Coefficient of Portfolio Management Correlation and Diversification

Learning outcomes
How to calculate return and risk of discrete distribution
How to calculate return and risk of continous distribution
What is coeffiecient of varaince
Covariance
Portfolio management
Correlation and diversification
What are the type sof risks
Security market line
Abstract
In investment, especially in the portfolio management, the risk and returns are two significant
measures in making investment decisions.This paper endeavors to furnish a concise
theoretical explanation with examples on identifying the return and related risk.The
delineations of tables can essentially contribute to the comprehension of a reader about to risk
and return.Basically in this chapter discuss about risk and return of discrete and continuous
distribution,portfolio management,systematic risk and security market line

01.Risk and return in discrete distribution
01.01.Return
Income received on a investment plus any changes in market price
Usually expressed as a percentage of the beginning market price of the investment.
01.01.01.Probability distribution
Illustration 01.
Find the estimated rate of return of A & B
Table 01.
Economin
condition
Probabi.of
occurrence
Return A % Return B % Estimated
return A %
Estimated
return B %
Boom 0.5 19 30 9.5 15
Bust 0.5 13 -5 6.5 -2.5
Estimated return 16 12.5
01.02.Risk
The variability of returns from those are expected
Two methods are available for the calculation of risk
Using range
Using standard deviation
01.02.01..Using standard deviation method
Illustration 02.
Find the standard deviation of company A using above illustration 01.
Table 02.
Economin
condition
Probabi.of
occurrence(P
)
Return(R) Estimated
return(ER)
(R-ER)2 (R-ER)2*P
Boom 0.5 0.19 0.16 0.0009 0.00045
Bust 0.5 0.12 0.16 0.0016 0.00080
R=[D+(Pt-Pt-1)]/Pt-1
R=Return
D=Divident
Pt=price at the end of year
Pt-1=Price at the end of
previous year

Variance 0.00125
Standard deviation=√0.00125=0.03535=3.535%
Using the above method we can calculate the standard deviation of company B also
02.Coefficient of variance
Statistical measure of the relative scattering of data points in an data arrangement
around the mean
In finance, the coefficient of variance permits investors to decide how much
unpredictability,or risk, is accepted in contrast with the amount of return anticipated
from investment[ CITATION HAY \l 1033 ]
03.Expected return and risk in continuous distribution
03.01.Expected return 03.02.Risk
04.Covariance
Statistical term used in security and portfolio evaluation.It measures the amount
which two assets move in relation to each other
Positive covariance = assets move in same direction
05.Portfolio management
05.01.Expected return
CV = σ σ=standard deviation
μ μ=Mean
nn
I=1σ=√[ Σ(Ri-R)2 ]/nI=1R= Σ (Ri)/(n)
R=expected rate for asset
Ri=return for the ith observation
n= Total No. of observations
COV(X,Y)= [Σ(Xi-X)(Yi-Y)]/(n-1)
n Rp=expected rate for portfolio
Wi=weight for ith asset
Ri=expected rate of i asset
RP= Σ (Wi)(Ri)I=1