A4 5c Consider the following information on three stocks in four possible future states of the economy: State of economy Probability of state of economy Stock A Stock B Stock C Boom 0.3 0.35 0.45 0.38 Good 0.3 0.15 0.20 0.12 Poor 0.3 0.05 –0.10 –0.05 Bust 0.1 0.00 –0.30 –0.10 stock A: State of economy Probability Rate of return Average (a) (b) (c) (d = b × c)(d = b × c) Boom 0.3 0.35 0.105 Good 0.3 0.15 0.045 Poor 0.3 0.05 0.015 Bust 0.1 0 0 Expected rate of return 0.165 stock B: State of economy Probability Rate of return Average (a) (b) (c) (d = b × c)(d = b × c) Boom 0.3 0.45 0.135 Good 0.3 0.2 0.06 Poor 0.3 -0.1 -0.03 Bust 0.1 -0.3 -0.03 Expected rate of return 0.135 Stock C: State of economy Probability Rate of return Average (a) (b) (c) (d = b × c)(d = b × c) Boom 0.3 0.38 0.114 Good 0.3 0.12 0.036 Poor 0.3 -0.05 -0.015 Bust 0.1 -0.1 -0.01 Expected rate of return 0.125 Calculating the expected rate of return on the portfolio: E(Rp) =(E(RA) ×WA) + (E(RB) ×WB)+(E(RC) ×WC) (0.165×0.30)+(0.135×0.50)+(0.125×0.20)0.1420 or 14.20%E(Rp) =(E(RA) ×WA) + (E(RB) ×WB)+(E(RC) ×WC)= (0.165×0.30)+(0.135×0.50)+(0.125×0.20)=0.1420 or 14.20% The expected rate of return on the portfolio is denoted by (E(Rp)), The expected rate of return on Stock A (E(RA)) is 16.5%, The expected rate of return on Stock B (E(RB)) is 13.5%, The expected rate of return on Stock C (E(RC)) is 12.5%, The weight of stock A (WA) is 30%, The weight of stock B (WB) is 50%, and The weight of stock C (WC) is 200%. Thus, the expected rate of return on the portfolio is 14.20%. c. What is the standard deviation of this portfolio?
A4 5c
Consider the following information on three stocks in four possible future states of the economy:
|
State of economy |
Probability of state of economy |
Stock A |
Stock B |
Stock C |
|
Boom |
0.3 |
0.35 |
0.45 |
0.38 |
|
Good |
0.3 |
0.15 |
0.20 |
0.12 |
|
Poor |
0.3 |
0.05 |
–0.10 |
–0.05 |
|
Bust |
0.1 |
0.00 |
–0.30 |
–0.10 |
stock A:
|
State of economy |
Probability |
|
Average |
|
(a) |
(b) |
(c) |
(d = b × c)(d = b × c) |
|
Boom |
0.3 |
0.35 |
0.105 |
|
Good |
0.3 |
0.15 |
0.045 |
|
Poor |
0.3 |
0.05 |
0.015 |
|
Bust |
0.1 |
0 |
0 |
|
Expected rate of return |
0.165 |
stock B:
|
State of economy |
Probability |
Rate of return |
Average |
|
(a) |
(b) |
(c) |
(d = b × c)(d = b × c) |
|
Boom |
0.3 |
0.45 |
0.135 |
|
Good |
0.3 |
0.2 |
0.06 |
|
Poor |
0.3 |
-0.1 |
-0.03 |
|
Bust |
0.1 |
-0.3 |
-0.03 |
|
Expected rate of return |
0.135 |
Stock C:
|
State of economy |
Probability |
Rate of return |
Average |
|
(a) |
(b) |
(c) |
(d = b × c)(d = b × c) |
|
Boom |
0.3 |
0.38 |
0.114 |
|
Good |
0.3 |
0.12 |
0.036 |
|
Poor |
0.3 |
-0.05 |
-0.015 |
|
Bust |
0.1 |
-0.1 |
-0.01 |
|
Expected rate of return |
0.125 |
Calculating the expected rate of return on the portfolio:
E(Rp) =(E(RA) ×WA) + (E(RB) ×WB)+(E(RC) ×WC) (0.165×0.30)+(0.135×0.50)+(0.125×0.20)0.1420 or 14.20%E(Rp) =(E(RA) ×WA) + (E(RB) ×WB)+(E(RC) ×WC)= (0.165×0.30)+(0.135×0.50)+(0.125×0.20)=0.1420 or 14.20%
The expected rate of return on the portfolio is denoted by (E(Rp)),
The expected rate of return on Stock A (E(RA)) is 16.5%,
The expected rate of return on Stock B (E(RB)) is 13.5%,
The expected rate of return on Stock C (E(RC)) is 12.5%,
The weight of stock A (WA) is 30%,
The weight of stock B (WB) is 50%, and
The weight of stock C (WC) is 200%.
Thus, the expected rate of return on the portfolio is 14.20%.
c. What is the standard deviation of this portfolio?
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