The table below contains records of rates of return for a mutual fund F and for the market portfolio during a 7 year period. These rates of return are denoted by RF (t) and RM (t), respectively (t = 1, 2, ..., 7). Yeart RF(t) RM(t) 1 0.14 0.12 2 -0.1 -0.07 3 0.19 0.2 4 -0.08 -0.04 0.23 0.12 6 0.28 0.2 7 0.18 0.17 Recall that the expectation and the variance of a random variable R based on the observed values R(1),..., R(n) of R are estimated respectively by: 1 R(t), VarR= ¬[(R(C) – ER)"; ER= n - 1 t=1 t=1 and the covariance of random variables R1 and R2 is estimated by 1 Cov(R1, R2) (R:(t) – ER,)(R2(t) – ER2). n - 1 t=1 (a) Compute the estimates of ER", ERM, Var(RM), Var(R*), oM, oF, Cov(R", RM) Cov(R" , RM) Var(RM) and the B for the mutual fund F, where B = (b) Assuming that cash is a riskless asset whose rate of return r is constant and is equal to 3%, write the equation of the efficient frontier in the ox – mx plane. Write the equation of the security market line. (c) Evaluate the performance of the mutual fund F by finding out whether: (i) F yields better expected returns than those predicted by CAPM. pM – pF < 3% (ii) F has a sufficiently high level of efficiency in the sense that where p is the Sharpe ratio of the fund and pM is the Sharpe ratio of the market portfolio.
The table below contains records of rates of return for a mutual fund F and for the market portfolio during a 7 year period. These rates of return are denoted by RF (t) and RM (t), respectively (t = 1, 2, ..., 7). Yeart RF(t) RM(t) 1 0.14 0.12 2 -0.1 -0.07 3 0.19 0.2 4 -0.08 -0.04 0.23 0.12 6 0.28 0.2 7 0.18 0.17 Recall that the expectation and the variance of a random variable R based on the observed values R(1),..., R(n) of R are estimated respectively by: 1 R(t), VarR= ¬[(R(C) – ER)"; ER= n - 1 t=1 t=1 and the covariance of random variables R1 and R2 is estimated by 1 Cov(R1, R2) (R:(t) – ER,)(R2(t) – ER2). n - 1 t=1 (a) Compute the estimates of ER", ERM, Var(RM), Var(R*), oM, oF, Cov(R", RM) Cov(R" , RM) Var(RM) and the B for the mutual fund F, where B = (b) Assuming that cash is a riskless asset whose rate of return r is constant and is equal to 3%, write the equation of the efficient frontier in the ox – mx plane. Write the equation of the security market line. (c) Evaluate the performance of the mutual fund F by finding out whether: (i) F yields better expected returns than those predicted by CAPM. pM – pF < 3% (ii) F has a sufficiently high level of efficiency in the sense that where p is the Sharpe ratio of the fund and pM is the Sharpe ratio of the market portfolio.
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
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Transcribed Image Text:2. The table below contains records of rates of return for a mutual fund F and for the market
portfolio during a 7 year period. These rates of return are denoted by RF (t) and RM (t),
respectively (t = 1, 2, ..., 7).
Yeart RF (t) RM (t)
1
0.14
0.12
-0.1
-0.07
3
0.19
0.2
4
-0.08
-0.04
5
0.23
0.12
6.
0.28
0.2
7
0.18
0.17
Recall that the expectation and the variance of a random variable R based on the observed
values R(1),..., R(n) of R are estimated respectively by:
1
ER=
1
> R(t), VarR =
n - 1
(R(t) – ER)";
t=1
t=1
and the covariance of random variables R1 and R2 is estimated by
1
Cov(R1, R2)
(R (t) – ER)(R2(t) – ER2).
%3D
n - 1
t=1
(a) Compute the estimates of ER", ERM, Var(RM), Var(R"), oM, oF, Cov(R", RM)
Cov(R" , RM)
Var(RM)
and the B for the mutual fund F, where B
(b) Assuming that cash is a riskless asset whose rate of return r is constant and is equal
to 3%, write the equation of the efficient frontier in the ox - mx plane. Write the
equation of the security market line.
(c) Evaluate the performance of the mutual fund F by finding out whether:
(i) F yields better expected returns than those predicted by CAPM.
(ii) F has a sufficiently high level of efficiency in the sense that
< 3%
where p is the Sharpe ratio of the fund and pM is the Sharpe ratio of the
market portfolio.
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