Suppose a portfolio manager wishes to construct a portfolio using two securities Coll and USR, both of their return data are shown in the Slide 5 with the title “Hypothetical Investment Alternatives”. Specifically, the manger allocates $60,000 in the Coll and $30,000 in the USR. Please calculate (1) Portfolio Expected Return (2) Portfolio Standard Deviation
Economy |
Prob. |
T-Bills |
HT |
Coll |
USR |
MP |
Recession |
0.1 |
5.5% |
-27.0% |
27.0% |
6.0% |
-17.0% |
Below avg |
0.2 |
5.5% |
-7.0% |
13.0% |
-14.0% |
-3.0% |
Average |
0.4 |
5.5% |
15.0% |
0.0% |
3.0% |
10.0% |
Above avg |
0.2 |
5.5% |
30.0% |
-11.0% |
41.0% |
25.0% |
Boom |
0.1 |
5.5% |
45.0% |
-21.0% |
26.0% |
38.0% |
Please do not use excel.
1) In order to calculate Portfolio Expected Return, we need to first calculate the expected return of the two securities i.e Coll and USR.
The expected return of Coll = 0.1*27+0.2*13+.4*0+0.2*(-11)+0.1*(-21)
= 2.7+2.6-2.2-2.1
=1%
The expected return of USR = 0.1*6+0.2*(-14)+0.4*3+0.2*41+0.1*26
= 0.6-2.8+1.2+8.2+2.6
=9.8%
The Expected Portfolio return = weight of Coll in portfolio* expected return of Coll + weight of USR in portfolio* expected return of USR
= 0.67*1+0.33*9.8
= 3.80%
2) In order to calculate portfolio standard deviation we need to calculate standard deviation of securities individually
Variance of Coll = 0.10(0.27-0.01)2 + (0.20)(0.13 - 0.01)2 + (0.40)(0.00 - 0.01)2 +(0.20)(-0.11 - 0.01)2+(0.10)(-0.21 - 0.01)2
= 0.10*0.0676+0.20*0.0144+0.00004+0.20*0.0144+0.10*0.0484
=0.00676+0.00288+0.00004+0.00288+0.00484
= 0.0174
Variance of USR =0.10(0.06-0.098)2+0.20(0.14 - 0.098)2 + (0.40)(0.03 - 0.098)2 +(0.20)(0.41 - 0.098)2+(0.10)(0.26 - 0.098)2
= 0.10*0.00144+0.0084+.00185+0.0194+0.0026
= 0.0324
Covariance between Coll and USR =0.10 (0.27-.01)(0.06-0.098)+0.20(0.13-0.01)(.14-0.098)+0.40(0.00-0.01)(0.03-0.098)+0.20(-0.11-0.01)*(0.41-0.098)+0.10(-0.21-.01)(0.26-0.098)
=-0.00098+0.00100+0.000272-0.00748-0.00356
=-0.010748
Portfolio Variance = w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cov(RA, RB)
=0.67*0.67*0.0174+0.33*0.33*0.0324+2*0.67*0.33*-0.010748
=0.00781+0.00353-0.00475
= 0.00659
The standard deviation is simply the square root of the variance therefore,
Portfolio Standard Deviation = 0.081 or 8.1%
Suppose a portfolio manager wishes to construct a portfolio using two securities Coll and USR, both...
Suppose a portfolio manager wishes to construct a portfolio using two securities Coll and USR. Specifically, the manger allocates $60,000 in the Coll and $30,000 in the USR. Please calculate (1) Portfolio Expected Return (2) Portfolio Standard Deviation Economy Prob. T-Bills HT Coll USR MP Recession 0.1 5.5% -27.0% 27.0% 6.0% -17.0% Below avg 0.2 5.5% -7.0% 13.0% -14.0% -3.0% Average 0.4 5.5% 15.0% 0.0% 3.0% 10.0% Above avg 0.2 5.5% 30.0% -11.0% 41.0% 25.0% Boom 0.1 5.5% 45.0% -21.0%...
Suppose a portfolio manager wishes to construct a portfolio using two securities Coll and USR, both of their return data are shown in the Slide 5 with the title “Hypothetical Investment Alternatives”. Specifically, the manger allocates $60,000 in the Coll and $30,000 in the USR. Please calculate (1) Portfolio Expected Return (2) Portfolio Standard Deviation Economy Prob. T-Bills HT Coll USR MP Recession 0.1 5.5% -27.0% 27.0% 6.0% -17.0% Below avg 0.2 5.5% -7.0% 13.0% -14.0% -3.0% Average 0.4 5.5%...
USE EXCEL TO CALCULATE THE FREQUENCIES AS SHOWN BELOW. PLEASE PROVIDE EXCEL FORMULA USED. Frequency Distribution Low High Bins Frequency -67.0 -56.6 (-67, -56.6] -56.6 -46.2 (-56.6, -46.2] -46.2 -35.8 (-46.2, -35.8] -35.8 -25.4 (-35.8, -25.4] -25.4 -15.0 (-25.4, -15] -15.0 -4.6 (-15, -4.6] -4.6 5.8 (-4.6, 5.8] 5.8 16.2 (5.8, 16.2] 16.2 26.6 (16.2, 26.6] 26.6 37.0 (26.6, 37] 37.0 47.4 (37, 47.4] 47.4 57.8 (47.4, 57.8] 57.8 68.2 (57.8, 68.2] 68.2 78.6 (68.2, 78.6] 78.6 89.0 (78.6, 89]...