SlideShare una empresa de Scribd logo
1 de 17
Hedging Strategies Using Futures Chapter 3
Long & Short Hedges ,[object Object],[object Object]
Arguments in Favor of Hedging ,[object Object]
Arguments against Hedging ,[object Object],[object Object],[object Object]
Convergence of Futures to Spot (Hedge initiated at time  t 1  and closed out at time  t 2 ) Time Spot  Price Futures Price t 1 t 2
Basis Risk ,[object Object],[object Object]
Long Hedge  ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Short Hedge ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Choice of Contract ,[object Object],[object Object]
Optimal Hedge Ratio ,[object Object],[object Object],[object Object],[object Object],[object Object]
Hedging Using Index Futures (Page 63) ,[object Object],[object Object]
Reasons for Hedging an Equity Portfolio ,[object Object],[object Object]
Example ,[object Object],[object Object],[object Object],[object Object]
Changing Beta ,[object Object],[object Object]
Hedging Price of an Individual Stock ,[object Object],[object Object],[object Object]
Why Hedge Equity Returns ,[object Object],[object Object]
Rolling The Hedge Forward  (page 67-68) ,[object Object],[object Object]

Más contenido relacionado

La actualidad más candente

7. Derivatives Part1 Pdf
7. Derivatives Part1 Pdf7. Derivatives Part1 Pdf
7. Derivatives Part1 Pdfdavidharper
 
Rkm chapter 06 hedging strategies using futures
Rkm chapter 06   hedging strategies using futuresRkm chapter 06   hedging strategies using futures
Rkm chapter 06 hedging strategies using futuresThrinath Mittoor
 
Unit principles of option pricing call
Unit  principles of option pricing callUnit  principles of option pricing call
Unit principles of option pricing callSudarshan Kadariya
 
Option Pricing Theory and Option Pricing Theory and Applications
Option Pricing Theory and Option Pricing Theory and Applications Option Pricing Theory and Option Pricing Theory and Applications
Option Pricing Theory and Option Pricing Theory and Applications izaacaura2
 
Hedging & arbitrage
Hedging & arbitrageHedging & arbitrage
Hedging & arbitrageVikram Singh
 
Chapter8 International Finance Management
Chapter8 International Finance ManagementChapter8 International Finance Management
Chapter8 International Finance ManagementPiyush Gaur
 
11. option pricing
11. option pricing11. option pricing
11. option pricingSanjiv Jha
 

La actualidad más candente (18)

Chapter 1
Chapter 1Chapter 1
Chapter 1
 
7. Derivatives Part1 Pdf
7. Derivatives Part1 Pdf7. Derivatives Part1 Pdf
7. Derivatives Part1 Pdf
 
Chapter 5 pricing
Chapter 5 pricingChapter 5 pricing
Chapter 5 pricing
 
Chap 3
Chap 3Chap 3
Chap 3
 
put call parity
put call parity put call parity
put call parity
 
Rkm chapter 06 hedging strategies using futures
Rkm chapter 06   hedging strategies using futuresRkm chapter 06   hedging strategies using futures
Rkm chapter 06 hedging strategies using futures
 
Unit principles of option pricing call
Unit  principles of option pricing callUnit  principles of option pricing call
Unit principles of option pricing call
 
002 Hedging With Futures
002 Hedging With Futures002 Hedging With Futures
002 Hedging With Futures
 
Option pricing
Option pricingOption pricing
Option pricing
 
Option Pricing Theory and Option Pricing Theory and Applications
Option Pricing Theory and Option Pricing Theory and Applications Option Pricing Theory and Option Pricing Theory and Applications
Option Pricing Theory and Option Pricing Theory and Applications
 
Chap 15
Chap 15Chap 15
Chap 15
 
Chap 18
Chap 18Chap 18
Chap 18
 
Hedging & arbitrage
Hedging & arbitrageHedging & arbitrage
Hedging & arbitrage
 
Chapter8 International Finance Management
Chapter8 International Finance ManagementChapter8 International Finance Management
Chapter8 International Finance Management
 
Swap
SwapSwap
Swap
 
11. option pricing
11. option pricing11. option pricing
11. option pricing
 
Option_Greeks
Option_GreeksOption_Greeks
Option_Greeks
 
HEDGING
HEDGINGHEDGING
HEDGING
 

Destacado

NY Sugar Week presentation (May 2013)
NY Sugar Week presentation (May 2013)NY Sugar Week presentation (May 2013)
NY Sugar Week presentation (May 2013)TOFPIK
 
Managing risks with derivative securities, CH 23 Financial Markets & Institut...
Managing risks with derivative securities, CH 23 Financial Markets & Institut...Managing risks with derivative securities, CH 23 Financial Markets & Institut...
Managing risks with derivative securities, CH 23 Financial Markets & Institut...Fawad Hussain
 
Managing transaction exposure and economic exposure
Managing transaction exposure and economic exposureManaging transaction exposure and economic exposure
Managing transaction exposure and economic exposureMaica Batiancela
 

Destacado (6)

Hedging product
Hedging productHedging product
Hedging product
 
Binary Options Hedging
Binary Options HedgingBinary Options Hedging
Binary Options Hedging
 
NY Sugar Week presentation (May 2013)
NY Sugar Week presentation (May 2013)NY Sugar Week presentation (May 2013)
NY Sugar Week presentation (May 2013)
 
Managing risks with derivative securities, CH 23 Financial Markets & Institut...
Managing risks with derivative securities, CH 23 Financial Markets & Institut...Managing risks with derivative securities, CH 23 Financial Markets & Institut...
Managing risks with derivative securities, CH 23 Financial Markets & Institut...
 
Managing transaction exposure and economic exposure
Managing transaction exposure and economic exposureManaging transaction exposure and economic exposure
Managing transaction exposure and economic exposure
 
Competency
CompetencyCompetency
Competency
 

Similar a Chap 3

Derivatives lecture3 & 4- futures
Derivatives lecture3 & 4- futuresDerivatives lecture3 & 4- futures
Derivatives lecture3 & 4- futuresiipmff2
 
Ch03 hullfundamentals7thed
Ch03 hullfundamentals7thedCh03 hullfundamentals7thed
Ch03 hullfundamentals7thedDinh Châu
 
Hedging, Speculation and Arbitrage using Futures.ppt
Hedging, Speculation and Arbitrage using Futures.pptHedging, Speculation and Arbitrage using Futures.ppt
Hedging, Speculation and Arbitrage using Futures.pptShoaib Mohammed
 
Derivatives project
Derivatives projectDerivatives project
Derivatives projectDharmik
 
Derivatives paper trading ppt information
Derivatives paper trading ppt informationDerivatives paper trading ppt information
Derivatives paper trading ppt informationupttiankur1
 
Derivatives-Overview.ppt
Derivatives-Overview.pptDerivatives-Overview.ppt
Derivatives-Overview.pptRohanJindal14
 
Pricing forward & future contracts
Pricing forward & future contractsPricing forward & future contracts
Pricing forward & future contractsAmeya Ranadive
 
Derivatives Primer
Derivatives PrimerDerivatives Primer
Derivatives Primerwilbut31
 
PROFIT YOUR TRADE EDUCATION Series - By Kutumba Rao - Feb 7th 2021.pptx
PROFIT YOUR TRADE EDUCATION Series - By Kutumba Rao - Feb 7th 2021.pptxPROFIT YOUR TRADE EDUCATION Series - By Kutumba Rao - Feb 7th 2021.pptx
PROFIT YOUR TRADE EDUCATION Series - By Kutumba Rao - Feb 7th 2021.pptxSAROORNAGARCMCORE
 
Investment Banking
Investment BankingInvestment Banking
Investment BankingYasir Sheikh
 
VBA & ADO MS Access – Part 2
VBA & ADO  MS Access – Part 2VBA & ADO  MS Access – Part 2
VBA & ADO MS Access – Part 2Khader Shaik
 
Introduction to Derivatives Market
Introduction to  Derivatives MarketIntroduction to  Derivatives Market
Introduction to Derivatives MarketKhader Shaik
 
Ch03HullFundamentals9thEd.ppt human resource
Ch03HullFundamentals9thEd.ppt human resourceCh03HullFundamentals9thEd.ppt human resource
Ch03HullFundamentals9thEd.ppt human resourceNazmulIslam726003
 
cash future forward market
cash future forward marketcash future forward market
cash future forward marketTanvi Pagare
 

Similar a Chap 3 (20)

Derivatives lecture3 & 4- futures
Derivatives lecture3 & 4- futuresDerivatives lecture3 & 4- futures
Derivatives lecture3 & 4- futures
 
Ch03 hullfundamentals7thed
Ch03 hullfundamentals7thedCh03 hullfundamentals7thed
Ch03 hullfundamentals7thed
 
Hedging, Speculation and Arbitrage using Futures.ppt
Hedging, Speculation and Arbitrage using Futures.pptHedging, Speculation and Arbitrage using Futures.ppt
Hedging, Speculation and Arbitrage using Futures.ppt
 
hedging strategy
hedging strategyhedging strategy
hedging strategy
 
Derivatives project
Derivatives projectDerivatives project
Derivatives project
 
Derivatives paper trading ppt information
Derivatives paper trading ppt informationDerivatives paper trading ppt information
Derivatives paper trading ppt information
 
Derivatives-Overview.ppt
Derivatives-Overview.pptDerivatives-Overview.ppt
Derivatives-Overview.ppt
 
Pricing forward & future contracts
Pricing forward & future contractsPricing forward & future contracts
Pricing forward & future contracts
 
Derivatives
DerivativesDerivatives
Derivatives
 
Derivatives Primer
Derivatives PrimerDerivatives Primer
Derivatives Primer
 
PROFIT YOUR TRADE EDUCATION Series - By Kutumba Rao - Feb 7th 2021.pptx
PROFIT YOUR TRADE EDUCATION Series - By Kutumba Rao - Feb 7th 2021.pptxPROFIT YOUR TRADE EDUCATION Series - By Kutumba Rao - Feb 7th 2021.pptx
PROFIT YOUR TRADE EDUCATION Series - By Kutumba Rao - Feb 7th 2021.pptx
 
Investment Banking
Investment BankingInvestment Banking
Investment Banking
 
VBA & ADO MS Access – Part 2
VBA & ADO  MS Access – Part 2VBA & ADO  MS Access – Part 2
VBA & ADO MS Access – Part 2
 
Introduction to Derivatives Market
Introduction to  Derivatives MarketIntroduction to  Derivatives Market
Introduction to Derivatives Market
 
Derivatives
DerivativesDerivatives
Derivatives
 
02 lecture21
02 lecture2102 lecture21
02 lecture21
 
Ch03HullFundamentals9thEd.ppt human resource
Ch03HullFundamentals9thEd.ppt human resourceCh03HullFundamentals9thEd.ppt human resource
Ch03HullFundamentals9thEd.ppt human resource
 
003 Futures And Forwards
003 Futures And Forwards003 Futures And Forwards
003 Futures And Forwards
 
Guide to Financial Derivatives
Guide to Financial DerivativesGuide to Financial Derivatives
Guide to Financial Derivatives
 
cash future forward market
cash future forward marketcash future forward market
cash future forward market
 

Más de uichong

F B E559f15 Trading Strategies
F B E559f15 Trading  StrategiesF B E559f15 Trading  Strategies
F B E559f15 Trading Strategiesuichong
 
F B E559f2 Binomial Pricing
F B E559f2 Binomial  PricingF B E559f2 Binomial  Pricing
F B E559f2 Binomial Pricinguichong
 
Derivatives Binomial Option Pricing Model Examples
Derivatives  Binomial  Option  Pricing  Model  ExamplesDerivatives  Binomial  Option  Pricing  Model  Examples
Derivatives Binomial Option Pricing Model Examplesuichong
 
F B E559f3 B S Formula
F B E559f3 B S  FormulaF B E559f3 B S  Formula
F B E559f3 B S Formulauichong
 

Más de uichong (20)

Chap 9
Chap 9Chap 9
Chap 9
 
Chap 7
Chap 7Chap 7
Chap 7
 
Chap 5
Chap 5Chap 5
Chap 5
 
Chap 2
Chap 2Chap 2
Chap 2
 
Chap 1
Chap 1Chap 1
Chap 1
 
Chap 4
Chap 4Chap 4
Chap 4
 
Chap 6
Chap 6Chap 6
Chap 6
 
Chap 8
Chap 8Chap 8
Chap 8
 
F B E559f15 Trading Strategies
F B E559f15 Trading  StrategiesF B E559f15 Trading  Strategies
F B E559f15 Trading Strategies
 
Chap 12
Chap 12Chap 12
Chap 12
 
Chap 30
Chap 30Chap 30
Chap 30
 
Chap 32
Chap 32Chap 32
Chap 32
 
F B E559f2 Binomial Pricing
F B E559f2 Binomial  PricingF B E559f2 Binomial  Pricing
F B E559f2 Binomial Pricing
 
Derivatives Binomial Option Pricing Model Examples
Derivatives  Binomial  Option  Pricing  Model  ExamplesDerivatives  Binomial  Option  Pricing  Model  Examples
Derivatives Binomial Option Pricing Model Examples
 
F B E559f3 B S Formula
F B E559f3 B S  FormulaF B E559f3 B S  Formula
F B E559f3 B S Formula
 
Chap 10
Chap 10Chap 10
Chap 10
 
Chap 29
Chap 29Chap 29
Chap 29
 
Chap 28
Chap 28Chap 28
Chap 28
 
Chap 26
Chap 26Chap 26
Chap 26
 
Chap 23
Chap 23Chap 23
Chap 23
 

Último

MAHA Global and IPR: Do Actions Speak Louder Than Words?
MAHA Global and IPR: Do Actions Speak Louder Than Words?MAHA Global and IPR: Do Actions Speak Louder Than Words?
MAHA Global and IPR: Do Actions Speak Louder Than Words?Olivia Kresic
 
(Best) ENJOY Call Girls in Faridabad Ex | 8377087607
(Best) ENJOY Call Girls in Faridabad Ex | 8377087607(Best) ENJOY Call Girls in Faridabad Ex | 8377087607
(Best) ENJOY Call Girls in Faridabad Ex | 8377087607dollysharma2066
 
Pitch Deck Teardown: Geodesic.Life's $500k Pre-seed deck
Pitch Deck Teardown: Geodesic.Life's $500k Pre-seed deckPitch Deck Teardown: Geodesic.Life's $500k Pre-seed deck
Pitch Deck Teardown: Geodesic.Life's $500k Pre-seed deckHajeJanKamps
 
Future Of Sample Report 2024 | Redacted Version
Future Of Sample Report 2024 | Redacted VersionFuture Of Sample Report 2024 | Redacted Version
Future Of Sample Report 2024 | Redacted VersionMintel Group
 
Intro to BCG's Carbon Emissions Benchmark_vF.pdf
Intro to BCG's Carbon Emissions Benchmark_vF.pdfIntro to BCG's Carbon Emissions Benchmark_vF.pdf
Intro to BCG's Carbon Emissions Benchmark_vF.pdfpollardmorgan
 
NewBase 19 April 2024 Energy News issue - 1717 by Khaled Al Awadi.pdf
NewBase  19 April  2024  Energy News issue - 1717 by Khaled Al Awadi.pdfNewBase  19 April  2024  Energy News issue - 1717 by Khaled Al Awadi.pdf
NewBase 19 April 2024 Energy News issue - 1717 by Khaled Al Awadi.pdfKhaled Al Awadi
 
8447779800, Low rate Call girls in Tughlakabad Delhi NCR
8447779800, Low rate Call girls in Tughlakabad Delhi NCR8447779800, Low rate Call girls in Tughlakabad Delhi NCR
8447779800, Low rate Call girls in Tughlakabad Delhi NCRashishs7044
 
Marketplace and Quality Assurance Presentation - Vincent Chirchir
Marketplace and Quality Assurance Presentation - Vincent ChirchirMarketplace and Quality Assurance Presentation - Vincent Chirchir
Marketplace and Quality Assurance Presentation - Vincent Chirchirictsugar
 
Organizational Structure Running A Successful Business
Organizational Structure Running A Successful BusinessOrganizational Structure Running A Successful Business
Organizational Structure Running A Successful BusinessSeta Wicaksana
 
8447779800, Low rate Call girls in Uttam Nagar Delhi NCR
8447779800, Low rate Call girls in Uttam Nagar Delhi NCR8447779800, Low rate Call girls in Uttam Nagar Delhi NCR
8447779800, Low rate Call girls in Uttam Nagar Delhi NCRashishs7044
 
Youth Involvement in an Innovative Coconut Value Chain by Mwalimu Menza
Youth Involvement in an Innovative Coconut Value Chain by Mwalimu MenzaYouth Involvement in an Innovative Coconut Value Chain by Mwalimu Menza
Youth Involvement in an Innovative Coconut Value Chain by Mwalimu Menzaictsugar
 
2024 Numerator Consumer Study of Cannabis Usage
2024 Numerator Consumer Study of Cannabis Usage2024 Numerator Consumer Study of Cannabis Usage
2024 Numerator Consumer Study of Cannabis UsageNeil Kimberley
 
8447779800, Low rate Call girls in Saket Delhi NCR
8447779800, Low rate Call girls in Saket Delhi NCR8447779800, Low rate Call girls in Saket Delhi NCR
8447779800, Low rate Call girls in Saket Delhi NCRashishs7044
 
Kenya’s Coconut Value Chain by Gatsby Africa
Kenya’s Coconut Value Chain by Gatsby AfricaKenya’s Coconut Value Chain by Gatsby Africa
Kenya’s Coconut Value Chain by Gatsby Africaictsugar
 
Ms Motilal Padampat Sugar Mills vs. State of Uttar Pradesh & Ors. - A Milesto...
Ms Motilal Padampat Sugar Mills vs. State of Uttar Pradesh & Ors. - A Milesto...Ms Motilal Padampat Sugar Mills vs. State of Uttar Pradesh & Ors. - A Milesto...
Ms Motilal Padampat Sugar Mills vs. State of Uttar Pradesh & Ors. - A Milesto...ShrutiBose4
 
Annual General Meeting Presentation Slides
Annual General Meeting Presentation SlidesAnnual General Meeting Presentation Slides
Annual General Meeting Presentation SlidesKeppelCorporation
 
FULL ENJOY Call girls in Paharganj Delhi | 8377087607
FULL ENJOY Call girls in Paharganj Delhi | 8377087607FULL ENJOY Call girls in Paharganj Delhi | 8377087607
FULL ENJOY Call girls in Paharganj Delhi | 8377087607dollysharma2066
 
Digital Transformation in the PLM domain - distrib.pdf
Digital Transformation in the PLM domain - distrib.pdfDigital Transformation in the PLM domain - distrib.pdf
Digital Transformation in the PLM domain - distrib.pdfJos Voskuil
 
8447779800, Low rate Call girls in New Ashok Nagar Delhi NCR
8447779800, Low rate Call girls in New Ashok Nagar Delhi NCR8447779800, Low rate Call girls in New Ashok Nagar Delhi NCR
8447779800, Low rate Call girls in New Ashok Nagar Delhi NCRashishs7044
 
Investment in The Coconut Industry by Nancy Cheruiyot
Investment in The Coconut Industry by Nancy CheruiyotInvestment in The Coconut Industry by Nancy Cheruiyot
Investment in The Coconut Industry by Nancy Cheruiyotictsugar
 

Último (20)

MAHA Global and IPR: Do Actions Speak Louder Than Words?
MAHA Global and IPR: Do Actions Speak Louder Than Words?MAHA Global and IPR: Do Actions Speak Louder Than Words?
MAHA Global and IPR: Do Actions Speak Louder Than Words?
 
(Best) ENJOY Call Girls in Faridabad Ex | 8377087607
(Best) ENJOY Call Girls in Faridabad Ex | 8377087607(Best) ENJOY Call Girls in Faridabad Ex | 8377087607
(Best) ENJOY Call Girls in Faridabad Ex | 8377087607
 
Pitch Deck Teardown: Geodesic.Life's $500k Pre-seed deck
Pitch Deck Teardown: Geodesic.Life's $500k Pre-seed deckPitch Deck Teardown: Geodesic.Life's $500k Pre-seed deck
Pitch Deck Teardown: Geodesic.Life's $500k Pre-seed deck
 
Future Of Sample Report 2024 | Redacted Version
Future Of Sample Report 2024 | Redacted VersionFuture Of Sample Report 2024 | Redacted Version
Future Of Sample Report 2024 | Redacted Version
 
Intro to BCG's Carbon Emissions Benchmark_vF.pdf
Intro to BCG's Carbon Emissions Benchmark_vF.pdfIntro to BCG's Carbon Emissions Benchmark_vF.pdf
Intro to BCG's Carbon Emissions Benchmark_vF.pdf
 
NewBase 19 April 2024 Energy News issue - 1717 by Khaled Al Awadi.pdf
NewBase  19 April  2024  Energy News issue - 1717 by Khaled Al Awadi.pdfNewBase  19 April  2024  Energy News issue - 1717 by Khaled Al Awadi.pdf
NewBase 19 April 2024 Energy News issue - 1717 by Khaled Al Awadi.pdf
 
8447779800, Low rate Call girls in Tughlakabad Delhi NCR
8447779800, Low rate Call girls in Tughlakabad Delhi NCR8447779800, Low rate Call girls in Tughlakabad Delhi NCR
8447779800, Low rate Call girls in Tughlakabad Delhi NCR
 
Marketplace and Quality Assurance Presentation - Vincent Chirchir
Marketplace and Quality Assurance Presentation - Vincent ChirchirMarketplace and Quality Assurance Presentation - Vincent Chirchir
Marketplace and Quality Assurance Presentation - Vincent Chirchir
 
Organizational Structure Running A Successful Business
Organizational Structure Running A Successful BusinessOrganizational Structure Running A Successful Business
Organizational Structure Running A Successful Business
 
8447779800, Low rate Call girls in Uttam Nagar Delhi NCR
8447779800, Low rate Call girls in Uttam Nagar Delhi NCR8447779800, Low rate Call girls in Uttam Nagar Delhi NCR
8447779800, Low rate Call girls in Uttam Nagar Delhi NCR
 
Youth Involvement in an Innovative Coconut Value Chain by Mwalimu Menza
Youth Involvement in an Innovative Coconut Value Chain by Mwalimu MenzaYouth Involvement in an Innovative Coconut Value Chain by Mwalimu Menza
Youth Involvement in an Innovative Coconut Value Chain by Mwalimu Menza
 
2024 Numerator Consumer Study of Cannabis Usage
2024 Numerator Consumer Study of Cannabis Usage2024 Numerator Consumer Study of Cannabis Usage
2024 Numerator Consumer Study of Cannabis Usage
 
8447779800, Low rate Call girls in Saket Delhi NCR
8447779800, Low rate Call girls in Saket Delhi NCR8447779800, Low rate Call girls in Saket Delhi NCR
8447779800, Low rate Call girls in Saket Delhi NCR
 
Kenya’s Coconut Value Chain by Gatsby Africa
Kenya’s Coconut Value Chain by Gatsby AfricaKenya’s Coconut Value Chain by Gatsby Africa
Kenya’s Coconut Value Chain by Gatsby Africa
 
Ms Motilal Padampat Sugar Mills vs. State of Uttar Pradesh & Ors. - A Milesto...
Ms Motilal Padampat Sugar Mills vs. State of Uttar Pradesh & Ors. - A Milesto...Ms Motilal Padampat Sugar Mills vs. State of Uttar Pradesh & Ors. - A Milesto...
Ms Motilal Padampat Sugar Mills vs. State of Uttar Pradesh & Ors. - A Milesto...
 
Annual General Meeting Presentation Slides
Annual General Meeting Presentation SlidesAnnual General Meeting Presentation Slides
Annual General Meeting Presentation Slides
 
FULL ENJOY Call girls in Paharganj Delhi | 8377087607
FULL ENJOY Call girls in Paharganj Delhi | 8377087607FULL ENJOY Call girls in Paharganj Delhi | 8377087607
FULL ENJOY Call girls in Paharganj Delhi | 8377087607
 
Digital Transformation in the PLM domain - distrib.pdf
Digital Transformation in the PLM domain - distrib.pdfDigital Transformation in the PLM domain - distrib.pdf
Digital Transformation in the PLM domain - distrib.pdf
 
8447779800, Low rate Call girls in New Ashok Nagar Delhi NCR
8447779800, Low rate Call girls in New Ashok Nagar Delhi NCR8447779800, Low rate Call girls in New Ashok Nagar Delhi NCR
8447779800, Low rate Call girls in New Ashok Nagar Delhi NCR
 
Investment in The Coconut Industry by Nancy Cheruiyot
Investment in The Coconut Industry by Nancy CheruiyotInvestment in The Coconut Industry by Nancy Cheruiyot
Investment in The Coconut Industry by Nancy Cheruiyot
 

Chap 3