 बिस्मिल सोग लगाग माड़ें! भे परइप़टा बडर श्मनज मेंट! आज हमार तोपीक है मुल्ती पक्टर मोडलि़्स अमने धिस्तिः के सिंगल फक्टर मोडल्स की बात की थी बागी को रवत बोगाग नीक श्थाज आद नहीं जी छोगाग just yet we talked aboutoundly when we talked about next stage that is multi-factor model. multi-factor model permit announced view of the risk that is granular more granular than single factor. single factor see isadha diversified hota while spread hota and capturing hota better hota. these describe return on risk in terms of risk as it with respect to factors that factors ka sadh risk ka kya relationships naya usko ye capture ka rah hota hai in order to give us a better indication. such model generally include systematic factors and prized risk. prized risk se murad kya? wo risk jis ke liye investor kahenge ke hum ye risk leh rahe hain to we should get a return. so these are prized risk. so multi-factor model unko capture ka rahenge aur mainly systematic risk to ye tek rahe hota hain. arbitrage pricing theory. one of the starting point for this multi-factor is apt. apt describe the expected return on asset aur portfolio as a linear function. kye relationship develop hoti hai uske through ye returns ko calculate kar sekte. like cap-m cap-m humne baad kaafi jaga ki bhi hai cap-m ki domain be hai. apt describe financial market equilibrium. but apt make less strong assumption. cap-m ki tera assumptions tori si zada strong hai. apt ki itni rigid assumptions nahin hai to thotta sa relatively ye flex hai with respect to assumptions. iski major assumptions hai kya asset returns are described by factor models. ke ek factor nahin hai multi-factor model hai jiski through ye determine hota hai. there are many assets so asset specific risk can be eliminated. jisko in simple word aap kate hai diversification possible hai aap spread out kar hain to individual jo risks nahin aap eliminate kar sekte. assets are priced such that there is no arbitrage possibility hai. ne ke wo fairly priced hai. arbitrage opportunity exist nahin kati hai. apt ki assumptions hai. equation iski kya hai with this in front of you right in front of you abhi meski detail se baad karenge main gist kya hai that we want to calculate the expected return to kya se nikal aega. expected return asset jo hai wo humara iski jo main humara jo calculation hai for this formula. rz rfp use kate hai is risk free rate. then it is the sensitivity jisko beta ki form mein hum use karenge aur risk premium hai jo ke humare us particular factor ka with respect to i. esko zara formula ko ek doa duwara dekhlein. expected return nikal nahin hai if this is the way we compute it. having the factor incorporated humare pas expected return aajata hai. multi factor models are broadly categorized according to types of factor used as follows. to income further three categories mein divide kattein ke kisth raha ke factor use kiye mein. to un factors ki base pe main sko subcategorize kare. macroeconomic factors, fundamental factors aur statistical. these are the types of factors jo ke humin sab ki different types aur aage for the examples ko dekhene. in macroeconomic the factors are surprised to macroeconomic variables ke jo hume surprises aate hai aur wo surprise se murad kya hai humare actual minus the forecasted value and that has expected value of zero. yani ke originally mara hai ke surprises nahin honge. so macroeconomic indicators hai unki saad hum apne linkage ko develop kare haute in macroeconomic factors. fundamental factors kya hai? factors attributable to stocks aur companies that are important for explaining cross sectional differences in price. yani ke fundamental factors mara hi yani ke unki jo specific related to the companies yaw stocks related jo hai wo un factors ke saad linkage create ke jaati to fundamental factors ke saad multi factor model use rata hai. in statistical factors the statistical methods applied to set of historical return to determine portfolio that explain historical turn in one or two senses. matta mein jo statistical models ko historical se link karke then we try to come up with the solution on factors ke saad linkage create kate to the three main categories jo multi factor mein exist kafi hai. multi factor model have application to return attribution risk attribution portfolio construction strategic investment decision yani ke bada critically utilization hai iski ke portfolio ka return kaha se aar hai risk ki kya attributes hai kise links hai aur mari decision making mein hame ye help out kata. a factor portfolio is a portfolio which unit sensitivity to a factor and zero sensitivity to other factor. unit sensitivity matlab ke ek factor ke saad uska sensitivity hai baki on ke saad sensitivity zero hai. so this is also one of the method we are going to see. to hum ye multi factor models ki further detail mein bhi jaayenge aur hum isko work out karenge to make sure we have a basic understanding ki ye factors work kese katne aur inka jis spirit kya. thank you