Chapter 5-HW2
6. a. calculate the expected holding-period return and standard deviation of the holding-period return. All three scenarios are equally likely.
HPR= (ending price-beginning price+cash dividend)/beginning price
Boom: HPR= (50-40+2)/40=0.3 =30%
Normal economy: HPR= (43-40+1)/40=0.1 =10%
Recession: HPR= (34-40+0.5)/40= -0.1375 =-13.75%
Standard Deviation=17.79 Scenario | Probability | HPR(%) | Probability*HPR | Deviation from Mean Return | Prob.*squared Deviation | Boom | 0.33 | 30 | 9.9 | 21.34 | 150.28 | Normal | 0.33 | 10 | 3.3 | 1.34 | 0.59 | Recession | 0.33 | -13.75 | -4.54 | -22.41 | 165.73 | Column sums | | | 8.66 | Variance= | 316.6 | | | | | Standard deviation | 17.79 |

b. Calculate the expected return and standard deviation of a portfolio invested half in Business Adventures and half in Treasury bills. The return on bills is 4%.

Expected return: (8.66%* 0.5)+ (4%*0.5)= 0.0633=6.33%
Standard deviation: 17.79%*0.5= 8.89%

7. a. What are the arithmetic and geometric average time-weighted rates of return for the investor?
HPR 2010-2011: (110-100+4)/100= 0.14= 14%
HPR 2011-2012: (90-110+4)/110= -0.1455= -14.55%
HPR 2012-2013: (95-90+4)/90= 0.1= 10%

Arithmetic: (0.14-0.1455+0.1)/3= 0.0315=3.15%
Geometric: [(1+0.14)*(1-0.1455)*(1+0.1)]1/3 -1= 0.0233= 2.33%

b. What is the dollar-weighted rate of return? | 2010 | 2011 | 2012 | 2013 | Net cash Flow | (-100*3)= -300 | (-110*2)+(4*3)=-208 | (90*1)+(4*5)=110 | (95*4)+(4*4)=396 |
0= (-300) + [-208/ (1+IRR)] + [110/(1+IRR)2] + [396/(1+IRR)3]
Dollar-weighted rate of return= IRR= -0.1661%

12. a. What is the expected return and standard deviation of your client’s portfolio?
Expected return= yE(rp)+(1-y)rf = (0.7*0.17) +(0.3*0.07)= 0.14= 14%
Standard deviation= y *σrp = (0.7*0.27)= 0.189= 18.9%

b. What are the investment proportions of your client’s