(i) Calculate the expected rate of return(r) and risk(o) for the following portfolios: 1.40% security 1 and 60% security 2 II.80% security 1 and 20% security 2 (ii) Given a risk-free rate of 4%, describe how Mr. Adani can use a combination of a risk- free instrument and a risky portfolio with an expected return of 15% to achieve an expected return of 26%.
(i) Calculate the expected rate of return(r) and risk(o) for the following portfolios: 1.40% security 1 and 60% security 2 II.80% security 1 and 20% security 2 (ii) Given a risk-free rate of 4%, describe how Mr. Adani can use a combination of a risk- free instrument and a risky portfolio with an expected return of 15% to achieve an expected return of 26%.
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
Related questions
Question
![Appendix: Formula sheet
1. P12 =
012
0102
Where P12: correlation coefficient between security 1 and security 2
012: covariance between security 1 and security 2
₁: standard deviation of security 1
0₂: standard deviation of security 2
2. 012 = 1 Pi [(R₁i — E (R₁)) ((R₂i – E(R₂)]
-
Where 12: covariance between security 1 and security 2
P₁: probabilities of the return at i
3.
R₁i: rate of return of security 1 at i
R₂i: rate of return of security 2 at i
E (R₁) expected rate of return of security 1
E (R₂) expected rate of return of security 2
02-012
W1(min)+02-2012
Where W₁(min): the weight of security 1 given the minimum variance in the two
securities case
012: covariance between security 1 and security 2
₁: standard deviation of security 1
0₂: standard deviation of security 2
o2: variance of security 2
4.02= w202 + w20₂ + 2w₁W₂010₂P12
Where
: variance of the portfolio
w₁: weighting of security 1
w₂: weighting of security 2
0₁: standard deviation of security 1
0₂: standard deviation of security 2
P12: correlation coefficient between security 1and security 2
5. VaR (0) = P (ασνΔt - μΔt)
Where P: investment position
a: one tailed probability of z value
σ: volatility (standard deviation)
At: time horizon/holding period
μ: expected annual return
(1+R₂) T
(1+Rpv)T
Where F: risk adjusted factor
6. F=-
RPV: the cost of capital of the project
R₁: the risk free rate
1-fd
fu-fa'
Where p: the probability of the cash flow Cu generated by the project
f and fa: deviation factors
o: the standard deviation
At: time horizon of the project
7. p=
fu=e°√At i fa=—=;
fu](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55a2f5e2-2562-4a63-8199-89250e06b38a%2F1430b15c-85cd-4afe-aef1-cdc18ed44b2f%2Feqrbss7_processed.png&w=3840&q=75)
Transcribed Image Text:Appendix: Formula sheet
1. P12 =
012
0102
Where P12: correlation coefficient between security 1 and security 2
012: covariance between security 1 and security 2
₁: standard deviation of security 1
0₂: standard deviation of security 2
2. 012 = 1 Pi [(R₁i — E (R₁)) ((R₂i – E(R₂)]
-
Where 12: covariance between security 1 and security 2
P₁: probabilities of the return at i
3.
R₁i: rate of return of security 1 at i
R₂i: rate of return of security 2 at i
E (R₁) expected rate of return of security 1
E (R₂) expected rate of return of security 2
02-012
W1(min)+02-2012
Where W₁(min): the weight of security 1 given the minimum variance in the two
securities case
012: covariance between security 1 and security 2
₁: standard deviation of security 1
0₂: standard deviation of security 2
o2: variance of security 2
4.02= w202 + w20₂ + 2w₁W₂010₂P12
Where
: variance of the portfolio
w₁: weighting of security 1
w₂: weighting of security 2
0₁: standard deviation of security 1
0₂: standard deviation of security 2
P12: correlation coefficient between security 1and security 2
5. VaR (0) = P (ασνΔt - μΔt)
Where P: investment position
a: one tailed probability of z value
σ: volatility (standard deviation)
At: time horizon/holding period
μ: expected annual return
(1+R₂) T
(1+Rpv)T
Where F: risk adjusted factor
6. F=-
RPV: the cost of capital of the project
R₁: the risk free rate
1-fd
fu-fa'
Where p: the probability of the cash flow Cu generated by the project
f and fa: deviation factors
o: the standard deviation
At: time horizon of the project
7. p=
fu=e°√At i fa=—=;
fu
Transcribed Image Text:Question 2
(a)
Mr Adani invests in two risky securities with the following details:
Security 1: r₁=0.16; ₁=0.30; Security 2:1₂=0.08; 0₂=0.25
Where ₁ is the expected return of security 1 and ₁ is the standard deviation of returns
of security 1;
12 is the expected return of security 2 and ₂ is the standard deviation of returns of
security 2
The correlation coefficient (P12) between the returns of the two securities is -0.5
(i) Calculate the expected rate of return(r) and risk(o) for the following portfolios:
1.40% security 1 and 60% security 2
II.80% security 1 and 20% security 2
(ii) Given a risk-free rate of 4%, describe how Mr. Adani can use a combination of a risk-
free instrument and a risky portfolio with an expected return of 15% to achieve an
expected return of 26%.
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