# Chapter 6 answers to Introduction to finance

**Topics:**Modern portfolio theory, Variance, Standard deviation

**Pages:**7 (3147 words)

**Published:**October 27, 2014

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 volatility compared to the original portfolio. The other three funds have shortcomings in terms of either expected return enhancement or volatility reduction through diversification benefits. Fund A offers the potential for increasing the portfolio’s return, but is too highly correlated to provide substantial volatility reduction benefits through diversification. Fund B provides substantial volatility reduction through diversification benefits, but is expected to generate a return well below the current portfolio’s return. Fund C has the greatest potential to increase the portfolio’s return, but is too highly correlated to provide substantial volatility reduction benefits through diversification. 4.a.One would expect variance to increase because the probabilities of the extreme outcomes are now higher. 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 0.40 -11 -4.40 -19.30 372.49 148.996

Normal 0.25 13 3.25 4.70 22.09 5.523

Boom 0.35 27 9.45 18.70 349.69 122.392

Expected Return = 8.30 Variance = 276.911

Standard Deviation = 16.641

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 0.40 -19.30 10 -193.0 -77.20

Normal 0.25 4.70 0 0.0 0.00

Boom 0.35 18.70 -10 -187.0 -65.45

Covariance = -142.65

Covariance has increased because the probabilities of the more extreme returns in the recession and boom periods are now higher. This makes the tendency for stock returns to be poor when bond returns are good (and vice versa) more dramatic. 5.a.Subscript OP refers to the original portfolio, ABC to the new stock, and NP to the new portfolio. i.E(rNP) = wOP E(rOP ) + wABC E(rABC ) = (0.9 0.67) + (0.1 1.25) = 0.728% ii.Cov = r OP ABC = 0.30 2.37 2.95 = 2.097 2.10

iii.NP = [wOP2...

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