Soo saar qaaciidooyinka qaabka calaamadeynta latekska xisaabta si loo xisaabiyo soo noqoshada iyo kala duwanaanshaha faylalka ku jira aragtida casriga ah ee faylalka https://en.wikipedia.org/wiki/Modern_portfolio_theory
Context:MPT waxay u maleyneysaa in maalgashadayaashu ay yihiin kuwa ka fogaada khatarta, taas oo macnaheedu yahay in la siiyo laba faylal oo bixiya isla soo celinta la filayo, maalgashadayaashu waxay doorbidaan midka khatarta yar. Sidaa darteed, maalgashadehu wuxuu qaadi doonaa khatar kordhay oo keliya haddii ay ka soo baxdo soo-celin sare oo la filayo. Taas bedelkeeda, maalgashade doonaya inuu helo faa'iido badan waa inuu qaataa khatar badan. Qiimaha saxda ah ee ganacsigu ma noqon doono mid isku mid ah dhammaan maalgashadayaasha. Maalgashadayaasha kaladuwan ayaa si kala duwan u qiimeyn doona isbedelka iyadoo lagu saleynayo astaamaha halista shakhsi ahaaneed. Taas macnaheedu waxa weeye in maal-galiyaha caqliga leh uusan maalgelin doonin sanduuq haddii sanduuq labaad uu jiro oo leh khatar ka wanaagsan oo la filayo inuu soo laabto - taas oo ah, haddii heerka khatartaas ay jirto sanduuq kale oo leh soo laabasho la filayo oo ka wanaagsan.  Qaabka hoos ku xusan:  Dakhliga ku soo gala sanduuqa waa isku darka la miisaamay ee dakhliga ku soo gala hantida. Isbeddelka soo noqoshada ee faylalka \sigma _{p} waa shaqo isku xidhka ρij ee hantida qaybta, dhammaan lammaanaha hantida (i, j). Isbedbedelka ayaa muujinaya khatarta la xiriirta maalgashiga. Hadii ay sarreyso isbedelka, khatarta ayaa kor u kacaysa.
- Soo noqoshada la filayo: $$ \mathrm{E}\left{R_p\right) =\sum_i w_i \mathrm{E}\left{R_i\right) $$ halkaas oo $R_p$ ay tahay soo celinta faylalka, $R_i$ ay tahay soo celinta hantida $i$ iyo $w_i$ ay tahay miisaanka hantida qaybta $i$ (taas oo ah, saamiga hantida "i" ee faylalka, si $\sum_i w_i=1$). - Kala duwanaanshaha soo noqoshada hantida: $$ Marka la eego tirada guud ee isugeynta isugeynta isugeynta isugeynta isugeynta isugeynta isugeynta $$ halkaas oo $\sigma_i$ ay tahay (sawirka) kala duwanaanshaha caadiga ah ee soo noqoshada xilliyeed ee hantida $i$, iyo $\rho_{i j}$ waa isku dheelitirka u dhexeeya soo noqoshada hantida $i$ iyo $j$. Waxaa kale oo loo qori karaa: $$ Waxan rabaa in aan ogaado in aan ka soo horjeedo. $$ Halka $\rho_{i j}=1$ ee $i=j$, ama $$ Waxan rabaa in aan ogaado sida aan uga faa'iideysan karo. $$ halkaas oo $\sigma_{i j}=\sigma_i \sigma_j \rho_{i j}$ ay tahay (sawirka) isbadalka soo noqnoqoshada xilliyeed ee labada hanti, ama haddii kale waxaa lagu calaamadeeyay $\sigma(i, j)$, $\operatorname{cov}{ }_{i j}$ ama $\operatorname{cov}(i, j)$. - Isbedbedelka heerka dakhliga ku soo gala (kala duwanaanshaha caadiga ah): $$ \sigma_p=\sqrt{\sigma_p^2} waxaa loo yaqaanaa $$ Hantida laba hanti: - Dakhliga ku soo gala: $$\mathrm{E}\left(R_p\right) =w_A \mathrm{E}\left(R_A\right) +w_B \mathrm{E}\left(R_B\right) =w_A \mathrm{E}\left(R_A\right) +\left(1-w_A\right) \mathrm{E}\left(R_B\right) $$  - Kala duwanaanshaha faylalka: $$\sigma_p^2=w_A^2 \sigma_A^2+w_B^2 \sigma_B^2+2 w_A w_B \sigma_A \sigma_B \rho_{A B}$$ Hantida saddexda hanti: - Dakhliga ku soo gala: $$\mathrm{E}\left(R_p\right) =w_A \mathrm{E}\left(R_A\right) +w_B \mathrm{E}\left(R_B\right) +w_C \mathrm{E}\left(R_C\right) $$ - Kala duwanaanshaha faylalka: $$\sigma_p^2=w_A^2 \sigma_A^2+w_B^2 \sigma_B^2+w_C^2 \sigma_C^2+2 w_A w_B \sigma_A \sigma_B \rho_{A B}+2 w_A w_C \sigma_A \sigma_C \rho_{A C}+2 w_B w_C \sigma_B \sigma_C \rho_{B C}$$