Ntša liforomo ka mokhoa oa lipalo tsa latex markdown ho bala ho khutla ha setoko le ho fapana ho Modern Portfolio Theory https://en.wikipedia.org/wiki/Modern_portfolio_theory
Context:MPT e nka hore batseteli ha ba rate ho ipeha kotsing, ho bolelang hore ha ho fanoa ka li-portfolio tse peli tse fanang ka phaello e lekanang e lebelletsoeng, batseteli ba tla khetha e nang le kotsi e fokolang. Ka hona, motseteli o tla nka kotsi e eketsehileng feela haeba a lefshoa ka litefello tse phahameng tse lebelletsoeng. Ka lehlakoreng le leng, motseteli ea batlang ho fumana chelete e ngata o tlameha ho amohela kotsi e eketsehileng. Tekanyo e tobileng ea phapanyetsano e ke ke ea tšoana bakeng sa batseteli bohle. Bahoebi ba fapaneng ba tla lekola phapanyetsano ka tsela e fapaneng ho latela litšobotsi tsa motho ka mong tsa ho qoba kotsi. Se boleloang ke sena ke hore motsetedi ya nang le kelello a ke ke a tsetela potefolio haeba ho na le potefolio ya bobedi e nang le boemo bo botle ba tjhelete e ka fumanwang ka lebaka la kotsi eo a ipehang ho yona - ke hore, haeba bakeng sa boemo boo ba kotsi ho na le potefolio e nngwe e nang le tjhelete e ka fumanwang ka lebaka la kotsi eo e ka fumanwang ka lebaka la yona.  Tlas'a mohlala:  Ho khutla ha setoko ke motsoako o lekantsoeng ka karolelano oa ho khutla ha thepa ea motheo. Ho fetoha ha phaello ea li-portfolio \sigma _{p} ke mosebetsi oa likamano ρij tsa thepa ea karolo, bakeng sa lipara tsohle tsa thepa (i, j). Ho hloka botsitso ho fana ka leseli la kotsi e amanang le letsete. Ha ho hloka botsitso ho le hoholo, kotsi e ba kholo.
- Ho khutla ho lebelletsoeng: $$ \mathrm{E}\left{R_p\right) =\sum_i w_i \mathrm{E}\left{R_i\right) $$ moo $R_p$ e leng ho khutla ha potefolio, $R_i$ ke ho khutla ha letlotlo $i$ le $w_i$ ke boima ba letlotlo la karolo $i$ (ke hore, karolo ea letlotlo "i" potefolio, e le hore $\sum_i w_i=1$). - Phapang ea phaello ea letlole: $$ \sigma_p^2=\sum_i w_i^2 \sigma_i^2+\sum_i \sum_{j \neq i} w_i w_j \sigma_i \sigma_j \rho_{i j} $$ moo $\sigma_i$ e leng (sample) standard deviation ea nako le nako e khutlang ka letlotlo $i$,'me $\rho_{i j}$ ke khokahano coefficient pakeng tsa e khutlang ka matlotlo $i$ le $j$. Ho seng joalo polelo e ka ngoloa e le: $$ \sigma_p^2=\sum_i \sum_j w_i w_i \sigma_i \sigma_j \rho_{i j} $$ moo $\rho_{i j}=1$ bakeng sa $i=j$, kapa $$ \sigma_p^2=\sum_i \sum_j w_i w_i \sigma_{i j} $$ moo $\sigma_{i j}=\sigma_i \sigma_j \rho_{i j}$ e leng (sample) covariance ea nako le nako e khutlang ka matlotlo a mabeli, kapa ka tsela e 'ngoe e tšoauoa e le $\sigma(i, j) $, $\operatorname{cov}{ }_{i j}$ kapa $\operatorname{cov}(i, j) $. - Ho feto-fetoha ha phaello ea setoko (ho kheloha ho tloaelehileng): $$ \sigma_p=\sqrt{\sigma_p^2} Ha ho letho le ka etsahalang $$ Bakeng sa potefolio ea thepa e'meli: - Ho khutla ha setoko: $$\mathrm{E}\left(R_p\right) =w_A \mathrm{E}\left(R_A\right) +w_B \mathrm{E}\left(R_B\right) =w_A \mathrm{E}\left(R_A\right) +\left(1-w_A\right) \mathrm{E}\left(R_B\right) $$  - Phapang ea li-portfolio: $$\sigma_p^2=w_A^2 \sigma_A^2+w_B^2 \sigma_B^2+2 w_A w_B \sigma_A \sigma_B \rho_{A B}$$ Bakeng sa letlole la thepa e meraro: - Ho khutla ha setoko: $$\mathrm{E}\left(R_p\right) =w_A \mathrm{E}\left(R_A\right) +w_B \mathrm{E}\left(R_B\right) +w_C \mathrm{E}\left(R_C\right) $$ - Phapang ea li-portfolio: $$\sigma_p^2=w_A^2 \sigma_A^2+w_B^2 \sigma_B^2+w_C^2 \sigma_C^2+2 w_A w_B \sigma_A \sigma_B \rho_{A B}+2 w_A w_C \sigma_A \sigma_C \rho_{A C}+2 w_B w_C \sigma_B \sigma_C \rho_{B C}$$