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Unformatted text preview: ted value of
the gamble.
.
80 Certified Financial Controller CFC 40 Determining Portfolio
Expected Return
m RP = Σ ( Wj )( Rj )
J=1 RP is the expected return for the portfolio, Wj is the weight (investment proportion)
for the
for the jth asset in the portfolio,
in the portfolio, Rj is the expected return of the jth asset,
81 m is the total number of assets in the
portfolio.
Certified Financial Controller CFC Determining Portfolio
Standard Deviation
σP = m m Σ Σ Wj Wk σ jk J=1 K=1 Wj is the weight (investment
proportion) for the jth asset in the
portfolio,
portfolio, Wk is the weight (investment
82 proportion) for the kth asset in the
portfolio,
Certified Financial Controller CFC 41 What is Covariance?
σ jk = σ j σ k r jk σj is the standard deviation of the jth
asset in the portfolio, σk is the standard deviation of the kth
the standard deviation of the
asset in the portfolio, rjk is the correlation coefficient between the
jth and kth assets in the portfolio.
83 Certified Financial Controller CFC Correlation Coefficient
A standardized statistical measure
standardized statistical measure
of the linear relationship between
two variables.
Its range is from –1.0 (perfect
negative correlation), through 0
(no correlation), to +1.0 (perfect
positive correlation).
84 Certified Financial Controller CFC 42 Portfolio
Portfolio Risk and
Expected Return Example
You are creating a portfolio of Stock D and Stock
BW (from earlier). You are investing $2,000 in
Stock BW and $3,000 in Stock D Remember that
D.
the expected return and standard deviation of
Stock BW is 9% and 13.15% respectively. The
13.15%
expected return and standard deviation of Stock D
is
is 8% and 10.65% respectively. The correlation
10
The correlation
coefficient
coefficient between BW and D is 0.75.
75 What is the expected return and standard
deviation of the portfolio?
85 Certified Financial Controller CFC Determining Portfolio
Expected Return
WBW = $2,000/$5,000 = 0.4
WD = $3,000/$5,000 = 0.6 RP = (WBW)(RBW) + (WD)(RD)
RP = (0.4)(9%) + (0.6)(8%)
RP = (3.6%) + (4.8%) = 8.4%
86 Certified Financial Controller CFC 43 Determining Portfolio
Standard Deviation
Twoasset portfolio:
portfolio
Col 1 Col 2 Row 1 WBW WBW σBW,BW WBW WD σBW,D Row 2 WD WBW σD,BW
BW WD WD σD,D This represents the variance – covariance
matrix for the twoasset portfolio.
87 Certified Financial Controller CFC Determining Portfolio
Standard Deviation
Twoasset portfolio:
portfolio
Col 1 Col 2 Row 1 (0.4)(0.4)(0.0173) (0.4)(0.6)(0.0105) Row 2 (0.6)(0.4)(0.0105) (0.6)(0.6)(0.0113) This represents substitution into the
variance – covariance matrix.
88 Certified Financial Controller CFC 44 Determining Portfolio
Standard Deviation
Twoasset portfolio:
portfolio
Col 1 Col 2 Row 1 (0.0028) (0.0025) Row 2 (0.0025) (0.0041) This represents the actual element values
in the variance – covariance matrix.
89 Certified Financial Controller CFC Determining Portfolio
Standard Deviation
σP = 0.0028 + (2)(0.0025) + 0.0041
σP = SQRT(0.0119)
σP = 0.1091 or 10.91% A weighted average of the individual
standard deviations is INCORRECT.
90 Certified Financial Controller CFC 45 Determining Portfolio
Standard Deviation
The WRONG way to calculate is a
WRONG way to calculate is
weighted average like:
σP = 0.4 (13.15%) + 0.6(10.65%)
σP = 5.2...
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This note was uploaded on 05/28/2013 for the course FINANCE economy taught by Professor Nill during the Fall '12 term at Bronx School Of Law And Finance.
 Fall '12
 nill
 Time Value Of Money

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