The document discusses efficient portfolios and the single index model. It defines efficient portfolios as those with the smallest risk for a given level of expected return or largest expected return for a given level of risk. The single index model assumes the risk of return from each security has two components: the market-related component and a company-specific residual error component. It provides an equation to model the return of a security based on its sensitivity to market returns and a residual error term. The model can also be applied to portfolios to find the minimum variance set of portfolios. Finally, it mentions analyzing a portfolio of 10 companies to determine which provides maximum return with minimum risk using the single index model.

1. Portfolio Management
Efficient Portfolio
Single Index Model

2. EFFICIENT PORTFOLIO
The proportion that security market are efficient, in the sense that price of
securities reflect their economic value based on price sensitive information.
Efficient diversification takes place in an efficient portfolio that has the smallest
portfolio risk for a given level of expected return or the largest expected return for
a given level of risk. Investors can specify a portfolio risk level they are willing to
assume and maximise the expected return on the portfolio for this level of risk.
Rational investors look for the efficient portfolios, because these portfolio are
optimized on the 2 dimensions of most importance to investors – return and risk.
SINGLE INEX MODEL:
Single- -Index model assumes that the risk of return from each Index
model assumes that the risk of return from each security has two components
security has two components- - „ „the market related component( the market
related component(βi Rm)caused by macro events and )caused by macro events and
the company the company- -specific component( specific component(ei) which is a
random residual ) which is a random residual error caused by micro events. error
caused by micro events.
„ „ The security responds only to market index movement as The security
responds only to market index movement as residual errors of the securities are
uncorrelated. The residual residual errors of the securities are uncorrelated. The
residual al errors occur due to deviations from the fitted relationship errors occur
due to deviations from the fitted relationship between security return and market
return. For any period, it between security return and market return. For any
period, it represents the difference between the actual return( represents the
difference between the actual return(Ri) and the ) and the return predicted by the
parameters of the model( return predicted by the parameters of the model(βi Rm) )
„ „ The Single Index model is given by the equation: The Single Index model is
given by the equation:
Ri = αi + βirm+ ei
Ri = the return on security

3. Rm =the return from the market index
αi=risk free part of security
βi=sensitivity of security
ei=random residual error, which is company specific
Total risk of a security , as measured by its variance, consists of 2
components: market risk and unique risk and given by
α2 = β2 (αm
2) +αei
2
= market risk + company
This simplification also applies to portfolios, providing an This simplification also
applies to portfolios, providing an alternative expression to use in finding the
minimum variance se alternative expression to use in finding the minimum
variance set t of portfolios:
α p2 = βp2 [αm
2]+ αei
2
Here, the portfolio of ten companies such as
 Jindal saw ltd
 Canara bank
 ICICI bank
 M&M
 PSB
 HERO
 Honda
 NAKODA
 Indian bank
 PFS
Are presented and we are going to find which company is giving maximum return
with minimum risk in single index model