For a two-security portfolio, the formula for portfolio risk is: Portfolio varia
ID: 2766195 • Letter: F
Question
For a two-security portfolio, the formula for portfolio risk is:
Portfolio variance = x12s12 + x22s22 + 2x1x2rr12s1s2
If security one is Treasury bills and security two is the market portfolio, then s1 is zero, s2 is 20%. Therefore:
Portfolio variance = x22s22 = x22(0.20)2
Standard deviation = 0.20x2
Portfolio expected return = x1(0.06) + x2(0.06 + 0.85)
Portfolio expected return = 0.06x1 + 0.145x2
Portfolio
X1
X2
Exp Return
Std Deviation
1
1.0
0.0
0.060
0.000
2
0.8
0.2
0.077
0.040
3
0.6
0.4
0.094
0.080
4
0.4
0.6
0.111
0.120
5
0.2
0.8
0.128
0.160
6
0.0
1.0
0.145
0.200
How do you calculate to find the answers for everything after line 1? I know the answers for 1 - 6 but I do not understand what formula was used to get the answers for lines 2 - 6. I need to see the step by step answer for x1, x2, expected return, and standard deviation for the remaining 5 lines.
Portfolio
X1
X2
Exp Return
Std Deviation
1
1.0
0.0
0.060
0.000
2
0.8
0.2
0.077
0.040
3
0.6
0.4
0.094
0.080
4
0.4
0.6
0.111
0.120
5
0.2
0.8
0.128
0.160
6
0.0
1.0
0.145
0.200
Explanation / Answer
In question itself they have simplified formulla for Portfolio expected return = 0.06x1 + 0.145x2 and for Standard deviation = 0.20x2. So we can directly put figures in equationto arrive at answers.Security one is Treasury bills so standard deviation of it is always zero so s1=0 . so anything multiplied by o is zero.
Portfolio variance = x12s12 + x22s22 + 2x1x2rr12s1s2
= (0)s12 + x22s22 + 2(0)x2rr12s1s2
= x22s22
Std Deviation is underroot of Portfolio variance = x2 s2 = x2 is 0.20
Std Deviation=0.20s2
Portfolio expected return = x1(0.06) + x2(0.06 + 0.085)
Portfolio expected return = 0.06x1 + 0.145x2
By putting all values in above equation we will get follwing
Portfolio X1 X2 Exp Return Std Deviation Portfolio expected return = 0.06x1 + 0.145x2 Standard deviation = 0.20x2 1 1 0 0.06 0 0.06(1) + 0.145(0) =0.06 0.20*0 = 0 2 0.8 0.2 0.077 0.04 0.06(0.8) + 0.145(0.2)=0.077 0.20*0.2 = 0.04 3 0.6 0.4 0.094 0.08 0.06(0.6) + 0.145(0.4)=0.094 0.20*0.4=0.08 4 0.4 0.6 0.111 0.12 0.06(0.4) + 0.145(0.6)=0.111 0.20*0.6=0.12 5 0.2 0.8 0.128 0.16 0.06(0.2) + 0.145(0.8)=0.128 0.20*0.8=0.16 6 0 1 0.145 0.2 0.06(0) + 0.145(1)=0.145 0.2*1=0.2Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.