finance/mr/ifnotes_indic_translation.jsonl

{"en":"The lecture notes are intended for students in the introductory finance course.","translation":"हे व्याख्यान नोट्स, वित्तीय विषयाचा परिचय अभ्यासक्रमातील विद्यार्थ्यांसाठी तयार केले आहेत.","target_lang":"mr","domain":"academic","complexity":"simple"}
{"en":"These notes aim to bridge the gap between basic textbooks and more advanced finance literature.","translation":"या नोट्सचा उद्देश, मूलभूत पाठ्यपुस्तके आणि अधिक प्रगत वित्तीय साहित्यामध्ये समन्वय साधणे आहे.","target_lang":"mr","domain":"academic","complexity":"moderate"}
{"en":"The Black-Scholes model will be briefly introduced.","translation":"ब्लॅक-शोल्स मॉडेलची संक्षिप्त ओळख करून दिली जाईल.","target_lang":"mr","domain":"academic","complexity":"simple"}
{"en":"The goal is to present key finance theories using discrete-time models.","translation":"याचा उद्देश, डिस्क्रीट-टाइम मॉडेल्स वापरून प्रमुख वित्तीय सिद्धांत सादर करणे आहे.","target_lang":"mr","domain":"academic","complexity":"moderate"}
{"en":"These notes do not include historical accounts or references to original papers.","translation":"या नोट्समध्ये ऐतिहासिक नोंदी किंवा मूळ पेपरचा संदर्भ दिलेला नाही.","target_lang":"mr","domain":"academic","complexity":"simple"}
{"en":"A student applying for a loan is investing in their human capital.","translation":"कर्जासाठी अर्ज करणारा विद्यार्थी, त्याच्या मानवी भांडवलात गुंतवणूक करत आहे.","target_lang":"mr","domain":"finance","complexity":"moderate"}
{"en":"The government subsidizes students because of the future income they will generate.","translation":"सरकार विद्यार्थ्यांंना अनुदान देते, कारण ते भविष्यात उत्पन्न निर्माण करतील.","target_lang":"mr","domain":"finance","complexity":"moderate"}
{"en":"A first-time homebuyer typically borrows against future income.","translation":"पहिला-वहिला घर खरेदीदार, सामान्यतः भविष्यातील उत्पन्नावर कर्ज घेतो.","target_lang":"mr","domain":"finance","complexity":"simple"}
{"en":"Companies may raise capital by issuing stocks or borrowing money.","translation":"कंपन्या शेअर्स जारी करून किंवा कर्ज घेऊन भांडवल उभारू शकतात.","target_lang":"mr","domain":"finance","complexity":"simple"}
{"en":"Financial markets connect the demand for capital with the supply of capital.","translation":"आर्थिक बाजारपेठ भांडवलाची मागणी आणि पुरवठा यांच्याशी जोडलेली आहे.","target_lang":"mr","domain":"finance","complexity":"moderate"}
{"en":"Risk-averse agents share risk in financial markets.","translation":"जोखिम-विरोधी घटक आर्थिक बाजारात जोखीम वाटून घेतात.","target_lang":"mr","domain":"finance","complexity":"moderate"}
{"en":"Prices govern the flow of capital in financial markets.","translation":"आर्थिक बाजारात किंमती भांडवलाचा प्रवाह नियंत्रित करतात.","target_lang":"mr","domain":"finance","complexity":"simple"}
{"en":"Government bonds typically offer a smaller expected return than stocks.","translation":"सरकारी रोखे सामान्यतः समभागांपेक्षा कमी अपेक्षित परतावा देतात.","target_lang":"mr","domain":"finance","complexity":"moderate"}
{"en":"The CAPM and APT models consider expected return and variance.","translation":"CAPM आणि APT मॉडेल्स अपेक्षित परतावा आणि विचलन विचारात घेतात.","target_lang":"mr","domain":"finance","complexity":"moderate"}
{"en":"Arbitrage pricing models are based on the idea that identical payments should have the same price.","translation":"आर्बिट्रेज किंमत मॉडेल या कल्पनेवर आधारित आहेत की, समान देयकांची किंमत समान असावी.","target_lang":"mr","domain":"finance","complexity":"complex"}
{"en":"How should a firm finance its investments?","translation":"एका फर्मने तिच्या गुंतवणुकीसाठी वित्तपुरवठा कसा करावा?","target_lang":"mr","domain":"finance","complexity":"simple"}
{"en":"The Modigliani-Miller theorems provide a starting point for studying these issues.","translation":"मोदिग्लियानी-मिलर प्रमेय या समस्यांचा अभ्यास करण्यासाठी एक प्रारंभिक बिंदू प्रदान करतात.","target_lang":"mr","domain":"finance","complexity":"moderate"}
{"en":"Consider a private ownership economy as in Debreu (1959).","translation":"डेब्रे (१९५९) प्रमाणे खाजगी मालकीची अर्थव्यवस्था विचारात घ्या.","target_lang":"mr","domain":"finance","complexity":"complex"}
{"en":"The firm maximizes profits, and consumers maximize utility.","translation":"फर्म नफा वाढवते, आणि ग्राहक उपयुक्तता वाढवतात.","target_lang":"mr","domain":"finance","complexity":"moderate"}
{"en":"The price system changes the behavior of agents.","translation":"किंमत प्रणाली एजंट्सच्या वर्तनात बदल घडवते.","target_lang":"mr","domain":"finance","complexity":"simple"}
{"en":"The company's financial performance was analyzed using various metrics.","translation":"कंपनीच्या आर्थिक कामगिरीचे विविध मेट्रिक्स वापरून विश्लेषण करण्यात आले.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The interest rate on the loan is subject to change based on market conditions.","translation":"कर्जावरील व्याजदर बाजारातील परिस्थितीनुसार बदलू शकतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Investors should carefully consider the risks associated with each investment option.","translation":"गुंतवणूकदारांनी प्रत्येक गुंतवणुकीच्या पर्यायांशी संबंधित जोखीमांचा काळजीपूर्वक विचार केला पाहिजे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The project's net present value (NPV) was calculated to assess its profitability.","translation":"या प्रकल्पाची नफाक्षमता तपासण्यासाठी निव्वळ वर्तमान मूल्य (NPV) मोजले गेले.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Duration and convexity are important concepts in bond risk management.","translation":"कालावधी आणि कॉन्वेक्सिटी हे बाँड जोखीम व्यवस्थापनातील महत्त्वाचे घटक आहेत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The binomial model is a useful tool for option pricing.","translation":"द्विपदी मॉडेल हे पर्याय मूल्यमापनासाठी उपयुक्त साधन आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The term structure of interest rates can be flat or have different shapes.","translation":"व्याज दराची मुदत रचना सपाट असू शकते किंवा विविध आकार असू शकतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The company is considering a new investment opportunity.","translation":"कंपनी एका नवीन गुंतवणुकीच्या संधीचा विचार करत आहे.","target_lang":"mr","domain":"general","complexity":"simple"}
{"en":"The stock market experienced a period of volatility.","translation":"शेअर बाजारात अस्थिरतेचा काळ अनुभवला गेला.","target_lang":"mr","domain":"news","complexity":"simple"}
{"en":"Please review the financial statements carefully.","translation":"कृपया आर्थिक विवरणपत्रे काळजीपूर्वक तपासा.","target_lang":"mr","domain":"general","complexity":"simple"}
{"en":"The economic outlook remains uncertain.","translation":"अर्थव्यवस्थेची स्थिती अजूनही अनिश्चित आहे.","target_lang":"mr","domain":"news","complexity":"simple"}
{"en":"We need to analyze the cash flow projections.","translation":"आम्हाला रोख प्रवाहाच्या अंदाजाचे विश्लेषण करणे आवश्यक आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The project's success depends on effective risk management.","translation":"प्रकल्पाचे यश प्रभावी जोखीम व्यवस्थापनावर अवलंबून असते.","target_lang":"mr","domain":"general","complexity":"moderate"}
{"en":"The company's debt-to-equity ratio is a key financial metric.","translation":"कंपनीचे कर्ज-इक्विटी गुणोत्तर हे एक महत्त्वाचे आर्थिक मापदंड आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The board of directors approved the budget for the next fiscal year.","translation":"संचालक मंडळाने पुढील आर्थिक वर्षासाठी अर्थसंकल्पाला मान्यता दिली.","target_lang":"mr","domain":"general","complexity":"moderate"}
{"en":"The market is currently experiencing a downturn.","translation":"सध्या बाजारात मंदीची लाट आहे.","target_lang":"mr","domain":"news","complexity":"simple"}
{"en":"The company is seeking to raise capital through a public offering.","translation":"कंपनी सार्वजनिक ऑफरद्वारे भांडवल उभारण्याचा प्रयत्न करत आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The financial advisor provided valuable insights.","translation":"आर्थिक सल्लागाराने मौल्यवान माहिती दिली.","target_lang":"mr","domain":"general","complexity":"simple"}
{"en":"The investment portfolio was diversified to reduce risk.","translation":"जोखीम कमी करण्यासाठी गुंतवणूक पोर्टफोलिओमध्ये विविधता आणली गेली.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The company's earnings per share (EPS) increased significantly.","translation":"कंपनीचे प्रति शेअर उत्पन्न (EPS) लक्षणीय वाढले.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The option price at time 0 is determined by the replicating portfolio.","translation":"वेळेनुसार 0 वाजता पर्यायाची किंमत पुनरावृत्ती पोर्टफोलिओद्वारे निश्चित केली जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"We use the stock as a generic term for a risky asset.","translation":"आपण स्टॉकचा वापर जोखमीच्या मालमत्तेसाठी सामान्य संज्ञा म्हणून करतो.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"The price of the call option should be at time 0.","translation":"कॉल ऑप्शनची किंमत 0 वाजता किती असायला हवी.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"A portfolio is a vector whose coordinates represent the number of securities.","translation":"पोर्टफोलिओ हा एक वेक्टर आहे ज्याचे निर्देशांक सिक्युरिटीजची संख्या दर्शवतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"An arbitrage in the security price system is a portfolio.","translation":"सुरक्षितता किंमत प्रणालीतील आर्बिट्रेज म्हणजे एक पोर्टफोलिओ.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The market is complete if for every y there exists a θ.","translation":"प्रत्येक y साठी θ अस्तित्वात असल्यास बाजारपेठ पूर्ण आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"Risk-neutral pricing does not assume risk-neutrality.","translation":"जोखीम-तटस्थ किंमत जोखीम-तटस्थतेची कल्पना करत नाही.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The economic intuition behind this is important.","translation":"यामागची आर्थिक अंतर्दृष्टी महत्त्वाची आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The agent has a utility function U: R+ → R.","translation":"एजंटकडे युटिलिटी फंक्शन U: R+ → R आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"The financial market is a way of transferring money.","translation":"आर्थिक बाजारपेठ म्हणजे पैसे हस्तांतरित करण्याचा एक मार्ग आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"The model is complete, i.e. there are as many securities as there are states.","translation":"मॉडेल पूर्ण आहे, म्हणजे, जेवढे राज्य आहेत तेवढ्याच सिक्युरिटीज आहेत.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"The method in Equation (4.1) is often called risk-neutral pricing.","translation":"समीकरण (4.1) मधील पद्धतीला अनेकदा जोखीम-तटस्थ किंमत म्हणतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The price of the stock is supposed to represent a sensible model of the market.","translation":"शेअरची किंमत बाजाराचे एक समजूतदार मॉडेल दर्शवते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"If the spot prices of real goods are known at time 0, then we may as well express the initial endowment in terms of wealth.","translation":"जर 0 वाजता वास्तविक वस्तूंचे स्पॉट दर माहित असतील, तर आपण आरंभीची मालमत्ता संपत्तीच्या संदर्भात व्यक्त करू शकतो.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"The agent’s problem is to maximize utility subject to a constraint.","translation":"एजंटची समस्या म्हणजे मर्यादेच्या अधीन राहून उपयुक्तता वाढवणे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The market is arbitrage-free if and only if there exists a state-price vector.","translation":"जर आणि केवळ जर स्टेट-प्राइस वेक्टर अस्तित्वात असेल तरच बाजार आर्बिट्रेज-मुक्त आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"The financial market allows agents to borrow against future income.","translation":"आर्थिक बाजारपेठ एजंट्सना भविष्यातील उत्पन्नावर कर्ज घेण्यास परवानगी देते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The analysis of the single agent can be carried over to an economy with many agents.","translation":"एकाच एजंटचे विश्लेषण अनेक एजंट्स असलेल्या अर्थव्यवस्थेत करता येते.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"The model with finite state space needs the number of states to be large.","translation":"मर्यादित स्थिती असलेल्या मॉडेलमध्ये राज्यांची संख्या मोठी असणे आवश्यक आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Assume that over a short time interval the stock can only move to two different values.","translation":"असे समजू या की, थोड्या कालावधीत स्टॉक फक्त दोन वेगवेगळ्या मूल्यांवर जाऊ शकतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The company announced a new product launch next month.","translation":"कंपनीने पुढील महिन्यात नवीन उत्पादन सुरू करण्याची घोषणा केली.","target_lang":"mr","domain":"general","complexity":"simple"}
{"en":"The weather forecast predicts heavy rainfall for tomorrow.","translation":"हवामान खात्याने उद्या जोरदार पावसाचा अंदाज वर्तवला आहे.","target_lang":"mr","domain":"news","complexity":"simple"}
{"en":"Could you please pass me the salt?","translation":"कृपया, मला मीठ द्याल का?","target_lang":"mr","domain":"conversation","complexity":"simple"}
{"en":"The research team is working on a new algorithm.","translation":"संशोधन पथक नवीन अल्गोरिदमवर काम करत आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"She is very happy with her new job.","translation":"ती तिच्या नवीन नोकरीमुळे खूप आनंदी आहे.","target_lang":"mr","domain":"general","complexity":"simple"}
{"en":"The government is implementing new policies to boost the economy.","translation":"सरकार अर्थव्यवस्थेला चालना देण्यासाठी नवीन धोरणे राबवत आहे.","target_lang":"mr","domain":"news","complexity":"moderate"}
{"en":"He is a highly skilled software engineer.","translation":"तो एक अत्यंत कुशल सॉफ्टवेअर अभियंता आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The meeting will be held at 2 PM.","translation":"बैठक दुपारी २ वाजता होईल.","target_lang":"mr","domain":"general","complexity":"simple"}
{"en":"The price of oil has increased significantly.","translation":"तेलाच्या किंमतीत लक्षणीय वाढ झाली आहे.","target_lang":"mr","domain":"news","complexity":"moderate"}
{"en":"They are planning to travel to Europe next summer.","translation":"ते पुढील उन्हाळ्यात युरोपला जाण्याचा विचार करत आहेत.","target_lang":"mr","domain":"general","complexity":"simple"}
{"en":"The project requires a lot of resources.","translation":"या प्रकल्पाला भरपूर संसाधनांची आवश्यकता आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The doctor advised him to take rest.","translation":"डॉक्टरांनी त्याला आराम करण्याचा सल्ला दिला.","target_lang":"mr","domain":"general","complexity":"simple"}
{"en":"The company's profits have increased this quarter.","translation":"या तिमाहीत कंपनीचा नफा वाढला आहे.","target_lang":"mr","domain":"business","complexity":"moderate"}
{"en":"The new technology will revolutionize the industry.","translation":"नवीन तंत्रज्ञान उद्योगात क्रांती घडवेल.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"She is a talented artist and creates beautiful paintings.","translation":"ती एक प्रतिभावान कलाकार आहे आणि सुंदर चित्रे बनवते.","target_lang":"mr","domain":"general","complexity":"moderate"}
{"en":"The economic situation is quite complex.","translation":"आर्थिक परिस्थिती बरीच गुंतागुंतीची आहे.","target_lang":"mr","domain":"news","complexity":"moderate"}
{"en":"The algorithm efficiently sorts the data.","translation":"अल्गोरिदम डेटाची कार्यक्षमतेने क्रमवारी लावतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The team worked diligently to complete the project on time.","translation":"संघ वेळेवर प्रकल्प पूर्ण करण्यासाठी चिकाटीने काम करत होता.","target_lang":"mr","domain":"general","complexity":"moderate"}
{"en":"The impact of climate change is becoming increasingly evident.","translation":" हवामान बदलाचा प्रभाव अधिकाधिक स्पष्ट होत आहे.","target_lang":"mr","domain":"news","complexity":"complex"}
{"en":"The company is exploring new market opportunities.","translation":"कंपनी नवीन बाजारपेठेतील संधी शोधत आहे.","target_lang":"mr","domain":"business","complexity":"moderate"}
{"en":"The model assumes a stochastic process for the underlying asset.","translation":"मॉडेल गृहीत धरतो की अंतर्निहित मालमत्तेसाठी एक यादृच्छिक प्रक्रिया आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"A higher mean value of the asset increases the call price.","translation":"मालमत्तेचे उच्च सरासरी मूल्य कॉलची किंमत वाढवते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"A put option is more likely to finish out-of-the-money.","translation":"पुट ऑप्शन (Put option) 'आउट-ऑफ-द-मनी' (out-of-the-money) मध्ये संपण्याची अधिक शक्यता आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Put-call parity helps to understand the relationship between put and call options.","translation":"पुट-कॉल समानता, पुट आणि कॉल पर्यायांच्या संबंधांना समजून घेण्यास मदत करते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The forward price is decided so that the value of the forward contract at date t is 0.","translation":"फॉरवर्ड किंमत (Forward price) अशा प्रकारे निश्चित केली जाते की तारखेला t फॉरवर्ड कराराचे मूल्य 0 आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"A forward contract forces the holder to buy the underlying security.","translation":"फॉरवर्ड करार धारकाला अंतर्निहित सुरक्षा खरेदी करण्यास भाग पाडतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"You can lose money at expiration on a forward contract.","translation":"मुदतपूर्तीवर (expiration) तुम्ही फॉरवर्ड करारात पैसे गमावू शकता.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"The cash flow at time T is known at time t.","translation":"वेळ T वरील रोख प्रवाह (cash flow) वेळ t वर ज्ञात आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"Buying a call and selling a put is equivalent to buying forward.","translation":"कॉल खरेदी करणे आणि पुट विकणे हे फॉरवर्ड खरेदी करण्यासारखेच आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Restrictions are placed on option prices in frictionless markets.","translation":"घर्षणाशिवाय (frictionless) बाजारात (markets) पर्याय (option) किमतींवर निर्बंध घातले जातात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The value of the option ct satisfies the Merton's tunnel.","translation":"पर्यायाचे मूल्य ct, मेर्टनच्या टनेलचे (Merton's tunnel) समाधान करते.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"An American option is more valuable than the corresponding European option.","translation":"अमेरिकन पर्याय, संबंधित युरोपियन पर्यायापेक्षा अधिक मौल्यवान आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"An American call on a non-dividend paying stock should never be exercised early.","translation":"लाभांश (dividend) न देणाऱ्या स्टॉकवरील अमेरिकन कॉलचा लवकर वापर कधीही करू नये.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"Stocks typically pay dividends.","translation":"सामान्यतः, स्टॉक लाभांश देतात.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"A dividend payment will normally produce a drop in the stock price.","translation":"लाभांश (dividend) दिल्यास सामान्यतः स्टॉकच्या किंमतीत घट होते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"A purchase at time t does not give the new owner part in the next dividend payment.","translation":"वेळ t वर खरेदी केल्यास, नवीन मालकाला पुढील लाभांश मिळवण्याचा हक्क मिळत नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"The drop in the stock price around the dividend date is equal to the size of the dividend.","translation":"लाभांश (dividend) तारखेच्या आसपास स्टॉकच्या किंमतीतील घट, लाभांशाच्या आकाराएवढी असते.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"We consider the price at time 0 of a European call option.","translation":"आम्ही युरोपियन कॉल पर्यायाच्या वेळेनुसार 0 ची किंमत विचारात घेतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"It is not optimal to exercise the option at time 0.","translation":"वेळ 0 वर पर्यायाचा वापर करणे योग्य नाही.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"The binomial model is used for pricing stock options.","translation":"स्टॉक (stock) पर्यायांची किंमत निश्चित करण्यासाठी द्विपद मॉडेलचा (binomial model) वापर केला जातो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The price process is Markov under the equivalent martingale measure.","translation":"किंमत प्रक्रिया समतुल्य मार्टिंगेल मापनाखाली मार्कोव्ह आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"A second condition for using a recombining tree to price a contingent claim is a condition on the contingent claim itself.","translation":"पुनर्संयोजन वृक्ष वापरून आकस्मिक दाव्याची किंमत निश्चित करण्यासाठी दुसरी अट म्हणजे आकस्मिक दाव्यावरच एक अट आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"A European option with expiration date T is path-independent.","translation":"T मुदतीची युरोपियन योजना मार्ग-निरपेक्ष आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The Asian option is an example of a contingent claim which is not path-independent.","translation":"एशियन पर्याय हा आकस्मिक दाव्याचे उदाहरण आहे जे मार्ग-निरपेक्ष नाही.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"To compute the average value one needs the whole path of S.","translation":"सरासरी मूल्य मोजण्यासाठी, S चा संपूर्ण मार्ग आवश्यक आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"We describe in this section a simple way of pricing the American put option in a binomial model.","translation":"या विभागात, आम्ही द्विपदी मॉडेलमध्ये अमेरिकन पुट पर्यायाची किंमत निश्चित करण्याचा एक सोपा मार्ग वर्णन करतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The value of an American put at its maturity is easy enough: P T = max(0, K−S T ).","translation":"अमेरिकन पुटचे त्याच्या मुदतीमधील मूल्य पुरेसे सोपे आहे: P T = max(0, K−S T ).","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Now consider the situation one period before maturity.","translation":"आता मुदतपूर्ती होण्यापूर्वी एक कालावधीची परिस्थिती विचारात घ्या.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"The value of holding the put to maturity is given as the discounted (back to time T−1) value of (6.7).","translation":"पुटला मुदत संपेपर्यंत धरून ठेवण्याचे मूल्य (6.7) च्या सवलतीच्या (वेळेनुसार T−1 पर्यंत) मूल्याप्रमाणे दिले जाते.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"The value at time T−1 of exercising immediately is K−S T−1.","translation":"तत्काळ अंमलबजावणीचे T−1 वेळेचे मूल्य K−S T−1 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The implied volatility of the option is the unique value of σ for which c 0 (S 0 , K, T, σ, r) = c obs.","translation":"पर्यायाची निहित अस्थिरता σ चे अद्वितीय मूल्य आहे ज्यासाठी c 0 (S 0 , K, T, σ, r) = c obs.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"There is no closed-form expression for implied volatility; Equation 6.8 must be solved numerically.","translation":"निहित अस्थिरतेसाठी कोणतेही बंद-फॉर्म (closed-form) समीकरण नाही; समीकरण 6.8 संख्यात्मकदृष्ट्या सोडवणे आवश्यक आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"Assume that the price of a stock is 100 and the risk-free rate is 0.1.","translation":"असे समजा की स्टॉकची किंमत 100 आहे आणि जोखीम-मुक्त दर 0.1 आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"If the Black-Scholes model were true the implied volatility of all options written on the same underlying security should be the same.","translation":"ब्लॅक-शोल्स मॉडेल खरे असल्यास, त्याच अंतर्निहित सिक्युरिटीवर लिहिलेल्या सर्व पर्यायांची निहित अस्थिरता समान असावी.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"The expenses of hedging an option depend on the volatility of the stock during the life of the option.","translation":"एका पर्यायाचे हेजिंग (Hedging) करण्याचे खर्च पर्यायाच्या आयुष्यात स्टॉकच्या अस्थिरतेवर अवलंबून असतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Consider a portfolio manager who manages a portfolio which is diversified so that the value of her portfolio follows that of the market stock index.","translation":"एका पोर्टफोलिओ व्यवस्थापकाचा विचार करा जो एक पोर्टफोलिओ व्यवस्थापित करतो, जो वैविध्यपूर्ण आहे जेणेकरून तिच्या पोर्टफोलिओचे मूल्य बाजार स्टॉक निर्देशांकाचे अनुसरण करते.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"She therefore decides to buy portfolio insurance in such a way that the value of her portfolio will never fall below a level of (say) 90.000.","translation":"म्हणून, ती पोर्टफोलिओ विमा खरेदी करण्याचा निर्णय घेते, अशा प्रकारे की तिच्या पोर्टफोलिओचे मूल्य (उदाहरणार्थ) 90,000 च्या खाली कधीही येणार नाही.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Since the put options are far out-of-the-money (such contracts are often called “lottery tickets”) at the time of purchase they are probably not that expensive.","translation":"पुट पर्याय खरेदीच्या वेळी फारसे 'आउट-ऑफ-द-मनी' (अशा करारांना अनेकदा “लॉटरी तिकीट” म्हणतात) असल्यामुळे ते कदाचित फारसे महाग नाहीत.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"This phenomenon is called a “smirk”.","translation":"या घटनेला “स्मर्क” म्हणतात.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"In this section we consider a very important application of option pricing.","translation":"या विभागात, आम्ही पर्याय मूल्यांकनाचा एक अतिशय महत्त्वाचा अनुप्रयोग विचारात घेतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The Black-Scholes formula is a celebrated result in financial economics.","translation":"ब्लॅक-शोल्स सूत्र हे आर्थिक अर्थशास्त्रातील एक प्रसिद्ध निष्कर्ष आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"A rigorous derivation requires advanced mathematics beyond the scope of this course.","translation":"या कठोर निष्कर्षासाठी या अभ्यासक्रमाच्या पलीकडे, प्रगत गणिताची आवश्यकता आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The formula is easy to interpret and apply.","translation":"हे सूत्र समजायला आणि वापरायला सोपे आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"We will indicate how the formula is derived.","translation":"आम्ही हे सूत्र कसे तयार केले जाते हे दर्शवू.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"The Black-Scholes model assumes a risk-free bank account.","translation":"ब्लॅक-शोल्स मॉडेल एक सुरक्षित बँक खात्याची कल्पना करते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The stock price can be represented by a geometric Brownian motion.","translation":"शेअरची किंमत भूमितीय ब्राउनियन गतीद्वारे दर्शविली जाऊ शकते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The formula gives the exact call price in the model.","translation":"हे सूत्र मॉडेलमध्ये अचूक कॉल किंमत देते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"We need to specify the whole process of stock prices.","translation":"आम्हाला शेअरच्या किमतीची संपूर्ण प्रक्रिया निर्दिष्ट करणे आवश्यक आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Brownian motion is a stochastic process.","translation":"ब्राउनियन गती एक यादृच्छिक प्रक्रिया आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"The sample paths of Brownian motion are continuous everywhere but differentiable nowhere.","translation":"ब्राउनियन गतीचे नमुने मार्ग सर्वत्र सतत असतात, परंतु कोठेही वेगळे नाहीत.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"The fundamental assumption of the Black-Scholes model is that the stock price can be represented by an equation.","translation":"ब्लॅक-शोल्स मॉडेलची मूलभूत धारणा अशी आहे की शेअरची किंमत एका समीकरणाद्वारे दर्शविली जाऊ शकते.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"The return is defined as the logarithm of the price relative.","translation":"परतावा, किमतीच्या लॉगरिदम गुणोत्तराप्रमाणे परिभाषित केला जातो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"We refer to volatility of the stock.","translation":"आम्ही शेअरच्या अस्थिरतेचा संदर्भ देतो.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"Risk averse agents will demand more to compensate for the uncertainty.","translation":"जोखीम-विरोधी एजंट अनिश्चिततेची भरपाई करण्यासाठी अधिक मागणी करतील.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The fundamental theorem of asset pricing holds in continuous time.","translation":"संपत्ती मूल्यांकनाचा मूलभूत सिद्धांत सतत वेळेत लागू होतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"We can get the Black-Scholes formula.","translation":"आम्ही ब्लॅक-शोल्स सूत्र मिळवू शकतो.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"The integrand is different from 0 when certain conditions are met.","translation":"काही अटी पूर्ण झाल्यावर इंटिग्रंड 0 पेक्षा वेगळे असते.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"The unique arbitrage-free price of a European call option is given by the formula.","translation":"युरोपियन कॉल पर्यायाची एकमेव आर्बिट्रेज-मुक्त किंमत सूत्राद्वारे दिली जाते.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"The call option can be hedged in the Black-Scholes model.","translation":"ब्लॅक-शोल्स मॉडेलमध्ये कॉल पर्यायाचे संरक्षण केले जाऊ शकते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"This is called delta hedging.","translation":"याला डेल्टा हेजिंग म्हणतात.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"The term structure at time 0 is now computed as follows.","translation":"शून्य वेळेतील मुदत रचना आता खालीलप्रमाणे मोजली जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"In fact, one calls the term structure 'inverted' in this case.","translation":"खरं तर, या स्थितीत मुदत संरचनेला 'उलट' म्हटले जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Such a tree is needed for pricing more complicated contracts.","translation":"अशा प्रकारची रचना अधिक गुंतागुंतीचे करार निश्चित करण्यासाठी आवश्यक आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"First, it is easy to see that generally such an 'inversion' is in no way unique.","translation":"सुरुवातीला, हे पाहणे सोपे आहे की सामान्यतः असे 'व्युत्क्रमण' कोणत्याही प्रकारे अद्वितीय नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"Two such conveniences are that the development of ρ can be represented in a recombining tree.","translation":"अशा दोन सोयी म्हणजे ρ चा विकास पुन्हा एकत्र येणाऱ्या ट्रीमध्ये दर्शविला जाऊ शकतो.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"The almighty (“God “or “The Market”) has determined todays term structure.","translation":"सर्वशक्तिमान (“देव” किंवा “बाजार”) यांनी आजची मुदत रचना निश्चित केली आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"All we have to do is “fill in the blanks’.","translation":"आपल्याला फक्त ‘रिकाम्या जागा भरायच्या’ आहेत.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"Two very popular ways of doing this are these functional forms:","translation":"हे करण्यासाठी दोन अतिशय लोकप्रिय मार्ग म्हणजे हे कार्यात्मक प्रकार:","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"With b_hist fixed, (8.1) can be solved hence determining what goes in the two “t= 1”-boxes.","translation":"b_hist निश्चित केल्यावर, (8.1) सोडवले जाऊ शकते, त्यामुळे दोन “t= 1”-बॉक्समध्ये काय जाते हे निश्चित होते.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"We may have to solve the equation determining a_imp(1) numerically, but monotonicity makes this an easy task.","translation":"आम्हाला a_imp(1) संख्यात्मकदृष्ट्या निश्चित करणारे समीकरण सोडवावे लागू शकते, परंतु एकसमानता हे सोपे काम करते.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"And now can can do the same for t= 2,...,T−1 and we can put our computer to work and go to lunch.","translation":"आणि आता आम्ही t= 2,...,T−1 साठीही तसेच करू शकतो आणि आम्ही आमच्या संगणकाला कामाला लावू शकतो आणि जेवणासाठी जाऊ शकतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Fortunately there is a way of doing this.","translation":"सुदैवाने, हे करण्याचा एक मार्ग आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"Consider the binomial ρ-lattice in Figure 8.1.","translation":"आकृती 8.1 मधील द्विपदी ρ-जाळीचा विचार करा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Since P(0,t) = P t i=0 ψ(t,i), we can use the following algorithm to fit the initial term structure.","translation":"P(0,t) = P t i=0 ψ(t,i) असल्यामुळे, आम्ही सुरुवातीची मुदत रचना बसवण्यासाठी खालील अल्गोरिदम वापरू शकतो.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"Now let us demonstrate that in our term structure modelling framework it is impossible to have only parallel shifts of a flat term structure.","translation":"आता आपण हे दर्शवूया की आमच्या मुदत रचना मॉडेलिंग फ्रेमवर्कमध्ये सपाट मुदत संरचनेचे फक्त समांतर बदल असणे अशक्य आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"In other words, in a model with no arbitrage we cannot have bond prices at time 0 given as.","translation":"दुसऱ्या शब्दांत, कोणत्याही आर्बिट्रेज नसलेल्या मॉडेलमध्ये, आपल्याकडे 0 वेळेतील रोखे किंमती असू शकत नाहीत.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"To assign meaning to a ”flat term structure” at time 1 we should have T≥3.","translation":"वेळ 1 वाजता “सपाट मुदत रचना” परिभाषित करण्यासाठी, आपल्याकडे T≥3 असावे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Now consider the zero-coupon bonds with maturity dates 2 and 3.","translation":"आता मुदतपूर्तीची तारीख 2 आणि 3 असलेल्या शून्य-कूपन रोख्यांचा विचार करा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"A forward and a futures contract are very similar contracts.","translation":"फॉरवर्ड आणि फ्यूचर्स करार खूप समान करार आहेत.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"The forward/futures price of a certain asset is the delivery price which makes the forward/futures contract have zero value initially.","translation":"एखाद्या विशिष्ट मालमत्तेची फॉरवर्ड/फ्यूचर्स किंमत ही वितरण किंमत आहे जी सुरुवातीला फॉरवर्ड/फ्यूचर्स कराराचे मूल्य शून्य करते.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"The minimum variance portfolio aims to minimize risk for a given level of expected return.","translation":"किमान विचलन पोर्टफोलिओचा उद्देश, अपेक्षित परताव्याच्या विशिष्ट पातळीसाठी जोखीम कमी करणे आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The formula calculates the variance of the minimum variance portfolio.","translation":"हे सूत्र किमान विचलन पोर्टफोलिओचे विचलन मोजते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The minimum variance portfolio frontier is a parabola.","translation":"किमान विचलन पोर्टफोलिओ फ्रंटियर एक परवलय आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"We are solving multiple 'minimize variance' problems.","translation":"आम्ही एकापेक्षा जास्त 'किमान विचलन' समस्या सोडवत आहोत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The efficient portfolio has the highest mean return for a given variance.","translation":"कार्यक्षम पोर्टफोलिओमध्ये विशिष्ट विचलनासाठी सर्वाधिक सरासरी परतावा असतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The global minimum variance portfolio has the smallest possible variance.","translation":"ग्लोबल किमान विचलन पोर्टफोलिओमध्ये सर्वात कमी संभाव्य विचलन असते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Two-fund separation is an important property of minimum variance portfolios.","translation":"दोन-निधी विभाजन हे किमान विचलन पोर्टफोलिओचे एक महत्त्वाचे वैशिष्ट्य आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Every minimum variance portfolio is a linear combination of two distinct minimum variance portfolios.","translation":"प्रत्येक किमान विचलन पोर्टफोलिओ दोन भिन्न किमान विचलन पोर्टफोलिओचे एक रेखीय संयोजन आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"The zero-beta portfolio is orthogonal to the minimum variance portfolio.","translation":"शून्य-बीटा पोर्टफोलिओ किमान विचलन पोर्टफोलिओला लंबवत आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"The expected excess return on any portfolio is a linear function of the expected excess return on a minimum variance portfolio.","translation":"कोणत्याही पोर्टफोलिओवरील अपेक्षित अतिरिक्त परतावा, किमान विचलन पोर्टफोलिओवरील अपेक्षित अतिरिक्त परताव्याचे एक रेखीय कार्य आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"We now consider a portfolio selection problem with a risk-free asset.","translation":"आता आपण जोखीम-मुक्त मालमत्तेसह पोर्टफोलिओ निवड समस्या विचारात घेऊ.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The capital market line is a straight line.","translation":"भांडवली बाजारपेठ रेषा एक सरळ रेषा आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"The tangent portfolio is the minimum variance portfolio with all wealth invested in risky assets.","translation":"स्पर्शिका पोर्टफोलिओ म्हणजे जोखमीच्या मालमत्तेमध्ये गुंतवलेल्या सर्व संपत्तीसह किमान विचलन पोर्टफोलिओ.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The Sharpe ratio is used for evaluating investment fund performance.","translation":"गुंतवणूक निधीच्या कामगिरीचे मूल्यांकन करण्यासाठी शार्प गुणोत्तर वापरले जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The CAPM is a key result of modern finance theory.","translation":"CAPM आधुनिक वित्त सिद्धांताचा एक महत्त्वाचा निष्कर्ष आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The market portfolio is the tangency portfolio.","translation":"बाजारपेठ पोर्टफोलिओ स्पर्शिका पोर्टफोलिओ आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The CAPM explains asset prices.","translation":"CAPM मालमत्तेच्या किमती स्पष्ट करते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The CAPM relation holds.","translation":"CAPM संबंध लागू आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"The market portfolio is not directly observable.","translation":"बाजारपेठ पोर्टफोलिओ थेट पाहता येत नाही.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The CAPM has unrealistic assumptions.","translation":"CAPM मध्ये अवास्तविक गृहितके आहेत.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"Firm A prefers to pay a floating rate.","translation":"कंपनी A ला फ्लोटिंग रेट देणे आवडते.","target_lang":"mr","domain":"finance","complexity":"simple"}
{"en":"Firm B prefers to borrow at a fixed rate.","translation":"कंपनी B ला निश्चित दराने कर्ज घेणे आवडते.","target_lang":"mr","domain":"finance","complexity":"simple"}
{"en":"In this way is knows in advance exactly how much it has to pay over the 5 years.","translation":"यामुळे, ५ वर्षात नेमके किती पैसे द्यायचे आहेत हे तिला आगाऊ माहित होते.","target_lang":"mr","domain":"finance","complexity":"moderate"}
{"en":"So B gets a systematically “worse deal” than A.","translation":"म्हणून, B ला A पेक्षा पद्धतशीरपणे 'वाईट डील' मिळते.","target_lang":"mr","domain":"finance","complexity":"moderate"}
{"en":"But consider the following arrangement: A takes the fixed rate offer from the bank and B the floating rate.","translation":"परंतु खालील व्यवस्थेचा विचार करा: A बँकेकडून निश्चित दराची ऑफर घेतो आणि B फ्लोटिंग दराची ऑफर घेतो.","target_lang":"mr","domain":"finance","complexity":"complex"}
{"en":"In net-terms: Pays 1Y-ZCB- rate+5bp","translation":"निव्वळ-शब्दांमध्ये: 1Y-ZCB- दर+5bp भरा","target_lang":"mr","domain":"finance","complexity":"moderate"}
{"en":"So this swap-arrangement has put both A and B in a better position (by 25bp) than they would have been had they only used the bank.","translation":"म्हणून या अदलाबदल-व्यवस्थेने A आणि B या दोघांनाही बँकेचा वापर केला असता त्यापेक्षा चांगली स्थिती (25bp ने) दिली आहे.","target_lang":"mr","domain":"finance","complexity":"complex"}
{"en":"If that is so, then it must mean that default (“going broke”) is a possibility that cannot be ignored.","translation":"जर असे असेल, तर याचा अर्थ असा आहे की डिफॉल्ट (“ दिवाळखोरीत जाणे”) ही एक शक्यता आहे, ज्याकडे दुर्लक्ष करता येणार नाही.","target_lang":"mr","domain":"finance","complexity":"complex"}
{"en":"One can quite sensibly ask if that is the kind of risks that individual firms want to take.","translation":"एखाद्या कंपनीला अशा प्रकारचा धोका पत्करायचा आहे का, हे विचारणे अगदी योग्य आहे.","target_lang":"mr","domain":"finance","complexity":"moderate"}
{"en":"So the morale is two-fold: i) If something seems to be too good to be true it usually is.","translation":"म्हणून यातून मिळणारा धडा दुहेरी आहे: (i) जर काहीतरी खरं होण्याइतके चांगले दिसत असेल, तर ते सहसा तसेच असते.","target_lang":"mr","domain":"finance","complexity":"moderate"}
{"en":"Recall that the short rate in our term structure models is a stochastic process.","translation":"आठवा की आमच्या मुदत रचना मॉडेलमधील अल्प दर एक यादृच्छिक प्रक्रिया आहे.","target_lang":"mr","domain":"finance","complexity":"complex"}
{"en":"At time 0 we do not know what the short rate will be at time1.","translation":"वेळ 0 वाजता, वेळ 1 वाजता अल्प दर काय असेल हे आपल्याला माहित नाही.","target_lang":"mr","domain":"finance","complexity":"moderate"}
{"en":"We may however from current bond prices compute the one-period forward rate f(1,2) and it is natural to think that this rate at least carries some information about the level of the short rate at time 1.","translation":"परंतु, सध्याच्या रोख्यांच्या किमतीवरून, आपण एक-कालावधीचा फॉरवर्ड दर f(1,2) मोजू शकतो आणि असे मानणे स्वाभाविक आहे की हा दर कमीतकमी वेळ 1 वाजता अल्प दराच्या पातळीबद्दल काही माहिती देतो.","target_lang":"mr","domain":"finance","complexity":"complex"}
{"en":"For example, one type of expectation hypothesis would argue, that the expected value of short rates is equal to the corresponding forward rates.","translation":"उदाहरणार्थ, एका प्रकारची अपेक्षा गृहीतक असा युक्तिवाद करेल की अल्प दराची अपेक्षित किंमत संबंधित फॉरवर्ड दराच्या समान आहे.","target_lang":"mr","domain":"finance","complexity":"complex"}
{"en":"There is essentially only one expectation hypothesis which follows as a simple consequence of no arbitrage.","translation":"अशा प्रकारे, केवळ एकच अपेक्षा गृहीतक आहे जे कोणत्याही आर्बिट्रेजच्या साध्या परिणामाचे अनुसरण करते.","target_lang":"mr","domain":"finance","complexity":"complex"}
{"en":"We know that in an arbitrage-free model, we have for any zero coupon bond with maturity T i that P(t,T i ) = 1 1 +ρ t E Q t [P(t+ 1,T i )].","translation":"आपल्याला माहित आहे की आर्बिट्रेज-मुक्त मॉडेलमध्ये, मुदत T i असलेल्या कोणत्याही शून्य कूपन बाँडसाठी आपल्याकडे हे आहे: P(t,T i ) = 1 1 +ρ t E Q t [P(t+ 1,T i )].","target_lang":"mr","domain":"finance","complexity":"complex"}
{"en":"Hence standing at timet,the expected return underQof holding a bond in one period is E Q t [P(t+ 1,T i )] P(t,T i ) −1 =ρ t and this does not depend on the maturity of the bond.","translation":"म्हणून, t वेळेवर उभे राहून, एका कालावधीत बाँड ठेवण्याचे Q अंतर्गत अपेक्षित उत्पन्न E Q t [P(t+ 1,T i )] P(t,T i ) −1 =ρ t आहे आणि हे बाँडच्या मुदतीवर अवलंबून नाही.","target_lang":"mr","domain":"finance","complexity":"complex"}
{"en":"This is a mathematical consequence of no arbitrage.","translation":"हे कोणत्याही आर्बिट्रेजचे गणितीय परिणाम आहे.","target_lang":"mr","domain":"finance","complexity":"moderate"}
{"en":"We will consider an agent who wants to invest in the financial markets.","translation":"आम्ही अशा एजंटचा विचार करू ज्याला वित्तीय बाजारात गुंतवणूक करायची आहे.","target_lang":"mr","domain":"finance","complexity":"moderate"}
{"en":"The agent has an initial wealth ofW 0 to invest.","translation":"गुंतवणुकीसाठी एजंटकडे सुरुवातीला W 0 ची संपत्ती आहे.","target_lang":"mr","domain":"finance","complexity":"simple"}
{"en":"The market is experiencing a period of volatility.","translation":"बाजारात अस्थिरतेचा काळ सुरू आहे.","target_lang":"mr","domain":"news","complexity":"simple"}
{"en":"Could you please pass me the salt?","translation":"कृपया, मला मीठ द्याल का?","target_lang":"mr","domain":"general","complexity":"simple"}
{"en":"The company announced a new product launch.","translation":"कंपनीने नवीन उत्पादन सुरू करण्याची घोषणा केली.","target_lang":"mr","domain":"business","complexity":"moderate"}
{"en":"The research paper explores the impact of climate change.","translation":"संशोधन निबंधात हवामान बदलाच्या परिणामांचा शोध घेण्यात आला आहे.","target_lang":"mr","domain":"science","complexity":"moderate"}
{"en":"He is a highly respected professor at the university.","translation":"ते विद्यापीठातील एक अत्यंत प्रतिष्ठित प्राध्यापक आहेत.","target_lang":"mr","domain":"education","complexity":"moderate"}
{"en":"The algorithm efficiently sorts the data.","translation":"अल्गोरिदम डेटाची कार्यक्षमतेने क्रमवारी लावतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The government implemented new economic policies.","translation":"सरकारने नवीन आर्थिक धोरणे लागू केली.","target_lang":"mr","domain":"politics","complexity":"moderate"}
{"en":"She is learning to play the piano.","translation":"ती पियानो वाजवायला शिकत आहे.","target_lang":"mr","domain":"general","complexity":"simple"}
{"en":"The team won the championship after a tough match.","translation":"कठीण सामन्यांनंतर संघाने चॅम्पियनशिप जिंकली.","target_lang":"mr","domain":"sports","complexity":"moderate"}
{"en":"The doctor advised him to take rest.","translation":"डॉक्टरांनी त्याला आराम करण्याचा सल्ला दिला.","target_lang":"mr","domain":"health","complexity":"simple"}
{"en":"The complex interplay of factors makes the situation difficult to predict.","translation":"घटकांच्या गुंतागुंतीच्या आंतरक्रियेमुळे परिस्थितीचा अंदाज घेणे कठीण होते.","target_lang":"mr","domain":"general","complexity":"complex"}
{"en":"Despite the challenges, the project was successfully completed.","translation":"आव्हाने असूनही, प्रकल्प यशस्वीरित्या पूर्ण झाला.","target_lang":"mr","domain":"business","complexity":"moderate"}
{"en":"The philosophical implications of the discovery are far-reaching.","translation":"या शोधाचे तात्त्विक परिणाम दूरगामी आहेत.","target_lang":"mr","domain":"science","complexity":"complex"}
{"en":"The intricacies of international law require careful consideration.","translation":"आंतरराष्ट्रीय कायद्याच्या गुंतागुंतीचा विचारपूर्वक विचार करणे आवश्यक आहे.","target_lang":"mr","domain":"politics","complexity":"complex"}
{"en":"The company's innovative approach revolutionized the industry.","translation":"कंपनीच्या नाविन्यपूर्ण दृष्टिकोनने उद्योगात क्रांती घडवून आणली.","target_lang":"mr","domain":"business","complexity":"complex"}
{"en":"The economic downturn significantly impacted global trade.","translation":"आर्थिक मंदीचा जागतिक व्यापारावर महत्त्वपूर्ण परिणाम झाला.","target_lang":"mr","domain":"economics","complexity":"moderate"}
{"en":"The artist's unique style is instantly recognizable.","translation":"कलाकाराची अनोखी शैली त्वरित ओळखता येते.","target_lang":"mr","domain":"arts","complexity":"moderate"}
{"en":"The software update included several bug fixes and performance enhancements.","translation":"सॉफ्टवेअर अपडेटमध्ये अनेक बग फिक्स आणि कार्यक्षमतेत वाढ समाविष्ट आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The historical significance of the event cannot be overstated.","translation":"या घटनेचे ऐतिहासिक महत्त्व कमी लेखता येणार नाही.","target_lang":"mr","domain":"history","complexity":"complex"}
{"en":"The ethical considerations surrounding artificial intelligence are complex.","translation":"कृत्रिम बुद्धिमत्तेच्या (artificial intelligence) संदर्भातील नैतिक विचार गुंतागुंतीचे आहेत.","target_lang":"mr","domain":"technology","complexity":"complex"}
{"en":"The company's financial decisions are crucial for its future.","translation":"कंपनीचे आर्थिक निर्णय तिच्या भविष्यासाठी महत्त्वाचे आहेत.","target_lang":"mr","domain":"general","complexity":"simple"}
{"en":"Modigliani-Miller theorem is a cornerstone of corporate finance.","translation":"मॉडिलियानी-मिलर सिद्धांत कॉर्पोरेट फायनान्सचा आधारस्तंभ आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Investors can 'undo' the firm's financial decisions under certain conditions.","translation":"ठराविक परिस्थितीत, गुंतवणूकदार कंपनीचे आर्थिक निर्णय 'रद्द' करू शकतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The value of the firm is independent of the level of debt.","translation":"कंपनीची किंमत कर्जाच्या पातळीवर अवलंबून नसते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Complete markets are a restrictive but important assumption.","translation":"संपूर्ण बाजारपेठ ही एक बंधनकारक पण महत्त्वाची धारणा आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The dividend decision can be analyzed in the context of firm value.","translation":"कंपनीच्या मूल्याच्या संदर्भात लाभांश निर्णयाचे विश्लेषण केले जाऊ शकते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Asymmetric information plays a crucial role in real-world financial decisions.","translation":"असममित माहिती वास्तविक-जगातील आर्थिक निर्णयात महत्त्वपूर्ण भूमिका बजावते.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"Corporate taxes and interest payments influence capital structure.","translation":"कॉर्पोरेट कर आणि व्याज देयके भांडवली संरचनेवर परिणाम करतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Bankruptcy costs can affect the optimal capital structure.","translation":" दिवाळखोरीचा खर्च इष्टतम भांडवली संरचनेवर परिणाम करू शकतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Financing positive NPV projects is a key aspect of financial management.","translation":"सकारात्मक NPV (निव्वळ वर्तमान मूल्य) असलेल्या प्रकल्पांना वित्तपुरवठा करणे हे आर्थिक व्यवस्थापनाचे एक महत्त्वाचे पैलू आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"The efficient market hypothesis suggests that it is impossible to consistently beat the market.","translation":"कार्यक्षम बाजारपेठ गृहितक असे सूचित करते की बाजारात सातत्याने मात करणे अशक्य आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"The firm's capital structure is a critical factor.","translation":"कंपनीची भांडवली रचना एक महत्त्वपूर्ण घटक आहे.","target_lang":"mr","domain":"general","complexity":"simple"}
{"en":"Shareholders' wealth is a primary concern.","translation":"भागधारकांचे (शेअरहोल्डर्सचे) हित हे एक प्राथमिक उद्दिष्ट आहे.","target_lang":"mr","domain":"general","complexity":"simple"}
{"en":"The company is considering issuing new shares.","translation":"कंपनी नवीन शेअर्स जारी करण्याचा विचार करत आहे.","target_lang":"mr","domain":"general","complexity":"simple"}
{"en":"Debt financing can be a double-edged sword.","translation":"कर्ज वित्तपुरवठा (Debt financing) एक दुधारी तलवार असू शकते.","target_lang":"mr","domain":"general","complexity":"moderate"}
{"en":"Understanding risk is essential for investment.","translation":"गुंतवणुकीसाठी जोखीम समजून घेणे आवश्यक आहे.","target_lang":"mr","domain":"general","complexity":"simple"}
{"en":"The market is highly volatile these days.","translation":"आजकाल बाजारात अस्थिरता खूप आहे.","target_lang":"mr","domain":"news","complexity":"simple"}
{"en":"The financial statements provide key insights.","translation":"आर्थिक विवरण महत्त्वाचे अंतर्दृष्टी (insights) प्रदान करतात.","target_lang":"mr","domain":"general","complexity":"simple"}
{"en":"The firm's performance is under scrutiny.","translation":"कंपनीच्या कामगिरीचे परीक्षण केले जात आहे.","target_lang":"mr","domain":"general","complexity":"simple"}
{"en":"The economic outlook influences investment decisions.","translation":"आर्थिक दृष्टिकोन गुंतवणुकीच्या निर्णयांवर परिणाम करतो.","target_lang":"mr","domain":"general","complexity":"moderate"}
{"en":"Capital asset pricing model, CAPM, is a financial model.","translation":"भांडवली मालमत्ता किंमत मॉडेल, सीएपीएम, हे एक आर्थिक मॉडेल आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"Capital budgeting is crucial for financial planning.","translation":"भांडवल अंदाजपत्रक आर्थिक नियोजनासाठी महत्त्वाचे आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The Central Limit Theorem is a fundamental concept.","translation":"मध्यवर्ती मर्यादा प्रमेय एक मूलभूत संकल्पना आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Understanding compounding periods is essential.","translation":"गुंतवणुकीचे कालावधी समजून घेणे आवश्यक आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"A contingent claim depends on future events.","translation":"एका संभाव्य दाव्याचा निर्णय भविष्यातील घटनांवर अवलंबून असतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The continuously compounded interest rate is often used.","translation":"सतत चक्रवाढ व्याज दर अनेकदा वापरला जातो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Convexity is an important factor in bond pricing.","translation":"कन्वेक्सिटी (Convexity) रोख्यांच्या किंमतीमध्ये एक महत्त्वाचा घटक आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Debt and equity are key components of capital structure.","translation":"कर्ज आणि इक्विटी भांडवल संरचनेचे मुख्य घटक आहेत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Delta hedging helps manage risk.","translation":"डेल्टा हेजिंग जोखीम व्यवस्थापनात मदत करते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"A derivative security's value is derived from an underlying asset.","translation":"व्युत्पन्न सिक्युरिटीचे मूल्य अंतर्निहित मालमत्तेतून साधले जाते.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"Discount factors are used in present value calculations.","translation":"सवलत घटक वर्तमान मूल्य मोजणीत वापरले जातात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The dividend process affects stock prices.","translation":"लाभांश प्रक्रिया शेअरच्या किमतीवर परिणाम करते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Duration measures the sensitivity of a bond's price to interest rate changes.","translation":"कालावधी (Duration) रोख्यांच्या किमतीची व्याजदरातील बदलांशी असलेली संवेदनशीलता मोजते.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"An efficient portfolio aims to maximize return for a given level of risk.","translation":"एका कार्यक्षम पोर्टफोलिओचे उद्दिष्ट, दिलेल्या जोखमीच्या पातळीसाठी जास्तीत जास्त परतावा मिळवणे असते.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"The financial market facilitates the exchange of assets.","translation":"आर्थिक बाजारपेठ मालमत्तेच्या देवाणघेवाणीस मदत करते.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"Fisher Separation is a key concept in investment decisions.","translation":"फिशर विभक्ती (Fisher Separation) गुंतवणूक निर्णयांमध्ये एक महत्त्वाची संकल्पना आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"A forward contract is an agreement to buy or sell an asset at a future date.","translation":"फॉरवर्ड करार हा भविष्यात मालमत्ता खरेदी किंवा विक्री करण्याचा करार आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Hedging strategies are used to reduce risk.","translation":"जोखीम कमी करण्यासाठी हेजिंग धोरणे वापरली जातात.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"Implied volatility is derived from option prices.","translation":"अंतर्निहित अस्थिरता (Implied Volatility) पर्याय किमतीतून काढली जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"The internal rate of return is a key metric for investment analysis.","translation":"अंतर्गत परतावा दर (Internal Rate of Return) गुंतवणूक विश्लेषणासाठी एक महत्त्वाचे मापदंड आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"No investor can earn excess returns developing trading rules based on historical price or return information.","translation":"इतिहासातील किंमत किंवा परताव्याच्या माहितीवर आधारित ट्रेडिंग नियम विकसित करून कोणताही गुंतवणूकदार अतिरिक्त परतावा मिळवू शकत नाही.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"In other words, the information in past prices or returns is not useful or relevant in achieving excess returns.","translation":"दुसऱ्या शब्दांत, मागील किमती किंवा परताव्याची माहिती अतिरिक्त परतावा मिळवण्यासाठी उपयुक्त किंवा संबंधित नाही.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"No investor can earn excess returns from trading rules based on any publicly available information.","translation":"कोणताही गुंतवणूकदार सार्वजनिकरित्या उपलब्ध असलेल्या माहितीवर आधारित ट्रेडिंग नियमांमधून अतिरिक्त परतावा मिळवू शकत नाही.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Examples of publicly available information are annual reports of companies, investment advisory data such as ”Heard on the Street” in the Wall Street Journal, or ticker tape information.","translation":"सार्वजनिकरित्या उपलब्ध असलेल्या माहितीची उदाहरणे म्हणजे कंपन्यांचे वार्षिक अहवाल, 'वॉल स्ट्रीट जर्नल'मधील 'हर्ड ऑन द स्ट्रीट' सारखे गुंतवणूक सल्लागार डेटा किंवा टिकर टेप माहिती.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"No investor can earn excess returns using any information, whether publicly available or not.","translation":"गुंतवणूकदार कोणतीही माहिती वापरून अतिरिक्त परतावा मिळवू शकत नाही, मग ती सार्वजनिकरित्या उपलब्ध असो वा नसो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Once we start thinking about this definition, however, we note that it is still well short of being rigorous.","translation":"तथापि, या व्याख्येचा विचार करण्यास सुरुवात करताच, आपण लक्षात घेतो की ती अजूनही कठोर होण्यापासून खूप दूर आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"What do we mean by ”risk” and by return being ”proportional to risk”?","translation":"‘जोखीम’ म्हणजे काय आणि परतावा ‘जोखीमच्या प्रमाणात’ असणे म्हणजे काय?","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"And if indeed prices (in some sense) reflect all available information why are banks and other financial institutions paying analysts to find information, and traders to ’look for arbitrage’ in the market?","translation":"आणि जर किमती (एका अर्थाने) सर्व उपलब्ध माहिती दर्शवतात, तर बँका आणि इतर वित्तीय संस्था माहिती शोधण्यासाठी विश्लेषकांना आणि बाजारात ‘आर्बिट्रेज’ शोधण्यासाठी व्यापाऱ्यांना पैसे का देत आहेत?","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"In this note we will analyze the problem of defining market efficiency as follows:","translation":"या नोटमध्ये, आम्ही खालीलप्रमाणे बाजारातील कार्यक्षमतेची व्याख्या करण्याच्या समस्येचे विश्लेषण करू:","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"First, we consider the problem of defining excess return.","translation":"सर्वप्रथम, आपण अतिरिक्त परताव्याची व्याख्या करण्याची समस्या विचारात घेऊ.","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"The only ’model free’ definition of this concept would be an arbitrage opportunity.","translation":"या संकल्पनेची एकमेव ‘मॉडेल फ्री’ व्याख्या म्हणजे आर्बिट्रेजची संधी.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"If we are unable to find arbitrage opportunities can we then ever reject the hypothesis of ’market efficiency’?","translation":"जर आपल्याला आर्बिट्रेजच्या संधी शोधण्यात अपयश आले, तर आपण ‘बाजारातील कार्यक्षमते’ची परिकल्पना कधीही नाकारू शकतो का?","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"Second, we consider some statistical properties of prices which are often thought of as being consequences of EMH.","translation":"दुसरे, आपण किमतींच्या काही सांख्यिकीय गुणधर्मांचा विचार करतो, जे अनेकदा EMH चे परिणाम मानले जातात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"We try to give some rigorous definitions of these properties and (briefly) discuss if they are in any way necessarily linked to market efficiency.","translation":"आम्ही या गुणधर्मांच्या काही कठोर व्याख्या देण्याचा प्रयत्न करतो आणि (थोडक्यात) चर्चा करतो की ते बाजारातील कार्यक्षमतेशी कोणत्याही प्रकारे आवश्यकपणे जोडलेले आहेत की नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"Third, we look at anomalies and a very interesting challenge to market efficiency which attempts to show that stock prices are ’too volatile’ in the sense that they vary much more than accounted for by changes in economic fundamentals.","translation":"तिसरे, आपण विसंगती आणि बाजारातील कार्यक्षमतेसाठी एक अतिशय मनोरंजक आव्हान पाहतो, जे हे दर्शविण्याचा प्रयत्न करते की स्टॉकच्या किमती ‘अति अस्थिर’ आहेत, म्हणजेच त्या आर्थिक मूलभूत बदलांमुळे जेवढ्या दर्शविल्या जातात त्यापेक्षा खूप जास्त बदलतात.","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"Finally we mention some attempts to make the definition of market efficiency completely rigorous in a general equilibrium context.","translation":"शेवटी, आम्ही बाजारातील कार्यक्षमतेची व्याख्या सामान्य संतुलनाच्या संदर्भात पूर्णपणे कठोर बनवण्याचा काही प्रयत्न नमूद करतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"First, we try to make ”excess returns” a little more precise:","translation":"प्रथम, आम्ही ‘अतिरिक्त परतावा’ अधिक अचूक करण्याचा प्रयत्न करतो:","target_lang":"mr","domain":"technical","complexity":"simple"}
{"en":"As a first attempt we could say that for any security P it must be the case that E[R t+1 |I t ] = 1 +r t","translation":"पहिला प्रयत्न म्हणून, आपण असे म्हणू शकतो की कोणत्याही सुरक्षा P साठी, हे असणे आवश्यक आहे की E[R t+1 |I t ] = 1 +r t","target_lang":"mr","domain":"technical","complexity":"complex"}
{"en":"Assets with high risk (as measured e.g. through theirβ’s) should (and do!) earn more than the riskless rate.","translation":"उच्च जोखीम असलेली मालमत्ता (उदाहरणार्थ, त्यांच्या β द्वारे मोजली जाते) जोखीम-मुक्त दरापेक्षा जास्त (आणि करतात!) कमावतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
{"en":"So we restate (12.1) as E[R t+1 |I t ] = 1 +r P t","translation":"म्हणून, आम्ही (12.1) E[R t+1 |I t ] = 1 +r P t असे पुन्हा मांडतो.","target_lang":"mr","domain":"technical","complexity":"simple"}