Dǎɣ asikin ən tabaraten dǎɣ əmik ən asikin ən latex ən maɗinan fal asikin ən azagar əd təbiɗawen dǎɣ təmusne tan ɗortfolio təšrayat.
Context:MPT ijja ɣur is as imassexdaran war raqqis nat, almaɣna n awen amos as a fal issin portfolios ikf-an alqim olahan, imassexdaran ad arhan fal wa war n ila tikma Dǎɣ awen, amanuzar adobat adakal ən asibab ogaran aśuhu ɣas afal eqal atiwafan dǎɣ azagar ogaran aśuhu. Dǎɣ amsuɣəl, amsədu was anihaga adigriwan azaway ən azəzjar atiwəjan, ilzam ad aliɣi as ajət ən aśahat. Trade-off wan tiditt war eqqel olahan i investor tan fuk Inuməɣan azlaynen adakalən assuhu as amək ən amək ən amək ən amək. Almaɣna net eqqal as investor war n ila alxidmat daɣ portfolio a fal portfolio wan issin ille s risk-expected return profile olaɣan - almaɣna n awen, a fal edag n risk wen ille portfolio iyyan s alwazab n riba olaɣan  Daɣ almital:  Alɣillas n portfolio eqqal tartit n alɣillas n asuj wan asuj Iddikud n azruf wan portfolio \sigma _{p} eqqal alxidmăt n iharojan ρij n asuj win ichrutan, i isuj fuk n asuj (i, j) Amutti n amutti ikfa afaham n tadhilt osaɣan id asidu A ogaran aśuhu ən təmotayen, ogaran aśuhu ən asibab.
- Alwaq wa id ewad: Dǎɣ $$ \mathrm{E}\left(R_p\right)=\sum_i w_i \mathrm{E}\left(R_i\right) Dǎɣ $$ ɣur $R_p$ eqqal amutti fal portfolio, $R_i$ eqqal amutti fal asuj $i$ d $w_i$ eqqal iddikud n asuj wan component $i$ (awen eqqal iddikud n asuj wan "i" daɣ portfolio s immik wa s $\sum_i w_i=1$)). - Portfolio return variance: Dǎɣ $$ Dᾰɣ awa ᾰtwašaɣalᾰn, əjjanen fᾰl ᾰddinᾰt ᾰjjootnen dᾰɣ ᾰddinᾰt ᾰjjootnen. Dǎɣ $$ ɣur $\sigma_i$ eqqal (sample) standard deviation n periodic returns fal asuj $i$ tolas $\rho_{i j}$ eqqal correlation coefficient jir returns fal asuj $i$ d $j$ Dǎɣ əmik iyan, aliɣi adobat adiqil ayktaban sund: Dǎɣ $$ \sigma_p^2=\sum_i \sum_j w_i w_j \sigma_i \sigma_j \rho_{i j} Dǎɣ $$ ɣur $\rho_{i j}=1$ i $i=j$ meɣ Dǎɣ $$ \sigma_p^2=\sum_i \sum_j w_i w_j \sigma_{i j} Dǎɣ $$ ɣur $\sigma_{i j}=\sigma_i \sigma_j \rho_{i j}$ eqqal (sample) covariance n timzal n azzaman fal issin haratan meɣ s immik wa yadan s $\sigma{i, j) $, $\operatorname{cov}{ }_{i j}$ meɣ $\operatorname{cov}{i, j) $ - Portfolio return volatility (standard deviation) Dǎɣ $$ \sigma_p=\sqrt{\sigma_p^2} Dǎɣ $$ Fal portfolio n issin ilalan: - Portfolio return: $$\mathrm{E}\left(R_p\right)=w_A \mathrm{E}\left(R_A\right)+w_B \mathrm{E}\left(R_B\right)=w_A \mathrm{E}\left(R_A\right)+\left(1-w_A\right) \mathrm{E}\left(R_B\right) $$  - Alɣillas n portfolio: $$\sigma_p^2=w_A^2 \sigma_A^2+w_B^2 \sigma_B^2+2 w_A w_B \sigma_A \sigma_B \rho_{A B}$$ Fal portfolio n karad alqim tan: - Portfolio return: $$\mathrm{E}\left(R_p\right) =w_A \mathrm{E}\left(R_A\right) +w_B \mathrm{E}\left(R_B\right) +w_C \mathrm{E}\left(R_C\right) $$ - Alɣillas n portfolio: $$\sigma_p^2=w_A^2 \sigma_A^2+w_B^2 \sigma_B^2+w_C^2 \sigma_C^2+2 w_A w_B \sigma_A \sigma_B \rho_{A B}+2 w_A w_C \sigma_A \sigma_C \rho_{A C}+2 w_B w_C \sigma_B \sigma_C \rho_{B C}$$