Question

An portfolio risk premium (return in excess of risk free rate) is determined to have the following factor sensitivities in the Carhart four-factor model (starting with the intercept on the first line):

What is the expected return on the portfolio in the next month, given the expected values of the factors, the sensitivities, as well as the expected risk free rate of 0.19?

Factor |
Sensitivity |
Expected value of factor |

alpha |
0.01 |
-- |

RMRF |
0.75 |
0.8 |

SMB |
-0.35 |
0.31 |

HML |
-0.6 |
0.11 |

WML |
0.22 |
0.19 |

**Correct Answer**

0.67 margin of error +/- 0.01

Hint: Review the 4-factor model. Note that the dependent variable in the model is the risk premium, not the total return.

**PLEASE DO THE PROBLEM ON EXCEL AND SHOW ALL THE
STEPS.**

Answer #1

Using the four factor mode, the expected can be calculated as: risk free rate + alpha + sum product of each factor's sensitivity and its expected value. The computation is as shown below:

The formulas used are:

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