Consider the following information: State of Probability of Rate of Return If St
ID: 2793999 • Letter: C
Question
Consider the following information:
State of
Probability of
Rate of Return If State Occurs
Economy
State of Economy
Stock A
Stock B
Stock C
Boom
.16
.363
.463
.343
Good
.44
.133
.113
.183
Poor
.34
.023
.033
.075
Bust
.06
.123
.263
.103
Your portfolio is invested 29 percent each in A and C and 42 percent in B. What is the expected return of the portfolio? (Round to 2 decimal points)
Expected return 11.41%
What is the variance of this portfolio? (Round to 2 decimal points)
Variance ?
What is the standard deviation of this portfolio? (Round to 2 decimal points)
Standard deviation 15.12%
State of
Probability of
Rate of Return If State Occurs
Economy
State of Economy
Stock A
Stock B
Stock C
Boom
.16
.363
.463
.343
Good
.44
.133
.113
.183
Poor
.34
.023
.033
.075
Bust
.06
.123
.263
.103
Explanation / Answer
Solution :-
Return of portfolio in boom state of economy = 0.29 * 0.363 + 0.42 * 0.463 + 0.29 * 0.343 = 0.3992 i.e., 39.92 %
Return of portfolio in good state of economy = 0.29 * 0.133 + 0.42 * 0.113 + 0.29 * 0.183 = 0.1391 i.e., 13.91 %
Return of portfolio in poor state of economy = 0.29 * 0.023 + 0.42 * 0.033 + 0.29 * (-) 0.075
= (-) 0.00122 i.e., (-) 0.122 %
Return of portfolio in bust state of economy = 0.29 * (-) 0.123 + 0.42 * (-) 0.263 + 0.29 * (-) 0.103
= (-) 0.176 i.e., (-) 17.60 %
Expected return of portfolio = 0.16 * 39.92 % + 0.44 * 13.91 % + 0.34 * (-) 0.122 % + 0.06 * (-) 17.60 %
= 6.3872 % + 6.1204 % - 0.04148 % - 1.056 %
= 11.41012 % (Rounded off to 11.41 %)
Conclusion :- Expected return on portfolio = 11.41 % (approx).
Calculation of variance of portfolio :-
= 0.16 * (39.92 % - 11.41 %)2 + 0.44 * (13.91 % - 11.41 %)2 + 0.34 * ( - 0.122 % - 11.41 %)2 + 0.06 * ( - 17.60 % - 11.41 %)2
= 0.16 * 812.8201 % + 0.44 * 6.25 % + 0.34 * 132.987024 % + 0.06 * 841.5801 %
= 130.051216 % + 2.75 % + 45.21558816 % + 50.494806 %
= 228.51161016 (Rounded off to 228.51 %)
Conclusion :- Variance of portfolio = 228.51 % (approx).
Standard deviation of portfolio = (228.51)1/2
= 15.12 %
Conclusion :- Standard deviation of portfolio = 15.12 % (approx).
Note :- Standard deviation is the square root (under root) of the variance.
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