modran Port ‌ folio theorylo Port ‌ folio return mariyu vaividhyaanni lekkinchadaniki ganita rubberu marque ‌ doun phormat ‌ loo suuthraalanu sangrahinchandi  https://en.wikipedia.org/wiki/Modern_portfolio_theory
MPT  pettubadidaarulu risky vimukhata kaligi untaruu ,  antey adae aasinchina raabadini andhinchay remdu Port ‌ foliyolanu andinchinatlayithe ,  pettubadidaarulu takuva risky unnadaanini istapadatara .  anevalla ,  ekuva aasinchina raabadula dwara bhartee cheyabadinappudu Bara pettubadidaarudu ekuva risky teesukuntaadu .  deeniki viruddhamgaa ,  ekuva aasinchina raabadini koorukuney pettubadidaarudu tappanisariga ekuva nastanni angeekarinchaali .  pettubadidaarulandarika khachitamaina trade - af okelaa undadhu .  vaervaeru pettubadidaarulu vyaktigata risky virakti lakshanhaala aadhaaramga trade - af ‌ nu vibhinnamgaa anchana vestaaru .  rendava Port ‌ folio marinta anukuulamaina risky - anchana raabadi profile ‌ thoo unnatlayithe hetubaddhamaina pettubadidaarudu Port ‌ pholiolo pettubadi pettadu - antey ,  aa stayi risky choose pratyaamnaaya Port ‌ folio vunte adi merugaina raabadini kaligi umtumdi .

 modal kindha :

 Port ‌ folio return anede raajyaamga aastula return ‌ l nishpatthi - waited kalaika .
 Port ‌ folio return astirata 
\sigma _{p}  anede anni aset jatalaku  (i, j)  component aastula yokka sahasambandhaala  ρij  yokka function .  astirata pettubaditho mudipadi unna risky ‌ pai antardrushtini estunde .  ekuva astirata ,  ekuva pramaadam .
-  aasinchina raabadi :
$$
\mathrm{E}\left(R_p\right)=\sum_i w_i \mathrm{E}\left(R_i\right)
$$
 ikda  $R_p$  anede Port ‌ pholiopai raabadi , $R_i$  anede aasti  $i$ pai raabadi mariyu  $w_i$  anede component aasti  $i$  yokka veyiting  ( antey ,  Port ‌ folioloni aasti  "i"  nishpatthi ,  tadwara  $\sum_i w_i=1$ ).
-  Port ‌ folio return variance :
$$
\sigma_p^2=\sum_i w_i^2 \sigma_i^2+\sum_i \sum_{j \neq i} w_i w_j \sigma_i \sigma_j \rho_{i j}
$$
 ikda  $\sigma_i$  anede aasti  $i$ pai aavartana raabadi yokka  ( namoonaa )  praamaanika vichalanam mariyu  $\rho_{i j}$  anede  $i$  mariyu  $j$  aastulapai raabadi Madhya sahasambandha gunakam .  pratyaamnaayamgaa vyakteekarananu ila vraayavachhu :
$$
\sigma_p^2=\sum_i \sum_j w_i w_j \sigma_i \sigma_j \rho_{i j}
$$
 ikda  $\rho_{i j}=1$  choose  $i=j$,  ledha 
$$
\sigma_p^2=\sum_i \sum_j w_i w_j \sigma_{i j}
$$
 ikda  $\sigma_{i j}=\sigma_i \sigma_j \rho_{i j}$  anede remdu aastulapai aavartana raabadi yokka  ( namoonaa )  coviarens ledha pratyaamnaayamgaa  $\sigma(i, j)$, $\operatorname gaaa suuchimchabadutumdi . {cov}{ }_{i j}$  ledha  $\operatorname{cov}(i, j)$.
-  Port ‌ folio return astirata  ( praamaanika vichalanam ):
$$
\sigma_p=\sqrt{\sigma_p^2}
$$
 remdu - aasti Port ‌ folio choose :
-  Port ‌ folio return :
$$\mathrm{E}\left(R_p\right)=w_A \mathrm{E}\left(R_A\right)+w_B \mathrm{E}\left(R_B\right)=w_A \mathrm{E}\  edama (R_A\ Kandla )+\ edama (1-w_A\ Kandla ) \mathrm{E}\left(R_B\right)$$

-  Port ‌ folio vyatyaasam :
$$\sigma_p^2=w_A^2 \sigma_A^2+w_B^2 \sigma_B^2+2 w_A w_B \sigma_A \sigma_B \rho_{A B}$$
 muudu - aasti Port ‌ folio choose :
-  Port ‌ folio return :
$$\mathrm{E}\left(R_p\right)=w_A \mathrm{E}\left(R_A\right)+w_B \mathrm{E}\left(R_B\right)+w_C \mathrm{E}\  edama  (R_C\ Kandla )$$
-  Port ‌ folio vyatyaasam :
$$\sigma_p^2=w_A^2 \sigma_A^2+w_B^2 \sigma_B^2+w_C^2 \sigma_C^2+2 w_A w_B \sigma_A \sigma_B \rho_{A B}+2 w_A w_C \sigma_A \ sigma_C \rho_{A C}+2 w_B w_C \sigma_B \sigma_C \rho_{B C}$$