Chapter 6 answers to Introduction to finance
CHAPTER 6: EFFICIENT DIVERSIFICATION
1.E(rP) = (0.5 16%) + (0.4 10%) + (0.10 6%) = 12.6%
2.a.The mean return should be less than the value computed in the spreadsheet. The fund's return is 5% lower in a recession, but only 3% higher in a boom. The variance of returns should be greater than the value in the spreadsheet, reflecting the greater dispersion of outcomes in the three scenarios.
b.Calculation of mean return and variance for the stock fund:
(A) (B) (C) (D) (E) (F) (G)
Scenario Probability Rate of Return Col. B
Col. C Deviation from Expected Return Squared Deviation Col. B
Col. F
Recession 0.3 -16 -4.8 -25.4 645.16 193.548
Normal 0.4 13 5.2 3.6 12.96 5.184
Boom 0.3 30 9.0 20.6 424.36 127.308
Expected Return = 9.4 Variance = 326.040
Standard Deviation = 18.057
c.Calculation of covariance:
(A) (B) (C) (D) (E) (F)
Deviation from
Mean Return Scenario Probability Stock
Fund Bond
Fund Col. C
Col. D Col. B
Col. E
Recession 0.3 -25.4 10 -254.0 -76.2
Normal 0.4 3.6 0 0.0 0
Boom 0.3 20.6 -10 -206.0 -61.8
Covariance = -138.0
Covariance has increased (in absolute value) because the stock returns are more extreme in the recession and boom periods. This makes the tendency for stock returns to be poor when bond returns are good (and vice versa) even more dramatic.
3.[Note: In the first table for Problem 3, the percentages in the column labeled “Percent of Total” should be 10%, 30% and 60%, respectively.]
Fund D represents the single best addition to complement Stephenson's current portfolio, given his selection criteria. First, Fund D’s expected return (14.0 percent) has the potential to increase the portfolio’s return somewhat. Second, Fund D’s relatively low correlation with his current portfolio (+0.65) indicates that Fund D will provide greater diversification benefits than any of the other alternatives except Fund B. The result of adding Fund D should be a portfolio with approximately the same expected return and somewhat lower
1.E(rP) = (0.5 16%) + (0.4 10%) + (0.10 6%) = 12.6%
2.a.The mean return should be less than the value computed in the spreadsheet. The fund's return is 5% lower in a recession, but only 3% higher in a boom. The variance of returns should be greater than the value in the spreadsheet, reflecting the greater dispersion of outcomes in the three scenarios.
b.Calculation of mean return and variance for the stock fund:
(A) (B) (C) (D) (E) (F) (G)
Scenario Probability Rate of Return Col. B
Col. C Deviation from Expected Return Squared Deviation Col. B
Col. F
Recession 0.3 -16 -4.8 -25.4 645.16 193.548
Normal 0.4 13 5.2 3.6 12.96 5.184
Boom 0.3 30 9.0 20.6 424.36 127.308
Expected Return = 9.4 Variance = 326.040
Standard Deviation = 18.057
c.Calculation of covariance:
(A) (B) (C) (D) (E) (F)
Deviation from
Mean Return Scenario Probability Stock
Fund Bond
Fund Col. C
Col. D Col. B
Col. E
Recession 0.3 -25.4 10 -254.0 -76.2
Normal 0.4 3.6 0 0.0 0
Boom 0.3 20.6 -10 -206.0 -61.8
Covariance = -138.0
Covariance has increased (in absolute value) because the stock returns are more extreme in the recession and boom periods. This makes the tendency for stock returns to be poor when bond returns are good (and vice versa) even more dramatic.
3.[Note: In the first table for Problem 3, the percentages in the column labeled “Percent of Total” should be 10%, 30% and 60%, respectively.]
Fund D represents the single best addition to complement Stephenson's current portfolio, given his selection criteria. First, Fund D’s expected return (14.0 percent) has the potential to increase the portfolio’s return somewhat. Second, Fund D’s relatively low correlation with his current portfolio (+0.65) indicates that Fund D will provide greater diversification benefits than any of the other alternatives except Fund B. The result of adding Fund D should be a portfolio with approximately the same expected return and somewhat lower