Financial Risk Manager Part 2

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Explanation:

To calculate the expected return using the Fama-French model extended with the momentum factor (Carhart four-factor model), we use the following formula:

$E(R_i) = R_f + \beta_{i,MKT} [E(R_M) - R_f] + \beta_{i,SMB} (SMB) + \beta_{i,HML} (HML) + \beta_{i,WML} (WML)$

First, we need to calculate the factor premiums:

Market risk premium = Expected return on the market - Risk-free rate = $7.5% - 2.5% = 5.0% = 0.05$
SMB (Small Minus Big) = Return of small-cap stocks - Return of large-cap stocks = $11% - 4.4% = 6.6% = 0.066$
HML (High Minus Low) = Return of high BV stocks - Return of low BV stocks = $13% - 5.5% = 7.5% = 0.075$
WML (Winners Minus Losers) = Return of winner stocks - Return of loser stocks = $15% - 7% = 8% = 0.08$

Next, we plug these values into the model: $E(R_i) = 0.025 + 1.10(0.05) + 1.30(0.066) + 0.90(0.075) + 1.20(0.08)$ $E(R_i) = 0.025 + 0.055 + 0.0858 + 0.0675 + 0.096$ $E(R_i) = 0.3293$ or $32.93%$

Explanation:

To calculate the expected return using the Fama-French model extended with the momentum factor (Carhart four-factor model), we use the following formula:

$E(R_i) = R_f + \beta_{i,MKT} [E(R_M) - R_f] + \beta_{i,SMB} (SMB) + \beta_{i,HML} (HML) + \beta_{i,WML} (WML)$

First, we need to calculate the factor premiums:

Market risk premium = Expected return on the market - Risk-free rate = $7.5% - 2.5% = 5.0% = 0.05$
SMB (Small Minus Big) = Return of small-cap stocks - Return of large-cap stocks = $11% - 4.4% = 6.6% = 0.066$
HML (High Minus Low) = Return of high BV stocks - Return of low BV stocks = $13% - 5.5% = 7.5% = 0.075$
WML (Winners Minus Losers) = Return of winner stocks - Return of loser stocks = $15% - 7% = 8% = 0.08$

Next, we plug these values into the model: $E(R_i) = 0.025 + 1.10(0.05) + 1.30(0.066) + 0.90(0.075) + 1.20(0.08)$ $E(R_i) = 0.025 + 0.055 + 0.0858 + 0.0675 + 0.096$ $E(R_i) = 0.3293$ or $32.93%$

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Q.29 Daniel Kevin, a portfolio manager, is estimating returns on a stock i. He has decided to use the Fama-French model for segregating asset returns. The prevailing risk-free rate is 2.5%. Kevin has gathered the following information:

Variable Value Variable Value
$\beta_{i,\text{MKT}}$ 1.10 Return of winner stocks 15%
$\beta_{i,\text{SMB}}$ 1.3 Return of loser stocks 7%
$\beta_{i,\text{HML}}$ 0.9 Return of high BV stocks 13%
$\beta_{i,\text{UMD}}$ 1.2 Return of low BV stocks 5.5%
$\beta_{i,\text{WML}}$ 1.2 Return of small-cap stocks 11%
Expected return on the market 7.5% Return of large-cap stocks 4.4%

Calculate the expected return of the underlying stock considering the momentum effect.

Variable	Value	Variable	Value
$\beta_{i,\text{MKT}}$	1.10	Return of winner stocks	15%
$\beta_{i,\text{SMB}}$	1.3	Return of loser stocks	7%
$\beta_{i,\text{HML}}$	0.9	Return of high BV stocks	13%
$\beta_{i,\text{UMD}}$	1.2	Return of low BV stocks	5.5%
$\beta_{i,\text{WML}}$	1.2	Return of small-cap stocks	11%
Expected return on the market	7.5%	Return of large-cap stocks	4.4%

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Last updated: July 5, 2026 at 07:12

0.1373

0.3043

0.3293

0.3568