谁能告诉我这些题怎么算？
Considerthetwosecuritieslistedbelow:•Riskysecurity:E(R)=10%,σ=20%.•Risk-f...
Consider the twosecurities listed below:
• Risky security: E(R) = 10%, σ = 20%.
• Risk-free security: Rf= 4.5%.
You wish to forma portfolio combining the risky security and the risk-free security.
a. What weights would you need to place in therisky and risk-free securities if you are able to tolerate a risk level of 25%?What is the expected return of this portfolio?
(2 marks)
b. Draw the capital allocation line (CAL).Label the points and the axes clearly. What is the reward-to-variability ratio?0.275
(3 marks)
Now, supposethat instead of one risky security and one risk-free security, you can investin two risky securities as follows: Security 1: E(R1) = 8%, σ1 = 12%;Security2: E(R2) = 13%, σ2 = 20%, and the correlation coefficient , 12, between themis 0.3.
c. Find the expected return and the standarddeviation of the minimum-variance portfolio (MVP) on the investment opportunityset. Draw a tangent from the risk-free rate to the investment opportunity set.
(5 marks) 展开
• Risky security: E(R) = 10%, σ = 20%.
• Risk-free security: Rf= 4.5%.
You wish to forma portfolio combining the risky security and the risk-free security.
a. What weights would you need to place in therisky and risk-free securities if you are able to tolerate a risk level of 25%?What is the expected return of this portfolio?
(2 marks)
b. Draw the capital allocation line (CAL).Label the points and the axes clearly. What is the reward-to-variability ratio?0.275
(3 marks)
Now, supposethat instead of one risky security and one risk-free security, you can investin two risky securities as follows: Security 1: E(R1) = 8%, σ1 = 12%;Security2: E(R2) = 13%, σ2 = 20%, and the correlation coefficient , 12, between themis 0.3.
c. Find the expected return and the standarddeviation of the minimum-variance portfolio (MVP) on the investment opportunityset. Draw a tangent from the risk-free rate to the investment opportunity set.
(5 marks) 展开
1个回答
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1. Portfolio risk= w(risky)*σ(risky)=25%(as stated in the question), thus w(risky)*20%=25%
the weight of risky security is 25%/20%=1.25, and the weight of risk-free is 1-1.25= -0.25
and E(Portfolio)=1.25*10%+(-0.25)*4.5%=11.375%
2. CAL是一条y轴截距（intercept）为4.5%（riskfree return），斜率（slope）为（10%-4.5%）/20%=0.275的直线；reward-to-variability等于斜率，即0.275
3. Variance（Portfolio）=(w1σ1)²+（w2σ2）²+2w1w2*ρ*（σ1σ2）²，其中w1+w2=1
带入数字化简：Variance（Portfolio）=0.0540544（w1）² - 0.0796544w1+0.04
求Variance（Portfolio）最小值（一元二次方程）：w1=73.68%时，Variance（Portfolio）最小
E（Portfolio）=73.68%*8%+26.32%*13%=9.316%
Var（Portfolio）=1.0655%
σ（Portfolio）=10.3225%
the weight of risky security is 25%/20%=1.25, and the weight of risk-free is 1-1.25= -0.25
and E(Portfolio)=1.25*10%+(-0.25)*4.5%=11.375%
2. CAL是一条y轴截距（intercept）为4.5%（riskfree return），斜率（slope）为（10%-4.5%）/20%=0.275的直线；reward-to-variability等于斜率，即0.275
3. Variance（Portfolio）=(w1σ1)²+（w2σ2）²+2w1w2*ρ*（σ1σ2）²，其中w1+w2=1
带入数字化简：Variance（Portfolio）=0.0540544（w1）² - 0.0796544w1+0.04
求Variance（Portfolio）最小值（一元二次方程）：w1=73.68%时，Variance（Portfolio）最小
E（Portfolio）=73.68%*8%+26.32%*13%=9.316%
Var（Portfolio）=1.0655%
σ（Portfolio）=10.3225%
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