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Hrolessor
lrank
J. Jones
Bus. 172 B. Project I
November 1,2009
1. Using these date in the portfolio optimization program develop the EF
(efficient
frontier). Also develop the CML (capital market line). Provide the equation for the CML.
What is the composition of the PM?
The data in the portfolio optimization:
PORTFOLIO OPTIMIZATION
INPUTS
EXPECTED
RETURN
STANDARD
DEVIATION
ONE
PLUS
EXP RATE
{1+E@}
ONES
Riskless Rate
@
5.00%
0.00%
105.00%
114.72%
100.00%
lA AllValue
114.5s%
100.00%
lA All GroMh
114.31o/o
100.00%
lA Monthlv Convertible Bond
'111.91%
100.00%
LB Aqqreqate Bond
109.25%
100.00%
LB HiYId
110.76%
100.00%
The EF (efficient frontier) and the CML (capital market line):
EFFICIENT
TRADE
OFF
LINE
&
EFFICIENT
FRONTIER
CURVE
z
t
f
F
lrJ
t
o
IJJ
F
o
lJl
o
x
lrJ
0.25
0.2
0.15
0.1
0.05
0
0.
0.05
lr
Seriesl
r
Series2
Series3
I
30.00%
STAT{DARD DEVIATION
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The equation of the CML:
f:
f1*
(fnl rr
/ om)
o
f the PM
No, there are no negative weights. If there were negative weights involved it would mean
the investor who borrows money to fund his/her purchase of the risky assets has free
weights.
2. Select the point on the CML which is your personally optimal point. Why did you
select this point? At this point, how much borrowing/ lending of the risk free asset is
involved?
The point which
I
selected is the standard deviation is 9,92o/o and the expected retum is
18.20%. Comparing with the related EF point which is the standard deviationis9.92Yo
and the expected return rs 14.90o/o, the EF and the
point
I
selected both have the same risk
(9.92%); however, the point
I
chose has the higher rate of retum (18.20%) than EF
(14.90%). T'his is the prime reason why I chose this point.
oo:
w^(o^)
9.92%:
wx
(4.96%)
Wx:2
e
ono
EFFICIENT
FRONTIER
CURVE
EFFICIENT
TRADE
OFF LINE
INDIVIDUAL
ASSET
INDEX
STANDARD
DEVIATION
EXPECTED
RETURN
EXPECTED
RETURN
OPTIMAL
GOMBINATION
OF RISKY
ASSETS IN
TANGENT
PORTFOLIO
17.49o/o
14.72%
11.860/r
lA AllValue
16.23Yo
14.55%
13.53%
lA All GroMh
20.52o/o
14.3'l%
8.25%
lA Monthly Gonvertible
Bond
12.96%
11.9'l%
15.13%
LB Aqqreqate Bond
6.34%
9.25%
39.46%
LB HiYId
13.51%
't0.76%
11.78%
Risk free rate is
5oZ
rp:
( w.f
*
rt+(
w^
*
r*)
0.1820:Wrf
*
5o/o+(2* 0.1160)
0.1820: Wrf
*
5oA+0.232
0.05:W6*5o/o
Wrf
:
1
:
l00Yo
From the calculation,
it
shows that lending 100% of risk free asset is involved.
3. What is the Sharpe Ratio for this PM and your personally optimal point?
Standard
Deviation
Expected
Return
OPTIMAL COMBINATION
4.96%
11.60%
EFFICIENT TRADE OFF
LINE
0,00%
0.00%
5.00%
100.00%
4.96%
11.60%
200.OYo
9.92%
'18.20%
The point
I
selected: standard deviation is 9.92Yo, and the expected return is 18.20%
Sharpe Ratio:
(f.
fr
)
I o^
The risk free rate ts
5Yo
The Sharpe Ratio for the
PM:
(11.60%
5n
I 4.96%
:
1.331
The Sharpe Ratio for the point
I
selected
:
(I8.20o/o

5%) I 9.92%
:
1.331
4. Identify the two points on the CML with risks 5.0% higher and
5 .0o/o
lower than your
personally optimal point and determine the Sharpe Ratios of these two points. Do the
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This note was uploaded on 09/08/2010 for the course BUS 172B at San Jose State University .
 '09
 Jones,Frank

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