weight in A	0.6500
Weight in B	0.3500
SD of A	21.00%
SD of B	21.00%
r(A,B)	0.5

Portfolio SD = SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(A,B)]
=SQRT[((0.65*0.21)^2)+((0.35*0.21)^2)+2*(0.65*0.21)*(0.35*0.21)*0.5]
=SQRT[((0.1365)^2)+((0.0735)^2)+2*(0.1365)*(0.0735)*0.5]
=SQRT[0.0341]
= 0.1846
= I.e 18.46 %

Part B:

Portfolio Ret :

Stock	Weight	Ret	WTd Ret
A	0.6500	15.00%	9.75%
B	0.3500	19.00%	6.65%
Portfolio Ret Return			16.40%

Portfolio SD:

Particulars	Amount
Weight in A	0.6500
Weight in B	0.3500
SD of A	21.00%
SD of B	21.00%
r(A,B)	-0.5

Portfolio SD = SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(A,B)]
=SQRT[((0.65*0.21)^2)+((0.35*0.21)^2)+2*(0.65*0.21)*(0.35*0.21)*-0.5]
=SQRT[((0.1365)^2)+((0.0735)^2)+2*(0.1365)*(0.0735)*-0.5]
=SQRT[0.014]
= 0.1183
= I.e 11.83 %

Part C:

Portfolio is performing better than Share A. Because it has higher Ret and lesser SD compared to Share A.

Better is correct answer