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What is modern portfolio theory?

An investment framework useful for diversifying the risk when allocating assets in a financial, liquid, tradable portfolio in order to minimise risk and enhance returns

Overarching goal is to minimise exposure to risk while enhancing returns

MPT provides tools to use in the selection of investments and calculate the optimum trade off between risk and return


History of MPT

1952 - Harry Markowitz
Publishes portfolio selection - stresses the importance of investment combination to spread risk in a portfolio

1958 - James Tobin
Adds leverage to MPT - including risk free investments and risk free rate of return as a means of enhancing returns

1964 - William Sharpe
Developed CAPM - in it risk is defined as 'beta' and it also introduced the concept of the market portfolio


Efficient financial markets and efficient financial markets hypothesis

Markets are efficient when new share price sensitive information is made available and is reflected in the market prices - almost instantly - MPT based of efficient markets

Three forms of efficient markets:

Strong form
Perfection - market where all information is factored in to price even insider information. In reality do it exist - closest real example is larger quoted companies whose activities are scrutinised and information reported by analysts

Weak form
Unpredictable - price movement tend to be erratic and based on historic information - release of new data may not confirm what markets expect - small company not really subject to analysts following its activities

Semi-strong form
Middle ground - most markets display semi-string characteristics as information is available and can be predicted by analysts. But events like mergers or other market shocks can still surprise and influence prices - there are opportunities for individuals to benefit from insider trading


Risk in context of MPT

Risk in the context of MPT can be systematic (risk due factors outside control such as 2008 financial crisis) or unsystematic risk (aka specific - linked to a precipice holding)

Only unsystematic risk can be diversified away

MPT uses statistics and mathematical calculations in order to diversify portfolio

MPT assumes that price fluctuations assume a 'normal distribution' and portfolio risk is measured by the standard deviation of returns from the weighted average of investments within the portfolio


What is correlation and how does it link to diversification?

Correlation is the relationship between two assets and is measured on a scale -1 to +1

If assets perfectly positively correlated - moved in exactly same direction and have a correlation of +1

If assets perfectly negatively correlated - move in opposite directions in same proportion correlation of -1

Correlation of 0 indicates no correlation between two assets

Tool to evaluate overall risk - risk in relation to other holdings and the impact one new addition would have on overall risk


What is variance in context of MPT

Variance helps an investor consider the risk being taken when adding new investment - calculates the difference between what we expect and what we will actually receive

Difference between actual return for each hr vs the average for a 10 yr period

Standard deviation is square root of variance - calculation used to avoid negative numbers - variance is standard deviation


Indifference curves

Indifference curve displays on a graph the various combinations of portfolios available that will satisfy an investors appetite for risk and return

Not all will be suitable - portfolios are plotted across risk appetite and most suitable is chosen form then


Efficient frontier

Graph used to represent all the possible combinations of risk and return than exists - the optimum portfolios will be plotted along ten efficient frontier - curved line along the graph

Rational investors would only select investments placed long this line


Risk free investments

Risk free (Rf) investments introduced by James Tobin

Bank accounts, treasury bills and gov bonds can be considered risk free

Adding these to a portfolio enhances returns without increasing risk - higher returns same level risk

Adding leverage (if borrowing is available to an investor at risk free rate) can also further enhance returns - above those of the market portfolio

Allows returns greater than those available from portfolios placed on the efficient frontier


Capital market line

Links in to Rf investments - on graph line plots the possible portfolios with inclusion of risk free - beyond efficient frontier

Borrowing at risk free rate could yield returns beyond those of the market portfolio

All rational investors would look to invest along that line


Capital asset pricing model

Developed by William Sharpe - 1964 - redefined risk as beta

Each portfolio and the market has its own beta - allows calculation of portfolio and investment beta

Beta of investment or portfolio can be compared against that of the market which is defined 1 - a beta of less than 1 deemed to be less risky than the market and a beta of more than 1 is more risky than the market

CAPM expected return calculation is
Rf + beta x (Rm - Rf)


What is Alpha

Alpha is the return after beta is stripped - how much better than the market are you doing

Beta x market portfolio = alpha


Sharpe ratio

Developed by William Sharpe - measure of portfolios risk adjusted returns - quantify return vs a benchmark

Rp - Rf / risk


Diversification and risk in MPT

Optimum portfolio

Risky investments can be combined with less risky investments to make a balanced portfolio and enhance returns - unsystematic risk can be diversified away - systematic risk cannot

Rational investors would not want a single investment portfolio

Risk/ reward performance of investments should not be analysed in isolation but rather in context of their impact on a portfolio