投资学答案7-11章

7. In Dode’s case:

σp=9.2%

The portfolio’s standard deviation will be at a maximum when the correlation between securities A and B is 1. That is: σp=23.3%

7. If the efficient set were not concave, it would be possible to construct portfolio that dominate

portfolios on the efficient set. By definition, the efficient set contains portfolios that offer maximum expected return for given levels of risk and minimum risk for given levels of expected return. Yet if offer lower risk for a given expected return or higher expected return for a given level of risk, then the efficient set portfolios are not truly “efficient” –a logical inconsistency.

That one could construct such portfolios if the efficient set were not concave can be seen by referring to the situation in which all securities had correlations of 1. In this case, combination of two portfolios on the efficient set would lie on a straight line. If the efficient set had a “dent” in it, it would be possible to produce portfolios that lay to the northwest of the this “dent”. Because securities do not have correlation of 1, combination of efficient portfolios along the “dent” will lie even further to the northwest, again dominating the efficient portfolios and producing the logical inconsistency referred to above. 8. rp=1.5%+0.9*12%=12.3% 15. ε1=17.2-1.2*14=0.4

ε2=-3.1-1.2*(-3.0)=0.5 ε3=13.3-1.2*10=1.3 ε4=28.5-1.2*25=-1.5 ε5=9.8-1.2*8=0.2

Average=(0.4+0.5+1.3-1.5+0.2)/5=0.2 σε=1.03%

14. The market risk of a portfolio depends on events that influence all securities to some

degree. That is these events are systematic. Because all securities are affected by these systematic events, diversifying a portfolio will not reduce exposure to them. Only if the securities added to a portfolio had lower sensitivities to systematic events would diversification reduce market risk. But there is no reason to assume that randomly selected securities will have such lower sensitivities.

The unique risk of a portfolio depends on events specific to individual securities comprising the portfolio. These events are systematic in the sense that an event that impacts one security (in either a good or bad sense) is not expected to impact other securities. As a result forming a diversified portfolio tends to cause the net impact of these unsystematic events to cancel each other out. The more diversified is the portfolio, the greater will be this canceling effect, and the lower is the portfolio’s unique risk. Mathematically.

p[(Xii)IXi2i2]1/2

22i1i1nnLooking at the market risk term:

(Xii)2I

2i1nClearly,

Iis unaffected by diversification. Further, the term

2

Xii1niis merely the

average beta of the securities in the portfolio. Again, it is nor affected by diversification. Thus market risk cannot be reduced by diversification. Looking at the unique risk term:

Xi1n2ii2

2As the number of securities increases, Xibecomes small very quickly, while

i2remains roughly constant. Thus the unique risk term goes to zero as diversification

increases.

17. p0.3*1.20.5*1.050.2*0.91.07

p19.7%

第八章答案

4、rp=1.20*15%+（-0.20*5%）=17% rp=0.90*15%+0.10*5%=14% rp=0.75*15%+0.25*5%=12.5% 5、24%X1*18%X2*5%

X1X21X1=1.46 X2=-0.46

6、p=1.3*20%=26%

p=0.90*20%=18% p=0.70*20%=14%

7、20%=X1*25% X1=0.8

rp=0.8*12%+(1-0.8)*7%=11%

14、a、The riskfree asset has a zero variance and has zero covariance with other assets. Thus, the

third security must be the riskfree asset. b、rp=0.5*10.1%+0.5*7.8%=9%

p=[0.52*210+0.52*90+2*0.5*0.5*60]1/2=10.2%

 c、rtp=0.75*9%+0.25*5%=8%

tp=0.75*10.2%=7.7%

第九章答案

9、The CML represents the efficient set in the world of the CAPM. All investors will hold a portfolio lying on the CML. An investor’s portfolio will be composed of the market portfolio combined with either riskfree borrowing or lending, depending on the investor’s level of risk aversion.

The vertical intercept of the CML is the riskfree rate, often referred to as the reward for waiting. The slope of the CML is often referred to as the reward for bearing risk. Thus the CML represents how the securities markets value time and risk. 10、rM=0.4*10%+0.6*15%=13%

M=[0.42*202+0.62*282+2*0.4*0.6*0.3*20*28]1/2=20.7% rp=5%+（13%-5%）/20.7%*p=5%+0.39p 12、M=[0.2*242+0.3*360+0.2*155+0.3*210]1/2=15.8% 16、rp5%[12%5%]*18612.7% 2(13%)20、p=0.3*0.9+0.1*1.3+0.6*1.05=1.03

21、prprfrMrf16.671.2

157

p=[1.22*212]1/2=25.2%

22、b、ri6%(10%6%)i6%4%i c、rA=6%+4%*0.85=9.4% rB=6%+4%*1.2=10.8%

23、b、1=0.9*20*12/122=1.5 2=0.8*9*12/122=0.6

25、M=0.392*160+0.612*340+2*0.39*0.61*190=241.2

2AM=0.39*160+0.61*190=178.3

BM=0.61*340+0.39*190=281.5

A=178.3/241.2=0.74 B=281.5/241.2=1.17

26、Market risk is the portion of a security’s total risk that is related to movements in the market portfolio and hence to the beta of the security. By definition, because the market portfolio is perfectly diversified, market risk in a portfolio cannot be reduced through diversification.

Nonmarket risk is the portion of a security’s total risk that is not related to moves in the market portfolio. Rather, it is related to events specific to the security. As a result, unique risk in a portfolio can be reduced through diversification.

第十章答案

7、a、Factor risk=(0.4*0.2+0.6*3.5)2*225=1069.3 b、Non-factor risk=0.42*49+0.62*100=43.8 c、p=（1069.3+43.8）=33.4% 9、F=[（-312.5）/（-0.5*1.25）]1/2=22.4% 10、A=[0.82*182+252]1/2=28.9%

B=[1.22*182+152]1/2=26.3%

11、10-security portfolio: 225/10=22.5 100-security portfolio: 225/100=2.25 1000-security portfolio: 225/1000=0.225

第十一章答案

6． a. 0.2+Xb+Xc=0

2*0.2+3.5*Xb+0.5*Xc=0 Xb=Xc=-0.1

b. 0.2*20%+(-0.1*10%)+(-0.1*5%)=2.5%

c. The market’s action of buying security A and selling securities B and C will drive up the price of security A (reducing its expected return) and drive down the prices of securities B and C (increasing their expected returns).

13. A pure factor portfolio possesses a unit sensitivity to the particular factor and zero sensitivity

to any other factor. Further, it has zero non-factor risk.

A pure factor portfolio can be formed by buying and short selling a large number of secutities in appropriate proportion to produce the characteristics cited above.

15. a. bp1=1.5*0.5+(-0.5)*1.5=0 bp2=1.5*0.8+(-0.5)*1.4=0.5

b. bp1=3*0.5+(-1)*1.5+(-1)*0=0 bp2=3*0.8+(-1)*1.4+(-1)*0=1

c. rp=3*16.2%+(-1)*21.6%+(-1)*10%=17% d. Expected return premium=17%-10%=7%

20. In speculating about the appropriate APT factors, researchers and practitioners typically turn

to economic theory. They focus on broad economic variables that can logically be expected to affect the performance of all securities to some degree. For example, both the level of economic activity and inflation affect corporate earnings and dividends. Further, the term structure of interest rates (as measured by the location and shape of the yield curve) affects the discounted value of future earnings and dividends. Consequently, one can state with some confidence that investors’ expectations concerning these types of economic variables will systematically affect security returns.

21. a. A=370/400*0.7=0.65 B=370/400*1.1=1.02

b. rA=6%+(12%-6%)*0.65=9.9% rB=6%+(12%-6%)*1.02=12.1%

22. A=(156/324)*0.8+(500/324)*1.1=2.08 B=(156/324)*1+(500/324)*0.7=1.56