Question

You invest $10,000 in portfolio XYZ. The portfolio XYZ is composed of a risky asset with an expected rate of return of 15% and a standard deviation of 20% over the one year time period. The risk free asset has a rate of return of 5% over the same time period. How much money should be invested in the risky asset so that the standard deviation of returns on XYZ portfolio is 10% over the one year time horizon

Answer #1

standard deviation for a two-asset portfolio σ_{p} =
(w_{1}^{2}σ_{1}^{2} +
w_{2}^{2}σ_{2}^{2} +
2w_{1}w_{2}Cov_{1,2})^{1/2}

where σ_{p} = standard deviation of the portfolio

w_{1} = weight of Asset 1

w_{2} = weight of Asset 2

σ_{1} = standard deviation of Asset 1

σ_{2} = standard deviation of Asset 2

Cov_{1,2} = covariance of returns between Asset 1 and
Asset 2

Cov_{1,2} = ρ_{1,2} * σ_{1} *
σ_{2,} where ρ_{1,2} = correlation of returns
between Asset 1 and Asset 2

For a risk free asset, the standard deviation is zero, and the covariance with the risky asset is zero

σ_{p} =
(w_{1}^{2}σ_{1}^{2} +
w_{2}^{2}σ_{2}^{2} +
2w_{1}w_{2}Cov_{1,2})^{1/2}

0.10 = (w_{1}^{2}0.20^{2} +
w_{2}^{2}0.00^{2} +
(2w_{1}w_{2} * 0)/)^{1/2}

0.10 =
(w_{1}^{2}0.20^{2})^{1/2}

0.10 = w_{1} * 0.20

w_{1} = 0.50

Proportion of portfolio to invest in risky asset = 0.50, or 50%

Money to invest in risky asset = $10,000 * 50%

Money to invest in risky asset = $5,000

You invest $10,000 in a complete portfolio. The complete
portfolio is composed of a risky asset with an expected rate of
return of 20% and a standard deviation of 21% and a treasury bill
with a rate of return of 5%. How much money should be invested in
the risky asset to form a portfolio with an expected return of
8%?

You invest $100,000 in a complete portfolio. The complete
portfolio is composed of a risky asset with an expected rate of
return of 20% and a standard deviation of 30%, and a Treasury bill
with a rate of return of 8%. How much money should be invested in
the risky asset to form a portfolio with an expected return of
17%?
a. $40,000
b. $60,000
c. $75,000
d. $25,000

You invest $1,700 in a complete portfolio. The complete
portfolio is composed of a risky asset with an expected rate of
return of 18% and a standard deviation of 25% and a Treasury bill
with a rate of return of 9%. __________ of your complete portfolio
should be invested in the risky portfolio if you want your complete
portfolio to have a standard deviation of 12%.

You invest $100 in a complete portfolio. The complete portfolio
is composed of a risky asset with an expected rate of return of 12%
and a standard deviation of 10% and a treasury bill with a rate of
return of 5%.
What would be the weight of your investment allocated to the
risk-free asset if you want to have a portfolio standard deviation
of 9%? (2 points)
How could you use these two investments to generate an expected
return of...

2)
You invest $1,500 in a complete portfolio. The complete
portfolio is composed of a risky asset with an expected rate of
return of 16% and a standard deviation of 20% and a Treasury bill
with a rate of return of 7%. __________ of your complete portfolio
should be invested in the risky portfolio if you want your complete
portfolio to have a standard deviation of 10%.
Multiple Choice
9%
13%
50%
33%

You invest $100 partly in a risky asset with an expected rate of
return of 11% and a standard deviation of 21% and partly in T-bills
with a yield of 4.5%. What percentages of your money must be
invested in the risk-free asset and the risky asset, respectively,
to form a portfolio with a standard deviation of 8.0%?

ou invest $1,000 in a risky asset with an expected rate of
return of 0.17 and a standard deviation of 0.40 and a T-bill with a
rate of return of 0.04.
What percentages of your money must be invested in the risky asset
and the risk-free asset, respectively, to form a portfolio with an
expected return of 0.11?
Select one:
a. 53.8% and 46.2%
b. 75% and 25%
c. 62.5% and 37.5%
d. 46.2% and 53.8%
e. Cannot be determined.

1. Suppose you have a portfolio that is 70% in the risk-free
asset and 30% in a stock. The stock has a standard deviation of
0.30 (i.e., 30%). What is the standard deviation of the portfolio?
A. 0.30 (i.e., 30%) B. 0.09 (i.e., 9%) C. 0.21 (i.e., 21%) D.
0
2. You have a total of $100,000 to invest in a portfolio of assets.
The portfolio is composed of a risky asset with an expected rate of
return of 15%...

There are 2 investment -- a risk-free security that returns 2%
and a risky asset that has expected return of 10% and standard
deviation of 18%.
1). What are the weights of the complete portfolio that has an
8% expected return?
2). What is the standard deviation of that portfolio?
3). If the portfolio is valued at $100,000, how much do you
invest in the risk-free security and how much do you invest in the
risky asset?

You are considering investing $10,000 in a complete portfolio.
The complete portfolio is composed of treasury bills that pay 6%
and a risky portfolio, P, with expected return of 12% and standard
deviation of 20%. How much you should invest of your
complete portfolio in the risky portfolio P to form a complete
portfolio with an expected rate of return of 9%?
$5000
$0
$10000
$20000

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