1. What are the portfolio weights for a portfolio that has 135 shares of Stock A that sells for $48 per share and 165 shares of Stock B that sells for $29
... [Show More] per share?
The portfolio weight of an asset is total investment in that asset divided by the total portfolio value. First, we will find the portfolio value, which is:
Total value = 135($48) + 165($29) = $6,480 + $4,785 = $11,265
The portfolio weight for each stock is:
WA = 135($48)/$11,265 = $6,480/$11,265 = 0.57523 = 57.52%
WB = 165($29)/$11,265 = $4,785/$11,265 = 0.42477 = 42.48%
2. You own a portfolio that is 35% invested in Stock X, 20% in Stock Y, and 45% in Stock Z. The expected returns on these three stocks are 8%, 16%, and 11%, respectively. What is the expected return on the portfolio?
The expected return of a portfolio is the sum of the weight of each asset times the expected return of each asset. So, the expected return of the portfolio is:
E(RP) = w1 E(R1) + w2 E(R2) + w3 E(R3) = 0.35(0.08) + 0.20(0.16) + 0.45(0.11) = 0.02800 + 0.03200 + 0.04950 = 0.10950 = 10.95%
3. Based on the following information, calculate the expected return and standard deviation for the two stocks:
Probability of State Economy
Rate of Return Stock A
Stock B Recession 15% 4% -17% Normal 55% 9% 12% Boom 30% 17% 27%
The expected return of an asset is the sum of the probability of each return occurring times the rate of return occurring. So, the expected return of each stock asset is:
E(RA) = p1 R1A + p2 R2A + p3 R3A
= 0.15(0.04) + 0.55(0.09) + 0.30(0.17)
= 0.00600 + 0.04950 + 0.05100
= 0.10650
= 10.65%
E(RB) = p1 R1B + p2 R2B + p3 R3B
= 0.15(-0.17) + 0.55(0.12) + 0.30(0.27)
= -0.002550 + 0.0660 + 0.08100
= 0.12150
= 12.15%
To calculate the standard deviation, we first need to calculate the variance. To find the variance, we find the squared deviations from the expected return. We then multiply each squared deviation by its probability, then add all of these up. The result is the variance:
The standard deviation is So, the variance and standard deviation of each stock is:
A2 = p1 (R1A - E(RA))2 + p2 (R2A - E(RA))2 + p3 (R3A - E(RA))2
= 0.15(0.04 - 0.1065)2 + 0.55(0.09 - 0.1065)2 + 0.30(0.17 - 0.1065)2
= 0.00066334 + 0.00014974 + 0.00120968
= 0.00202275 [Show Less]