Question

The risk-free rate is 5% and the expected return on the market is 12%. P&G Stock has a beta of 0.8. For a given year, P&G Stock returned 15% while the market returned 14%. The systematic portion of P&G Stock's unexpected return was _____% and the unsystematic portion was _____ %. Show your work

Answer 1

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Correct Answer:

The systematic portion of P& G's stock 's unexpected return was 1.6 %

The unsystematic portion1.76 %1.76 %

Working:

Parameters provided in the question are :

• The risk-free rate, Rf is 5%
• Expected return on the market. E(RM) is 12%
• P&G Stock has a beta, of 0.8.
• Now, For a given year,
• P&G Stock returned, R 15%
• The market returned, RM 14%

Now first calculating the expected return on the stock of P&G using CAPM(Capital Asset Pricing Model ),

E(R) = Risk free rate + Beta (Expected market return. - Risk free rate )

E(R) = Rf + ( E(RM)- Rf)

Substituting the values,

E(R) = 5 + 0.8( 12-5). =. 5 + 0.8(7) = 10.6

Thus E(R) = 10.6 %

Now the systematic portion of P&D stock's unexpected return is given by,

[ RM - E(RM) X ]

Thus Systematic portion = [(14 - 12 )X 0.8 ] = 1.6 %

Now unsystematic portion is given by the formula,

[(R- E(R)) - (RM- E(RM ))] X

Thus unsystematic portion is,

[ (15-10.6) - (14-12)] X 0.8 = ( 4.4 -2 ) X 0.8 = 2.2 X0. 8 = 1.76 %