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You have observed the following returns over time: Year Stock X Stock Y Market 2011 12 % 11 % 13 % 2012 20 6 9 2013 -14 -4 -13 2014 4 1 1 2015 20 10 16 Assume that the risk-free rate is 4% and the market risk premium is 6%
You have observed the following returns over time:
| Year | Stock X | Stock Y | Market | |||
| 2011 | 12 | % | 11 | % | 13 | % |
| 2012 | 20 | 6 | 9 | |||
| 2013 | -14 | -4 | -13 | |||
| 2014 | 4 | 1 | 1 | |||
| 2015 | 20 | 10 | 16 | |||
Assume that the risk-free rate is 4% and the market risk premium is 6%.
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What is the beta of Stock X? Do not round intermediate calculations. Round your answer to two decimal places.
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What is the beta of Stock Y? Do not round intermediate calculations. Round your answer to two decimal places.
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What is the required rate of return on Stock X? Do not round intermediate calculations. Round your answer to one decimal place.
What is the required rate of return on Stock Y? Do not round intermediate calculations. Round your answer to one decimal place.
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What is the required rate of return on a portfolio consisting of 80% of Stock X and 20% of Stock Y? Do not round intermediate calculations. Round your answer to one decimal place.
Expert Solution
Answer (a) and (b)
| YEAR | STOCK X : RETURN (IN %) | STOCK X : DEVIATION FROM AVERAGE RETURN (x- x?) | STOCK X : (DEVIATION FROM AVERAGE RETURN)² = (x- x?)² | STOCK Y : RETURN (IN %) | STOCK Y : DEVIATION FROM AVERAGE RETURN = (y-?) | STOCK Y : (DEVIATION FROM AVERAGE RETURN)² = (y-?)² | MARKET RETURN (IN %) | MARKET : DEVIATION FROM AVERAGE RETURN = (m-m?) | MARKET: (DEVIATION FROM AVERAGE RETURN)² = (m-m?)² | (m-m?)(x- x?) | (m-m?)(y-?) | ||||
| 2011 | 12.00 | 3.60 | 12.96 | 11.00 | 6.20 | 38.44 | 13.00 | 7.80 | 60.84 | 28.08 | 48.36 | ||||
| 2012 | 20.00 | 11.60 | 134.56 | 6.00 | 1.20 | 1.44 | 9.00 | 3.80 | 14.44 | 44.08 | 4.56 | ||||
| 2013 | -14.00 | -22.40 | 501.76 | -4.00 | -8.80 | 77.44 | -13.00 | -18.20 | 331.24 | 407.68 | 160.16 | ||||
| 2014 | 4.00 | -4.40 | 19.36 | 1.00 | -3.80 | 14.44 | 1.00 | -4.20 | 17.64 | 18.48 | 15.96 | ||||
| 2015 | 20.00 | 11.60 | 134.56 | 10.00 | 5.20 | 27.04 | 16.00 | 10.80 | 116.64 | 125.28 | 56.16 | ||||
| ∑x/n = x? = 42/5 | 8.40 | VARIANCE = ∑ (x- x?)²/n | 160.64 | ∑y/n = ? = 24/5 | 4.80 | VARIANCE = ∑ (y-?)²/n | 31.76 | ∑m/n = m? = 26/5 | 5.20 | VARIANCE = ∑ (m-m?)²/n | 108.16 | COVARIANCE (m,x) = ∑(m-m?)(x- x?)/n | 124.72 | COVARIANCE (m,x) = ∑(m-m?)(y-?)/n | 57.04 |
| STANDARD DEVIATION = √VARIANCE | 12.67 | STANDARD DEVIATION = √VARIANCE | 5.64 | STANDARD DEVIATION = √VARIANCE | 10.40 | BETA OF X = COVARIANCE (MARKET, STOCK X)/MARKET VARIANCE = 124.72/108.16 | 1.15 | BETA OF Y = COVARIANCE (MARKET, STOCK Y)/MARKET VARIANCE = 57.04/108.16 | 0.53 |
Answer (c) : Required return for Stock X using CAPM:
E(Rx) = Rf + (E(Rm)- Rf)βx
Where Rf = 0.04
(E(Rm)- Rf) = 0.06
βx =1.15 (computed in above table)
E(Rx) = 0.04+(0.06)1.15
= 0.109 or 10.9%
Answer (d): Required return for Stock Y using CAPM:
E(Ry) = Rf + (E(Rm)- Rf)βy
Where Rf = 0.04
(E(Rm)- Rf) = 0.06
βy =0.53 (computed in above table)
E(Ry) = 0.04+(0.06)0.53
= 0.0718 or 7.18%
Answer (e)
Beta of Stock X (Betax) = 1.15
Beta of Stock Y (Betay) = 0.53
Money invested in Stock X (Wx) = 80%
Money invested in Stock Y (Wy) = 20%
Beta of Portfolio = Wx(Betax) + Wy(Betay)
= 0.8(1.15) + 0.2(0.53)
= 1.026
Required return of this Portfolio using CAPM:
E(Rp) = Rf + (E(Rm)- Rf)βp
Where Rf = 0.04
(E(Rm)- Rf) = 0.06
βp =1.026 (computed in above)
E(Rp) = 0.04+(0.06)1.026
= 0.1016 or 10.16%
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