ACFI2070 Lecture Notes - Lecture 8: Watt, Systematic Risk, Market Risk
29 Jun 2018
School
Department
Course
Professor
Module 3 Part 2: Diversification and
Modern Portfolio Theory
LO1: Explain how diversification reduces risk.
Portfolio risk is not just the average of individual asset risks, covariance plays an important role.
Recall last week’s discussion regarding return covariance and correlation:
The model has two assets with equal E(r) and equal risk, but return correlation is p=-1. In this case,
portfolio return remains the same, but portfolio risk / variance is 0. This is an example of an extreme
case of how portfolio risk might be reduced or even eliminated by combining various types of assets.
As another example, consider:
Asset A Asset B
Expected Return E(R
i
) 12% 18%
Risk (Std Deviation)
i
20% 40%
W
A
W
B
Some P P1 1 0
portfolios P2 .67 .33
with asset P3 .50 .50
weights W
i
P4 .33 .67
( 0 W
i
+1 ) P5 0 1
We can calculate the expected rates of return of the various portfolios P that could comprise A and
B:
E(Rp) = [ WA x E(RA) ] + [ WB x E(RB) ]
To calculate the various portfolios standard deviation of returns, we need one other piece of
information: the covariance between the returns of assets A and B (ie. σAB ). We can use the
correlation coefficient version of covariance, recalling σAB = ρ AB σA σB such that:
In our analysis of these, we assume that investors are risk adverse and returns are normally
distributed (ie sometimes you earn more, sometimes less than the mean, but overall the average
investment return is around the mean. By holding a portfolio, we can diversify risk and thus appeal
more to risk adverse investors.
Note that the benefit of the diversification depends on the correlation between assets.
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Portfolio risk is not just the average of individual asset risks, covariance plays an important role. Recall last week"s discussion regarding return covariance and correlation: The model has two assets with equal e(r) and equal risk, but return correlation is p=-1. In this case, portfolio return remains the same, but portfolio risk / variance is 0. This is an example of an extreme case of how portfolio risk might be reduced or even eliminated by combining various types of assets. Some p portfolios with asset weights wi ( 0 wi +1 ) We can calculate the expected rates of return of the various portfolios p that could comprise a and. E(rp) = [ wa x e(ra) ] + [ wb x e(rb) ] To calculate the various portfolios standard deviation of returns, we need one other piece of information: the covariance between the returns of assets a and b (ie. ab ).
