Accounting & Finance
Financial Analysis, Information and Markets
Portfolio Theory & Capital Asset Pricing Model
Modern Portfolio Theory
Modern portfolio theory was devised by Harry Markowitz in 1952. A portfolio is a group
of at least two constituents which are under common ownership. Securities, businesses
and capital investments are examples of constituents in the context of portfolio theory.
The theory makes the assumption that investors (whether that be a private investor,
organisation or director) make decisions which are rational based purely on expected
returns such as NPVs or IRRs; and risk measured by the standard deviation of
expected returns (in line with probability analysis, covered separately).
Rational Investors
Rational investors apply mean-variance analysis to investment decisions. As such,
when they know the expected return and the risk, they:
Will choose an investment that has a higher expected return and a lower risk
than another.
Will choose the investment with the lowest risk where two investments have the
same expected returns.
Will choose the investment with the highest expected return where two
investments have the same risk.
In addition, when an investment has a lower risk and a lower return than another
(and vice versa), the choice depends on the investor’s degree of risk-aversion or
their risk appetite.
The Portfolio Effect
With a portfolio, the expected return is equal to the weighted average of its constituents’
expected returns, because adding constituents sees a relative and equal increase in
both expected return and the weighted average of it constituents expected return. One
can’t increase without the other and increases are relative.
However the standard deviation (or risk) within a portfolio is lower than the weighted
average of its constituents’ standard deviation. The reason for this is that a portfolio
consists of different constituents which are effected by different things. A simple way to
, explain this is an organisation who has invested in multiple products lines in different
industries (their portfolio) – if something effects one of these industries or the demand
for one of these products, then only a proportion of their investment is at risk. However,
if the organisation had only invested in one product line and something effected that
industry or the demand for that product, then the entire investment would be at risk.
Furthermore, the portfolio effect is the notion that overall risk is reduced with a larger
number of constituents.
The extent of the portfolio effect (the risk reduction) depends on the relative size of the
constituents and the (expected and constant) correlation coefficients (ρ) between the
returns of the constituents, i.e. how different or similar two or more constituents are.
Correlation coefficients (ρ) between the portfolio constituents can range from -1 to 1.
A perfect positive correlation (ρ = +1) is where constituents are the same, so
there is no risk reduction. In practice, this in almost an impossibility, as no two
constituents will pose the exact same risk, even if it were (for arguments sake) a
toy bear factory acquiring another toy bear factory of the same size who make
the same bears in the same way.
A perfect negative correlation (ρ = -1) is where constituents are opposites in
literal terms. In this theoretical situation (also not possible in practice), the
combination of constituents would completely eliminate risk. This would mean
that the constituents could not be effected by any of the same variances, even if
it was a variance such as deflation which would affect most if not all constituents.
An intermediate correlation (-1 < ρ < +1) is where constituents are similar (ρ > 0)
or dissimilar (ρ ≤ 0). Correlation coefficients in this range will have varying effects
on risk where the level of risk reduction increases as the correlation
coefficient falls from +1 to -1.
Two Asset Portfolio Formulae
To follow is formulae to calculate the expected return and the risk of a two asset
portfolio.
Expected Return:
Where:
• Erp Expected return of portfolio
• ErA Expected return of constituent A(lpha)
• ErD Expected return of constituent D(elta)
• x Percentage of portfolio in constituent A
Financial Analysis, Information and Markets
Portfolio Theory & Capital Asset Pricing Model
Modern Portfolio Theory
Modern portfolio theory was devised by Harry Markowitz in 1952. A portfolio is a group
of at least two constituents which are under common ownership. Securities, businesses
and capital investments are examples of constituents in the context of portfolio theory.
The theory makes the assumption that investors (whether that be a private investor,
organisation or director) make decisions which are rational based purely on expected
returns such as NPVs or IRRs; and risk measured by the standard deviation of
expected returns (in line with probability analysis, covered separately).
Rational Investors
Rational investors apply mean-variance analysis to investment decisions. As such,
when they know the expected return and the risk, they:
Will choose an investment that has a higher expected return and a lower risk
than another.
Will choose the investment with the lowest risk where two investments have the
same expected returns.
Will choose the investment with the highest expected return where two
investments have the same risk.
In addition, when an investment has a lower risk and a lower return than another
(and vice versa), the choice depends on the investor’s degree of risk-aversion or
their risk appetite.
The Portfolio Effect
With a portfolio, the expected return is equal to the weighted average of its constituents’
expected returns, because adding constituents sees a relative and equal increase in
both expected return and the weighted average of it constituents expected return. One
can’t increase without the other and increases are relative.
However the standard deviation (or risk) within a portfolio is lower than the weighted
average of its constituents’ standard deviation. The reason for this is that a portfolio
consists of different constituents which are effected by different things. A simple way to
, explain this is an organisation who has invested in multiple products lines in different
industries (their portfolio) – if something effects one of these industries or the demand
for one of these products, then only a proportion of their investment is at risk. However,
if the organisation had only invested in one product line and something effected that
industry or the demand for that product, then the entire investment would be at risk.
Furthermore, the portfolio effect is the notion that overall risk is reduced with a larger
number of constituents.
The extent of the portfolio effect (the risk reduction) depends on the relative size of the
constituents and the (expected and constant) correlation coefficients (ρ) between the
returns of the constituents, i.e. how different or similar two or more constituents are.
Correlation coefficients (ρ) between the portfolio constituents can range from -1 to 1.
A perfect positive correlation (ρ = +1) is where constituents are the same, so
there is no risk reduction. In practice, this in almost an impossibility, as no two
constituents will pose the exact same risk, even if it were (for arguments sake) a
toy bear factory acquiring another toy bear factory of the same size who make
the same bears in the same way.
A perfect negative correlation (ρ = -1) is where constituents are opposites in
literal terms. In this theoretical situation (also not possible in practice), the
combination of constituents would completely eliminate risk. This would mean
that the constituents could not be effected by any of the same variances, even if
it was a variance such as deflation which would affect most if not all constituents.
An intermediate correlation (-1 < ρ < +1) is where constituents are similar (ρ > 0)
or dissimilar (ρ ≤ 0). Correlation coefficients in this range will have varying effects
on risk where the level of risk reduction increases as the correlation
coefficient falls from +1 to -1.
Two Asset Portfolio Formulae
To follow is formulae to calculate the expected return and the risk of a two asset
portfolio.
Expected Return:
Where:
• Erp Expected return of portfolio
• ErA Expected return of constituent A(lpha)
• ErD Expected return of constituent D(elta)
• x Percentage of portfolio in constituent A
