Investments, tenth edition

  Sharpe  ratio,    

which is the slope of the CAL, is   

S

A

5

E(r

A

)

2 r

f

s

A

5

8.9

2 5

11.45

5 .34  

 Now consider the CAL that uses portfolio  B  

instead of  A.  Portfolio  B  invests 70% in bonds 

and 30% in stocks. Its expected return is 9.5% 

(a risk premium of 4.5%), and its standard devi-

ation is 11.70%. Thus the Sharpe ratio on the 

CAL supported by portfolio  B   is   

S

B

5

9.5

2 5

11.7

5 .38 

which is higher than the Sharpe ratio of the 

CAL using the minimum-variance portfolio and 

T-bills. Hence, portfolio  B  dominates  A.  

 But why stop at portfolio  B?  We can con-

tinue to ratchet the CAL upward until it ulti-

mately reaches the point of tangency with the 

investment opportunity set. This must yield the 

CAL with the highest feasible Sharpe ratio. 

Therefore, the tangency portfolio, labeled  P   in 

    7.3 

Asset Allocation with Stocks, Bonds, and Bills  

13

12

11

10

9

8

7

6

5

Standard Deviation (%)

0

5

10

15

20

25

Expected Return (%)

D

E

A

B

CAL(A)

CAL(B)

 Figure 7.6 

The opportunity set of the debt and equity 

funds and two feasible CALs  

bod61671_ch07_205-255.indd   215

bod61671_ch07_205-255.indd   215

6/18/13   8:11 PM

6/18/13   8:11 PM

Final PDF to printer

---