Question

Expected return and standard deviation.

Use the following information to answer the questions.

State of Economy		Probability of State		Return on Asset J in State		Return on Asset K in State		Return on Asset L in State
Boom		0.29		0.070		0.230		0.3
Growth		0.37		0.070		0.130		0.190
Stagnant		0.25		0.070		0.040		0.090
Recession		0.09		0.070		−0.050		−0.200

a. What is the expected return of each asset?

b. What is the variance and the standard deviation of each asset?

c. What is the expected return of a portfolio with

88 %

in asset J,

4545 %

in asset K, and

4747 %

in asset L?

d. What is the portfolio's variance and standard deviation using the same asset weights from part

(c )?

a. What is the expected return of asset J?

_____

(Round to four decimal places.)

What is the expected return of asset K?

-------

(Round to four decimal places.)

What is the expected return of asset L?

---------

(Round to four decimal places.)

b. What is the variance of asset J?

--------

(Round to four decimal places.)

What is the variance of asset K?

---------

(Round to four decimal places.)

What is the variance of asset L?

--------

(Round to four decimal places.)

What is the standard deviation of asset J?

------

(Round to four decimal places.)

What is the standard deviation of asset K?

------

(Round to four decimal places.)

What is the standard deviation of asset L?

-------

(Round to four decimal places.)

d. What is the portfolio's variance using the same asset weights from part

(c )____

(Round to four decimal places.

What is the portfolio's standard using the same asset weights from part

(c )?

Answer 1

The solution is given as follows:

a.

b.

c. Expected return of portfolio = Σ p.x^-

= Σ [(88 %* 7%)+ (45.45%* 12.03%) +(47.47%* 16.18%)]

= 19.308%

d. The portfolio's variance and standard deviation using the same asset weights from c :

= Σ [(88 %* 0%)+ (45.45%* 8.8016%) +(47.47%* 13.75%)]

= 10.52%