Consider the following information: Rate of Return if State Occurs State of Prob

Question

Consider the following information:
  
        Rate of Return if State Occurs
State of   Probability of  
Economy   State of Economy   Stock A   Stock B   Stock C
Boom      0.54         0.12         0.20         0.38     
Bust       0.46           0.14           0.04          0.07  
  
a.  
What is the expected return on an equally weighted portfolio of these three stocks? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Expected return ?
%
  
b.  
What is the variance of a portfolio invested 18 percent each in A and B and 64 percent in C? (Do not round intermediate calculations and round your answer to 6 decimal places. (e.g., 32.161616))

Variance ?
  

Explanation / Answer

Rate of Return if State Occurs:

State of Probability of  
Economy   State of Economy   Stock A   Stock B   Stock C

Boom 0.54 0.12 0.20 0.38     
Bust 0.46 0.14 0.04       0.07

Required a. The expected return on an equally weighted portfolio of these three stocks:

Expected Return = (0.12+0.20+0.38) * 0.54 + (0.14+0.04-0.07) * 0.46 = 0.378 + 0.0506 = 0.43

Required b. The variance of a portfolio invested 18 percent each in A and B and 64 percent in C:

Mean = mf / f = 0.2884 / 0.81 = 1.3561

Standard Deviation = SqRt [ f(d2) / f ] = SqRt [ 0.065596 / 0.81 ]

= 0.284574622

Variance = (Standard Deviation)2 = 0.080982

Co (Variance) = Standard Deviation / Mean * 100

= 0.284574622 / 1.3561 * 100 = 20.984781 %

weight (m) Portfolio (f) m X f deviation of 0.18 (d) d2 f(d2) 0.18 0.26 0.0468 0 0 0 0.18 0.24 0.0432 0 0 0 0.64 0.31 0.1984 0.46 0.2116 0.065596 0.81 0.2884 0.065596

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.