Question

Attention:Due to a bug in Google Chrome, this page may not function correctly. Click hare to lsarn mare 7. Using historical data to measure portfolio risk and correlation coefficient Aa Aa Michael is an investor who believes that past variability of stocks is a reasonably good estimate of future risk associated with the stocks. Michael works on creating a new portfolio and has already purchased stock A. Now he considers two other stocks, B and C. Michael collected data on the historic rates of retum for all three stocks, which are presented in the following table. Competehe table by calculating standard deviations for each stock: Year 2013 2014 2015 2016 Stock A 40% 10% 35% 5% Stock B 5% 40% 10% 35% Stock C 35% 5% 10% 40% Average return Standard deviation Suppose Michael can only afford to complement stock A by adding just one of the two other stocks, either stock B on stock C. Complete the following table by computing correlation coefficients between stocks A and B and between stocks A and C, and calculate average retums and standard deviation for the two pabential portfolios, AB and AC: Stocks A and EB Stocks A and Correlation coefficient Average return Standard deviation Suppose Michael has to choose between two portfolios, AB and AC. Michael will be better off choosing Portfolio AC Portfolio AB which of the following statements about portfolio diversifications are correct? Check all that apply Portfolios that include stocks of anly big companies minimize risk. Correlation between retums on stocks of small companies is smaller than retums on stocks of big companies. Diversification can reduce risk but not eliminate it. Retums on stocks in the same industry are more closely correlated than on stocks in differentindustries.

Answer 1

Calculation for Average return,Standard deviation and Corelation of Covarince of Portfolio A & B and Portfolio A & C

Yr   A   A-A mean   (A-A mean)square
13   40   25   625
14   -10   -25   625
15   35   20   400
16   -5   -20   400

1.A Mean(Average Return) =SUM(A data for all the years)/Number of Years
=(40+-10+35+-5)/4
=15
2.Variance(A) =(A-A mean)square/Number of Years
=(625+625+400+400)/4
=512.50
3.Standard deviation(A) =Square Root of Variance
=Sqrt(512.50)
=22.63846

Yr   B   B-B Mean   (B-B Mean)square
13   -5   -20   400
14   40   25   625
15   -10   -25   625
16   35   20   400

1.B Mean(Average Return) =SUM(A data for all the years)/Number of Years
=(-5+40+-10+35)/4
=15
2.Variance =(B-B mean)square/Number of Years
=(400+625+625+400)/4
=512.50
3.Standard deviation(B) =Square Root of Variance
=Sqrt(512.50)
=22.63846

Portfolio A&B Calculations
Yr   A-A mean   B-B Mean A-A Mean*    A   B   average    AB-AB mean (AB-AB
B-B Mean return A&B mean)square
13   25   -20   -500 40   -5   17.5   2.5   6.25
14   -25   25   -625 -10   40   15   0   0
15   20   -25   -500 35   -10   12.5   -2.5   6.25
16   -20   20   -400 -5   35   15   0   0

1.Average return of A&B(A&B Mean)=Average Sum of return of 2 Stocks
=(17.5+15+12.5+15)/4
=15
2.Standard deviation (A&B)=Square root (Average Sum of AB-AB mean square)
=Square root[(6.25+0+6.25+0)/4]
=1.7677
3. Correation of Covarianceo of stock A&B= [Average(A-A mean*B-B mean)/(Standard Deviation A*Standard
Deviation B)]
=[(-500+-625+-500+-400)/4]/(22.6384*22.6384)
= -.099
Portfolio A&B Calculations
Yr   A-A mean   C-C Mean A-A Mean*    A   B   average    AC-AC mean (AB-AB
B-B Mean return A&C mean)square
13   25   20   500 40   35   37.5   22.5   506.25
14   -25   -20   500 -10   -5   -7.5   -22.5   506.25
15   20   -25   -500 35   -10   12.5   -2.5   6.25
16   -20   25   -500 -5   40   17.5   2.5   6.25

1.Average return of A&C(A&C Mean)=Average Sum of return of 2 Stocks
=(37.5+-7.5+12.5+17.5)/4
=15
2.Standard deviation (A&C)=Square root (Average Sum of AC-AC mean square)
=Square root[(506.25+506.25+6.25+6.25)/4]
=16.007
3. Correation of Covarianceo of stock A&B= [Average(A-A mean*C-C mean)/(Standard Deviation A*Standard
Deviation C)]
=[(500+500+-500+-500)/4]/(22.6384*22.6384)
= 0

Portfolio A&B is Better Paid Of then Portfolio A&C