Rate of Return What is the rate of return on the portfolio in each scenario? (Do
ID: 2775824 • Letter: R
Question
Rate of Return
What is the rate of return on the portfolio in each scenario? (Do not round intermediate calculations. Round your answers to 1 decimal place.)
What are the expected rate of return and standard deviation of the portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Rate of Return
Scenario Probability Stocks Bonds Recession .20 ?5 % +19 % Normal economy .70 +20 +10 Boom .10 +32 +9 Rate of Return Probability Stocks Scenario Recession Normal economy Boom Bonds +19% 20 .70 .10 5% +20 +32 Consider a portfolio with weights of.6 in stocks and .4 in bonds. a. What is the rate of return on the portfolio in each scenario? (Do not round intermediate calculations. Round your answers to 1 decimal place.) Scenario Rate of Return Recession Normal economy Boom b. What are the expected rate of return and standard deviation of the portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Expected rate of return Standard deviation c. Which investment would you prefer? Portfolio Bonds StocksExplanation / Answer
a)
Portfolio return = Ws x Rs + Wb x Rb
Recession = 0.60 x-5% + 0.4 x19% =7.90%
Normal Economy = 0.60 x20% + 0.4 x10% =16%
Boom= 0.60 x32% + 0.4 x9% = 22.80%
b)
Expected return = sum of PxR
Probability P
R
PxR
D=R-ER
Px D^2
0.2
7.90%
0.0158
-4.600%
0.000423
0.7
16.00%
0.112
3.500%
0.000858
0.1
22.80%
0.0228
10.300%
0.001061
ER
0.1506
Variance
0.002342
Expected return = 15.06%
Variance = sum of Px D^2
= 0.002342
Standard deviation = variance ^0.50
=0.002342^0.50
= 4.84%
c) I would prefer portfolio as it has higher expected return and lower standard deviation.
Probability P
R
PxR
D=R-ER
Px D^2
0.2
7.90%
0.0158
-4.600%
0.000423
0.7
16.00%
0.112
3.500%
0.000858
0.1
22.80%
0.0228
10.300%
0.001061
ER
0.1506
Variance
0.002342
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