Start with the unique known heterotic background whose visible spectrum matches the pure MSSM - namely the heterotic MSSM. What are the Yukawa couplings and the fermion masses? Braun, He, and Ovrut compute the answer (in the zeroth approximation) tonight:
The resulting textures, affected by the selection rules implied by the Calabi-Yau geometry, make one generation of quarks and leptons naturally light. The word "light" means that the cubic terms contribute zero and the actual masses of the light family arise from higher-order and non-perturbative effects. That means that the cubic approximation is not enough for you to compute the mass of the electron.
The nonzero Yukawa couplings connect the "generation 1" with "generation 2", or "generation 1" with "generation 3", using the appropriate Higgs in each case (which is different for up and down quarks and/or leptons). The "generation i" are just some basis states, not the mass eigenstates. You can see that there are 8 couplings that are complex a priori. With two massive generations, you can assume, without a loss of generality, that the couplings are real. If you don't calculate the numerical value of the couplings, you will have no prediction for the quark and lepton masses: there are 4 quarks and 4 leptons in the two heavier generations, precisely parameterized by the 8 Yukawa couplings.
On the other hand, you may follow and surpass the authors and try to analyze the Yukawa couplings expressed as the integrals in the equation 22. If you're lucky enough, you could predict a non-trivial relation between the masses of the two heavier fermionic families. (The large masses of the right-handed neutrinos will, however, complicate the analysis in the neutrino sector.) The reason why it is complicated is that it is expected that with the non-trivial bundles turned on, the Yukawa couplings won't be simple integer-valued intersection numbers that are constant over the moduli space. Instead, they will be general functions of the moduli. The values of the stabilized moduli are therefore needed to predict the quark and lepton masses.
If you analyze what one can predict without much bigger effort than the already difficult calculation of Braun, He, and Ovrut that may be comprehensible roughly to 12 people in the world, it seems that one can exactly predict the lightness of a single generation relatively to the other two - which seems to be a correct prediction or more precisely a postdiction.