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An investor has $100 to invest, and two investments
Chapter 2, Problem 23E(choose chapter or problem)
An investor has $100 to invest, and two investments between which to divide it. If she invests the entire amount in the first investment, her return will be X, while if she invests the entire amount in the second investment, her return will be Y . Both X and Y have mean $6 and standard deviation (risk) $3. The correlation between X and Y is 0.3.
a. Express the return in terms of X and Y if she invests $30 in the first investment and $70 in the second.
b. Find the mean return and the risk if she invests $30 in the first investment and $70 in the second.
c. Find the mean return and the risk, in terms of K, if she invests $K in the first investment and
\($(100-K)\) in the second.
d. Find the value of K that minimizes the risk in part (c).
e. Prove that the value of K that minimizes the risk in part (c) is the same for any correlation \(\rho_{X, Y}\) with \(\rho_{X, Y} \neq 1\).
Equation Transcription:
Text Transcription:
$(100-K)
rho_{X,Y}
rho_{X,Y}{not=}1
Questions & Answers
QUESTION:
An investor has $100 to invest, and two investments between which to divide it. If she invests the entire amount in the first investment, her return will be X, while if she invests the entire amount in the second investment, her return will be Y . Both X and Y have mean $6 and standard deviation (risk) $3. The correlation between X and Y is 0.3.
a. Express the return in terms of X and Y if she invests $30 in the first investment and $70 in the second.
b. Find the mean return and the risk if she invests $30 in the first investment and $70 in the second.
c. Find the mean return and the risk, in terms of K, if she invests $K in the first investment and
\($(100-K)\) in the second.
d. Find the value of K that minimizes the risk in part (c).
e. Prove that the value of K that minimizes the risk in part (c) is the same for any correlation \(\rho_{X, Y}\) with \(\rho_{X, Y} \neq 1\).
Equation Transcription:
Text Transcription:
$(100-K)
rho_{X,Y}
rho_{X,Y}{not=}1
ANSWER:
Answer :
Step 1 of 6:
Given that, an investor has $100 to invest, and two investments between which to divide it.
Let X will be if she invests the entire amount in the first investment.
Let Y will be if she invests the entire amount in the second investment.
Here we have, both X and Y have mean $6 and standard deviation(risk) $3, and the correlation between X and Y is 0.3.