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 .18 .353 .453 .333 Good .42 .123 .103 .173 Poor .32 .013 .023 .053 Bust .08 .113 .253 .093 Requirement 1: Your portfolio is invested 29 percent each in A and C and 42 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) Expected return of the portfolio % Requirement 2: (a) What is the variance of this portfolio? (Do not round intermediate calculations. Round your answer to 5 decimal places (e.g., 32.16161).) Variance of the portfolio (b) What is the standard deviation of this portfolio? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) Standard deviation %

Explanation / Answer

(A) Calculation to compute Mean return, variance of each stock.

RA, RB,RC,RM RPF = Return on stock A, B, C, mean return & reurn of PF respectively.

(B) Computation of variance & Std. Deviation (SD) of portfolio(PF).

The above calculations can be used to answer type questions.

Q.1: Expected return on portfolio is 0.2815, i.e. 28.15% (please refer table A above )

Q.2(a): Variance of the portafolio is 0.00563 (please refer table B above)

Q.2(b): Std Deviation of PF = (Var PF)1/2 = (0.00563)1/2 = 0.07503, i.e. 7.503%

State of Economy Boom Good Poor Burst a Prob. (= P) 0.18 0.42 0.32 0.08 b RA 0.353 0.123 0.13 -0.113 c RB 0.453 0.103 0.23 -0.253 d RC 0.333 0.173 -0.53 -0.093 Mean R (=MR) e P x RA 0.0635 0.0517 0.0416 -0.0090 0.1478 f P x RB 0.0815 0.0433 0.0736 -0.0202 0.1782 g P x RC 0.0599 0.0727 -0.1696 -0.0074 -0.0444 h RA-MRA -0.0842 -0.0961 -0.1062 -0.1568 RPF0.2815 i RB-MRB -0.09662 -0.1349 -0.10456 -0.1984 j RC-MRC 0.10438 0.1171 -0.12516 0.037 Variance k P(RA-MRA)2 0.00128 0.00388 0.00361 0.00197 0.01073 l P(RB-MRB)2 0.00168 0.00764 0.00350 0.00315 0.01597 m P(RC-MRC)2 0.00196 0.00576 0.00501 0.00011 0.01284

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