Dr. Sudhakar Raju
FN 6100
ANSWERS TO ASSIGNMENT 2
1.) βP = WQ βQ + WR βR + WS S + WT T
= (.25) (.90) + (.20) (1.4) + (.15) (1.1) + (.40) (1.8)
= .2250 + .28 + .1650 + .72
= 1.39
2.) Equally weighted portfolio of three assets implies that the weights are equal to 33%.
P = WRF RF + WA WB B
1.0 = [.33] [0] + [.33] [ .80] + [.33] [

Total portfolio is as risky as the market implies that P = 1.0.
Risk free asset has no risk implies that RF = 0.
1 = 0 + .2640 + .33 B
.7360
= B
.33
3A). ERP
or

= WRF RRF + WA ERA
= (.50) (5) + (.50) (15)
= 10 (%)
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B). P
.60
= WRF RF + WA A
= WRF (0) + WA (1.10)
.60
= WA
1.10
WA = .5455
WRF = .4545
C. Figure out the respective weights, then compute the portfolio beta.

ERP = WRF RRF + WA ERA
9 = WRF (5) + WA (15)
9 = 5WRF + (1 – WRF) (15)
WA + WRF = 1
9 = 5WRF + 15 – 15 WRF
WA = (1 - WRF)
-6 = -10 WRF
WRF = .60


WA = .60
P = WRF RF + WA 
P = (.60) (0) + (.40) (1.10)
P = .44
D.P = WRF RF + WA A
2.20 = (WRF) (0) + WA (1.10)
WA =
2.20
= 2 (or 200%)
1.10
2
Since, WA + WRF = 1
2 + WRF = 1
2 + WRF = 1
WRF = 1-2 = -1
WRF = -1(-100%)
A positive weight means that one buys (or is long) the asset. A negative weight means that
one sells (or is short) the asset.
4.) Y = 1.45; ERY = 17(%); Z = .85; ERZ = 12(%); RF = 6 (%) ; Market Risk Premium
(ERM – RF) = 7.50(%).
If assets are priced correctly, the expected return on the asset is given by the SML
equation. Therefore, use the SML equation to figure out if both the stocks are being priced
correctly.
ERY = RF + (ERM – RF) Y
ERZ = RF + (ERM – RF) Z
ERY = 6 + (7.5) (1.45)
ERZ = 6 + (7.50) (.85)
ERY = 16.875 (%)
ERZ = 12.375 (%)
With regard to Stock Y, the CAPM implied return of 16.875% is slightly lower than the
expected return of 17%. Thus, the expected return on Stock Y over-compensates the
investor.
With regard to Stock Z, the CAPM implied return of 12.375% is slightly higher than the
expected return of 12%. Thus, the expected return of Stock X under-compensates the
investor.
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5.) All stocks that are priced correctly will lie on the SML. Stocks that are not priced
correctly will lie either above or below the SML. Since all correctly priced stocks lie on
the SML, all these stocks will have exactly the same slope. The slope of Stock Y is then
given by: (ERY - RF) / (βY). Similarly, the slope of Stock Z is given by: (ERZ - RF) / (βZ).
Equating the slopes of stocks Y and Z gives:
ERY  RF
=
Y
ERZ  RF
Z
17  RF
12  RF
=
.85
1.45
(17/1.45) - (1/1.45) RF = (12/.85) - (1/.85) RF
= 14.12 – 1.1765 RF
11.72 - .6897 RF
14.12 – 11.72
1.1765 RF - .6897 RF =
.4868 RF =
RF =
2.40
2.40
.4868
RF = 4.93 (%)
6.) P = WA A + WB B + WC C + WRF RF
Portfolio as risky as market implies that P = 1. Note that the beta of the risk free asset
(RF) is by definition equal to zero.
WA =
$200,000
= .20;
$1,000,000
WB =
$250,000
= .25;
$1,000,000
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Wc = ?
1.0 = (.20) (.70) + (.25) (1.10) + (WC) (1.60) + (WRF) (0)
1.0= .14 + .2750 + 1.60 WC
.5850 = 1.60 WC
WC =
.5850
Thus,
1.60
WC = .3656
WA + WB + WC = .20 +.25 + .3656 = .8156
Thus, WRF = 1-.8156 = .1844
WC = .3656 or .3656 x $1m = $ 365,600
WRF = .1844 or .1844 x $1m = $ 184,400
7.) ERP = 12.50; βP = .80; ERX = 28; ERY = 16; X = 1.60; Y = 1.20; RF = 7(%)
P = WXX + WY Y + WRF RF
.80 = WX (1.60) + WY (1.20) + (WRF) (0)
Above implies that
WY =
.80  1.60W X
or
1.20
WY = .67 – 1.33 WX
ERP = WX ERX + WY ERY + WRF RRF
12.50 = WX (28) + WY (16) + (1- WX – WY) (7)
Substitute WY = (.67 – 1.33Wx ) into the above equation.
Note: WX +WY +WRF = 1
Thus, WRF = (1 – WX – WY)
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Therefore:
12.50 = 28 WX + 16 [.67 - 1.33 WX] + [1 – WX – (.67 – 1.33 WX)] 7
12.50 = 28 WX+ 10.72 – 21.28 WX + [1-WX -.67 + 1.33 WX] 7
12.50 = 28 WX + 10.72 – 21.28 WX + 7 – 7 WX – 4.69 + 9.31 WX
12.50 = 9.03 WX + 13.03
-.53 = 9.03 WX
OR
WX =
 .53
9.03
WX = -.0587
= -5.87%
WY
= .67 – 1.33 WX
=.67 – 1.33 [-.0587]
= .7481 or 74.81%
WRF = 1 – WX – WY
=1- (-.0587) - .7481
WRF = .3106 or
31.06%
Notice that WX + WY + WRF = 1
Amount invested in Stock X = -5.87 % x $1,000,000
=-$58,700 [Sell $58,700 of Stock X]
8.) ERA = 20 (%); A = 1.30; ERB = 14 (%); B = .80.
If securities are priced correctly the expected return on the securities will be given the
SML/CAPM equations. Apply the CAPM equations to stocks A and B. Thus:
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ER = RF + (ERM – RF) CAPM Equation
20 = RF + (ERM – RF) 1.30 (STOCK A).................Equation 1
14 = RF + (ERM – RF) .80 (STOCK B)...................Equation 2
Subtract equation 2 from equation 1. Thus:
6 = (ERM – RF) (.50)
6
= ERM – RF
.50
Thus,
ERM – RF = 12 (%)
ERA = RF + (ERM – RF) A
20= RF + (12) (1.30)
20 = RF + 15.60
RF = 20 – 15.60. Thus,
Thus,
RF = 4.40 (%)
ERM – RF = 12
ERM – 4.40 = 12
ERM = 16.40 (%)
9.) Briefly discuss the following:
The Efficient Frontier
The Efficient frontier represents all return-risk (ER–SD) combinations corresponding to different portfolio
allocations. The upper arc of the portfolio frontier that lies above the minimum risk portfolio is called the
“efficient frontier”. The Efficient frontier represents the highest return for given levels of risk. On the
efficient frontier higher levels of return are associated with higher levels of risk.
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b.) Draw a variance-covariance matrix for a 50 stock portfolio. How many variance terms are there? How
many covariance terms are there?
The variance-covariance matrix will look thus:
1,1
1,2………….
1,50
50,1
50,2
50,50
The term 1,1; 2,2; 3,3; etc. represent the covariance of the first stock with itself; 2,2, represents the
covariance of the second stock with itself; and so on. The covariance of a stock with itself is simply the
variance. Thus, the diagonal terms [1,1; 2,2; 3,3;……..50,50] are the variance terms. The off-diagonal
terms are the covariance terms. There are thus 50 variance terms. The total number of covariance terms
are equal to [50 x 50] minus the 50 Variance Terms or [2500] – [50] = 2450 covariance terms. Note that
since the covariance term 1,2 is the same as 2,1 etc., the number of distinct covariance terms are
[2450/2] = 1225 distinct covariance terms.
c.) Is there a shortcut to quickly estimate the risk of a 50 stock portfolio?
Portfolio Variance = (1/N) (Average Value of all the Variance Terms) + [1 – (1/N)] (Average Value of all
the Covariance Terms)
N = Number of stocks in the portfolio
d.) What is beta? What factors affect beta? Can beta be negative?
While standard deviation measures the total risk of a stock, beta measures the systematic risk of a stock.
In essence, beta measures the linkage between a stock and the market. A beta of 2 means that a stock is
twice as volatile as the market whereas a beta of .50 means that a stock is only half as volatile as the
market.
For large well diversified portfolios, unsystematic risk is essentially zero. For such well diversified
portfolios, the only relevant risk is beta. Beta is affected by factors that affect the market as a whole such
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as interest rate changes, devaluation, etc. Beta measures the interaction of a stock with the market and
is given by;
BETA = [CORRMSFT, MARKET SDMSFT SDMARKET] / [SDMARKET,SDMARKET]
Note that if correlation is negative, beta can be negative. A negative beta means that a stock is
negatively correlated with the marker.
e.) What are the 3 factors that affect the return on an asset?
The CAPM implies that Expected Return is affected by:
RF
= The Risk Free Rate. This component measures the pure time value of money
(ERM- RF)
= Market Risk Premium. This component measures the average reward by the market for
bearing risk
Beta
= This component measures the quantity of systematic risk. Higher the beta, greater the
return
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