The expected return using the Carhart four-factor model (which considers the momentum effect in addition to the Fama-French three factors) is calculated using the following formula:

$E(R_i) = R_f + \beta_{i,MKT}[E(R_M) - R_f] + \beta_{i,SMB}[R_{small} - R_{large}] + \beta_{i,HML}[R_{high} - R_{low}] + \beta_{i,WML}[R_{winner} - R_{loser}]$

Given:

• Risk-free rate ($R_f$) = 2.5% = 0.025
• Expected return on market ($E(R_M)$) = 7.5% = 0.075
• $\beta_{i,MKT}$ = 1.10
• $\beta_{i,SMB}$ = 1.3
• Return of small-cap = 11% = 0.11
• Return of large-cap = 4.4% = 0.044
• $\beta_{i,HML}$ = 0.9
• Return of high BV = 13% = 0.13
• Return of low BV = 5.5% = 0.055
• $\beta_{i,WML}$ (or $\beta_{i,UMD}$) = 1.2
• Return of winner = 15% = 0.15
• Return of loser = 7% = 0.07

Substituting the values: $E(R_i) = 0.025 + 1.10(0.075 - 0.025) + 1.3(0.11 - 0.044) + 0.9(0.13 - 0.055) + 1.2(0.15 - 0.07)$ $E(R_i) = 0.025 + 1.10(0.05) + 1.3(0.066) + 0.9(0.075) + 1.2(0.08)$ $E(R_i) = 0.025 + 0.055 + 0.0858 + 0.0675 + 0.096 = 0.3293$

The expected return is 32.93% or 0.3293.