Question

Expected return and standard deviation.

Use the following information to answer the questions.

State of   Economy		Probability of State		Return on Asset R in State		Return on Asset S in State		Return on Asset T in State
Boom		0.29		0.020		0.300		0.450
Growth		0.38		0.020		0.140		0.300
Stagnant		0.22		0.020		0.170		0.015
Recession		0.11		0.020		−0.030		−0.165

a.  What is the expected return of each​ asset?

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

c.  What is the expected return of a portfolio with equal investment in all three​ assets?

d.  What is the​ portfolio's variance and standard deviation using the same asset weights in part ​(c​)?

​Hint: Make sure to round all intermediate calculations to at least seven​ (7) decimal places. The input​ instructions, phrases in parenthesis after each answer​ box, only apply for the answers you will type.

a. What is the expected return of asset​ R?  

​(Round to four decimal​ places.)

What is the expected return of asset​ S?  

​(Round to four decimal​ places.)

What is the expected return of asset​ T?  

​ (Round to four decimal​ places.)

b. What is the variance of asset​ R?  

​(Round to four decimal​ places.)

What is the variance of asset​ S?  

​(Round to four decimal​ places.)

What is the variance of asset​ T?  

​(Round to four decimal​ places.)

What is the standard deviation of asset​ R?   

​(Round to four decimal​ places.)

What is the standard deviation of asset​ S?   

​(Round to four decimal​ places.)

What is the standard deviation of asset​ T?  

​(Round to four decimal​ places.)

c.  What is the expected return of a portfolio with equal investment in all three​ assets? 

​(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​)?

​(Round to four decimal​ places.)

Answer 1

Answer to part a

Expected Return on Asset R = 0.29*0.020 + 0.38*0.020 + 0.22*0.020 + 0.11*0.020 = 0.0200

Expected Return on Asset S = 0.29*0.300 + 0.38*0.140 + 0.22*0.170 + 0.11*-0.030 = 0.1743

Expected Return on Asset T = 0.29*0.450 + 0.38*0.300 + 0.22*0.015 + 0.11*-0.165 = 0.2297

Answer to part b

Variance of Asset R = 0.29*(0.02-0.02)²+0.38*(0.02-0.02)²+0.22*(0.02-0.02)²+0.11*(0.02-0.02)² = 0

Variance of Asset S = 0.29*(0.300-0.1743)²+0.38*(0.140-0.1743)²+0.22*(0.170-0.1743)²+0.11*(-0.030-0.1743)²= 0.0096

Variance of Asset T= 0.29*(0.450-0.2297)²+0.38*(0.300-0.2297)²+0.22*(0.015-0.2297)²+0.11*(-0.165-0.2297)² = 0.0432

Standard Deviation of Asset = Square root of the Variance

Standard Deviation of Asset R = square root of 0 = 0

Standard Deviation of Asset S = square root of 0.0096 = 0.0980

Standard Deviation of Asset T = square root of 0.0432 = 0.2078

Answer to part c

Expected return of the portfolio = ER on asset R*1/3 + ER on asset S*1/3 + ER on asset T*1/3

Expected return of the portfolio = 0.0200/3 + 0.1743/3 + 0.2297/3 = 0.1413

Answer to part d

Variance of the portfolio = (0.02000-0.1413)/3+(0.1743-0.1413)/3+(0.2297-0.1413)/3 = 0.0000333

Answer to part e

Standard Deviation of the portfolio = square root of 0.0000333 = 0.0058