Question

3.1 (10 points) Describe the main assumptions of the Arbitrage Pricing Theory (APT) and contrast them with those of CAPM. Which set of assumptions is more restrictive? Define and the following concepts and explain the role played by them in the APT: (a) Well-diversified portfolio; (b) Risk-free arbitrage opportunity. 3.2 (10 points) Discuss how a simple one factor APT can be generalized to a multifactor version of the APT. What are the advantages and shortcomings of the multifactor APT? Discuss the Fama-French Three Factor Model.

Answer 1

Ans- The APT model is more detailed model as compared to CAPM model because it takes more risk factors. There are many extensions to this model which is known as multi factor factor models. These model takes more risk factors to make the model dynamic and more comprehensive

Ans: A scumptions of 1 1 7 Assumptions of Arbitrage Pruung Model! Factor model describes asset retvine arbituage Oppontunities exut among u No a dewersified portfolios V investors Conform eliminate Pouet assets, so portfolio to are many diversified well diversified specific rish porfolie CONTRAST OF APNT WITH CAPM! - APT theory does APT theory does not tell the exact no. of risk follor nuolved while CAPM one only takes u rusk factor le beto. APT theory assumes linear relationship between risk faction whereas CAPM assumes linear relationship between asset classes. - The Cill au assumption is mone restrictive as it allows that there is no arbitrage opportunities available it is available which could by coptuned by High frequency trading) or algo trading models. investor Somelime there u no available that it u WELL DIVERSIFIED PORTFOLIWO Diversification means putting the money in different suet classes to reduce the risk of porfolio Generally diversification happens when we het Tasset classes having negative correlation on (2ew) correlation,

Let us undi h MRA has puta more chance But if he put o & 50000 in Us understand by an example! has put & 100,000 in onur one There ar stock. hances of losses of the market crashed you in other stour, the chances of losses con reduced because there is O correlation government semities are musk free, so there cewnities and 550.000 con be o correlation, SISK thee Habitrage Opportunity. It is an opportunity in which investor earns positive cash flowe without no investment. Let us understand by an examples if an investor trai 3 portfolio factor sensitivity Portfolio B CE Return 7.5.1. 0.5 us 0.4 1 8- 0 .45 C In this case and put A and B do opposite 11 investor sells portfolo for f 400,000 money into equally proportionate portfolio he can get a return and but the he could get more selon Cash flow factor senetivily Return - loool 0.45 1,07,950 750 0:45 108,000 A&B 1,00,000 u he sells A&B equally on take money from of market @ 7251 re (50% off and 501-877.6)

in pow.) mooncy LUTH, no with o take money @ 735) and post money, C and earns 84 he can get 6.75% with T con be generalized into following models: videconomic factor model -> Movieronomie Stolestial factor model Fundo mental model. > ADVANTAGE It all Stumel mone IDVANTAGES OF ART MULTIFACTOR one uk as compared to CAPM wherein there u only one wk facton' It u more acurate over longer period of time ? DISADVANTAGES: > > The factor A mavoeronomie model are backed by statutual evidence which u not in care of fundomental On the other hand macroeconomic model dou not have expronatory power as compared to fundomental as it assumes more nuk attributes. FAMA - FRENCH MODEL: in 1993 rresearchers Eugene Faro and Kenneth French addressed the problems of CAPM and comes ith three factor model! They add a more u failor into CAPPM to make it more detailed and Undoutondoble WIH

SMB is decouse in small cop.. - HML (High RMRF Rm-Rf a same in CAPM model SMB - (Small-Big Market capitalisations the average of 3 small cop portfolio 3 large . Cap pontol The equation has small -big, 2 in small cop seunities there are more eusk as compared to large cop HML (High Minus low) It takes two average high book to market pornolo minus two average low book to market portfolio High book to market meens value bras What is in small cop on medum Cop stocks and low Goook to market meent growth bias which is more profound in large cop stocks. Equation > e-Ret B (mkt) RMRE & Bsire (SMB) & Brature (AML) Extension of FANA - FRENCH MODEL: Pastor and starnbaugh extended this model by taking into one more factor e liquidity so equation si 8 = R + Bence RNRF Tore SMB & Bow HML YB 4Q