- CFA Exams
- CFA Level I Exam
- Topic 9. Portfolio Management
- Learning Module 63. Portfolio Risk and Return: Part II
- Subject 4. Applications of the CAPM

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**CFA Practice Question**

The slope of the SML in an economy is 8.9%. The risk-free rate prevailing in the economy is 4.9%. A security has a correlation coefficient of 0.23 with the market. The market's standard deviation is 15% while that of the security is 19%. The expected return on the portfolio equals ______.

A. 14.19%

B. 7.49%

C. 13.66%

**Explanation:**The Security Market Line (SML) is a plot of the expected returns on securities against their betas. CAPM implies that the slope of the SML equals the market risk premium and the intercept equals the risk-free rate. Hence, the data given in the problem imply that the market premium is 8.9%.

To calculate the expected return on the security using CAPM, we must first find its beta. The beta of the security equals the covariance between the security and the market divided by the market variance. Also, the covariance equals the product of the correlation coefficient and the individual standard deviations. Hence, the covariance between the security and the market equals 0.23 * 0.15 * 0.19 = 0.0066. Therefore, the beta of the security equals 0.0066/(0.15

^{2}) = 0.29. Therefore, the CAPM expected return on the security equals 4.9% + 0.29 * 8.9% = 7.49%.

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**User Contributed Comments**
14

User |
Comment |
---|---|

pablo |
Formulation well worth revising and knowing |

chenyx |
The slope(Rm-Rf) of the SML equals the market premium and the intercept equals the risk-free rate |

Will1868 |
If (Rm-Rf)=8.9, then wouldn't this imply that Rm= 8.9+4.9 =13.8%?, if the market has a std.dev of 15 and the stock has a std.dev of 19 (greater risk) how does the stock have a lower return than the market? |

murli |
Why beta = 0.29 and not simply 0.23, because beta = correlation not co-variance. |

murli |
Sorry , I was wrong. Beta is not correlation rather Covariance devided by variance of market standeard deivation. |

johnsk |
Will1868: you should not compare the std. dev of two securities (i.e. market vs the stock) and then try to determine which has a higher expected return. Correlation matters, not std. dev. |

johnsk |
Will1868: you should not compare the std. dev of two securities (i.e. market vs the stock) and then try to determine which has a higher expected return. Correlation matters, not std. dev. |

Sidd2000 |
good question |

dlo1 |
To clarify the question, it should be changed to "the expected return on the SECURITY equals ". Wasn't sure if I was asked to calculate E(Ri) or E(Rm). |

solnce |
The slope cannot be equal to the market premium simply because the slope, by definiton, is a ratio of a vertical run to a horizontal run. At least, until recently it has always been so in mathematics. And the market premium represents just a vertical run, while the market variance should be a horizontal run. |

octavianus |
Expected Return=Rf+Beta(Rm-Rf) So the slope of the SML is Rm-Rf or put another way, MRP (market risk premium), not Rm (Return on the Market)??? |

Kuki |
solnce: E(Ri) = [E(Rm) - Rf]*B + Rf y = m*x + c therefore: y is E(Ri) m is gradient(slope) = m = [E(Rm) - Rf] x is Beta (B) c is y intercept = Rf formula holds. |

StanleyMo |
more info on beta http://www.riskglossary.com/link/beta.htm |

enetis |
great Q!! |