Equity Stock Market: Concepts, Instruments, Derivatives and Risk
Prof. P C Narayan
Week 3
Equity Stock Markets: Concepts, Instruments, Risks and Derivatives
Week 3 – Summary
Equity Risks: An Overview
Equity stock markets around the world are perhaps the most vibrant as well as the biggest and the
most visible among the financial markets around the world because of the volume and value of
transactions traded in these markets by a broad spectrum of investors. Assessment of risk in
investing in equity markets have also evolved and matured over the last few decades grounded in
well-established and well-understood theories.
Equity markets, worldwide, are governed by the risk-return relationships, i.e. to generate a higher
return one needs to take a higher level of risk.
In order to measure risks associated with investment in equity stocks, several concepts and theories
have been postulated and practiced in the equity stock markets over the last few decades, based on
widely accepted statistical concepts such as ‘variance’, ‘beta’, ‘value-at-risk’, etc.
© All Rights Reserved. This document has been authored by Prof P C Narayan and is permitted for use only within the course "Equity Stock Market: Concepts,
Instruments, Derivatives and Risk" delivered in the online course format by IIM Bangalore. No part of this document, including any logo, data, illustrations, pictures,
scripts, may be reproduced, or stored in a retrieval system or transmitted in any form or by any means – electronic, mechanical, photocopying, recording or otherwise –
without the prior permission of the author.
, Equity Stock Market: Concepts, Instruments, Derivatives and Risk
Prof. P C Narayan
Week 3
An Introduction to Portfolio Theory (Coin Toss Example)
Risk and returns are very closely correlated and the challenge of investing in equity stocks is not to
take either of the extreme positions, i.e. very high-risk or very low-risk, but to identify a combination
of equity stocks that would provide the best return at the lowest level of risk.
This has been well articulated in one of the most profound theories in finance called The Harry
Markowitz Portfolio Theory named after its founder Harry Markowitz.
Harry Markowitz Portfolio Theory is built around the basic statistical concept of Mean, Median,
Variance, and Standard Deviation.
A simple example of coin-toss using two coins, based on the basic statistical concepts: returns,
variance and standard deviation, lucidly illustrates the idea behind the Harry Markowitz Portfolio
Theory (refer table below).
Different combinations for gain-on-heads and loss-on-tails generate different scores for expected
returns and standard deviation. Hence, an individual can easily choose from the possible outcomes,
based on his/her risk appetite.
If one expects a high expected return with
the lowest possible risk (lowest standard
deviation), the obvious choice would be
option 4 (refer the table on the right). On the
© All Rights Reserved. This document has been authored by Prof P C Narayan and is permitted for use only within the course "Equity Stock Market: Concepts,
Instruments, Derivatives and Risk" delivered in the online course format by IIM Bangalore. No part of this document, including any logo, data, illustrations, pictures,
scripts, may be reproduced, or stored in a retrieval system or transmitted in any form or by any means – electronic, mechanical, photocopying, recording or otherwise –
without the prior permission of the author.
, Equity Stock Market: Concepts, Instruments, Derivatives and Risk
Prof. P C Narayan
Week 3
other hand, if one is ready to take the highest
possible risk, the obvious choice would be
option 5 (refer the table on the right).
That indeed is the intuition behind the Harry Markowitz Portfolio Theory. The need and ability to
diversify your investments in the equity stock market by investing in a select number of equity stocks
with different expected returns and standard deviation in such a way that your investment portfolio
gives the best-expected return at the lowest level of risk, i.e the lowest level of standard deviation.
An Introduction to Portfolio Theory (Equity Stock Example)
The Harry Markowitz Portfolio Theory has evolved around the basic statistical concepts such as
variance, covariance, and standard deviation. To fully understand portfolio theory and the
fascinating relationship between expected returns and volatility, we built a portfolio of two equity
stocks and then added a third stock to that portfolio.
Take the stocks of two companies, Company A and company B. Using ‘probability’ and ‘expected
return’ compute their weighted average return and standard deviation.
The returns and standard deviation for both the companies can be compared to understand their
differing risk-return relationship. Expectedly, the results would prove the axiom ‘Higher the risk
higher the expected return’.
Furthermore, suppose that both the stocks are part of an equity stock portfolio. Based on the
proportion of each of the two stocks in that portfolio and their expected returns, Harry Markowitz
Portfolio suggests the optimum combination or the optimum portfolio where the standard deviation
(risk) of the portfolio is lowest and return is the highest. To achieve that outcome a new variable -
coefficient of correlation- is added, which is the crux of the Harry Markowitz Portfolio Theory. It is a
measure of the strength and direction of the linear relationship between the two variables in this
case expected return of company A and the expected return of company B. A coefficient of
correlation of one says that both the variables move in an identical fashion.
© All Rights Reserved. This document has been authored by Prof P C Narayan and is permitted for use only within the course "Equity Stock Market: Concepts,
Instruments, Derivatives and Risk" delivered in the online course format by IIM Bangalore. No part of this document, including any logo, data, illustrations, pictures,
scripts, may be reproduced, or stored in a retrieval system or transmitted in any form or by any means – electronic, mechanical, photocopying, recording or otherwise –
without the prior permission of the author.
Prof. P C Narayan
Week 3
Equity Stock Markets: Concepts, Instruments, Risks and Derivatives
Week 3 – Summary
Equity Risks: An Overview
Equity stock markets around the world are perhaps the most vibrant as well as the biggest and the
most visible among the financial markets around the world because of the volume and value of
transactions traded in these markets by a broad spectrum of investors. Assessment of risk in
investing in equity markets have also evolved and matured over the last few decades grounded in
well-established and well-understood theories.
Equity markets, worldwide, are governed by the risk-return relationships, i.e. to generate a higher
return one needs to take a higher level of risk.
In order to measure risks associated with investment in equity stocks, several concepts and theories
have been postulated and practiced in the equity stock markets over the last few decades, based on
widely accepted statistical concepts such as ‘variance’, ‘beta’, ‘value-at-risk’, etc.
© All Rights Reserved. This document has been authored by Prof P C Narayan and is permitted for use only within the course "Equity Stock Market: Concepts,
Instruments, Derivatives and Risk" delivered in the online course format by IIM Bangalore. No part of this document, including any logo, data, illustrations, pictures,
scripts, may be reproduced, or stored in a retrieval system or transmitted in any form or by any means – electronic, mechanical, photocopying, recording or otherwise –
without the prior permission of the author.
, Equity Stock Market: Concepts, Instruments, Derivatives and Risk
Prof. P C Narayan
Week 3
An Introduction to Portfolio Theory (Coin Toss Example)
Risk and returns are very closely correlated and the challenge of investing in equity stocks is not to
take either of the extreme positions, i.e. very high-risk or very low-risk, but to identify a combination
of equity stocks that would provide the best return at the lowest level of risk.
This has been well articulated in one of the most profound theories in finance called The Harry
Markowitz Portfolio Theory named after its founder Harry Markowitz.
Harry Markowitz Portfolio Theory is built around the basic statistical concept of Mean, Median,
Variance, and Standard Deviation.
A simple example of coin-toss using two coins, based on the basic statistical concepts: returns,
variance and standard deviation, lucidly illustrates the idea behind the Harry Markowitz Portfolio
Theory (refer table below).
Different combinations for gain-on-heads and loss-on-tails generate different scores for expected
returns and standard deviation. Hence, an individual can easily choose from the possible outcomes,
based on his/her risk appetite.
If one expects a high expected return with
the lowest possible risk (lowest standard
deviation), the obvious choice would be
option 4 (refer the table on the right). On the
© All Rights Reserved. This document has been authored by Prof P C Narayan and is permitted for use only within the course "Equity Stock Market: Concepts,
Instruments, Derivatives and Risk" delivered in the online course format by IIM Bangalore. No part of this document, including any logo, data, illustrations, pictures,
scripts, may be reproduced, or stored in a retrieval system or transmitted in any form or by any means – electronic, mechanical, photocopying, recording or otherwise –
without the prior permission of the author.
, Equity Stock Market: Concepts, Instruments, Derivatives and Risk
Prof. P C Narayan
Week 3
other hand, if one is ready to take the highest
possible risk, the obvious choice would be
option 5 (refer the table on the right).
That indeed is the intuition behind the Harry Markowitz Portfolio Theory. The need and ability to
diversify your investments in the equity stock market by investing in a select number of equity stocks
with different expected returns and standard deviation in such a way that your investment portfolio
gives the best-expected return at the lowest level of risk, i.e the lowest level of standard deviation.
An Introduction to Portfolio Theory (Equity Stock Example)
The Harry Markowitz Portfolio Theory has evolved around the basic statistical concepts such as
variance, covariance, and standard deviation. To fully understand portfolio theory and the
fascinating relationship between expected returns and volatility, we built a portfolio of two equity
stocks and then added a third stock to that portfolio.
Take the stocks of two companies, Company A and company B. Using ‘probability’ and ‘expected
return’ compute their weighted average return and standard deviation.
The returns and standard deviation for both the companies can be compared to understand their
differing risk-return relationship. Expectedly, the results would prove the axiom ‘Higher the risk
higher the expected return’.
Furthermore, suppose that both the stocks are part of an equity stock portfolio. Based on the
proportion of each of the two stocks in that portfolio and their expected returns, Harry Markowitz
Portfolio suggests the optimum combination or the optimum portfolio where the standard deviation
(risk) of the portfolio is lowest and return is the highest. To achieve that outcome a new variable -
coefficient of correlation- is added, which is the crux of the Harry Markowitz Portfolio Theory. It is a
measure of the strength and direction of the linear relationship between the two variables in this
case expected return of company A and the expected return of company B. A coefficient of
correlation of one says that both the variables move in an identical fashion.
© All Rights Reserved. This document has been authored by Prof P C Narayan and is permitted for use only within the course "Equity Stock Market: Concepts,
Instruments, Derivatives and Risk" delivered in the online course format by IIM Bangalore. No part of this document, including any logo, data, illustrations, pictures,
scripts, may be reproduced, or stored in a retrieval system or transmitted in any form or by any means – electronic, mechanical, photocopying, recording or otherwise –
without the prior permission of the author.
