Define modern portfolio theory
An investment framework that is useful in diversifying the risk when allocating assets in a financial, liquid (tradable)
... [Show More] portfolio in order to maximise the potential return given a specified level of risk appetite or tolerance.
Modern portfolio theory (MPT) is born out of investment common sense. The rationale is that minimising risk and maximising the potential return should be something that logical humans have in mind when allocating assets across a portfolio. The well-worn tenet that states 'the higher the risk, the higher the potential reward' is cast in an intelligent framework within MPT where the combination of holdings in a portfolio is assessed by what?
how they perform in relation to one another (correlation) and the risk and return characteristics of each, collectively.
MPT is essentially an investment framework that is useful in diversifying therisk when allocating assets in a financial, liquid (tradable) portfolio in order to maximise the potential return given a specified level of risk appetite or tolerance. In other words, by spreading risks across multiple investment holdings, the risk of potential loss can be minimised without necessarily reducing the returns from a portfolio. If only one investment is purchased, the portfolio will have the risk and return characteristics of that holding. Each single investment exhibits is own particular risk and return characteristics. What MPT looks to do is what?
Quantify the risk mathematically and eliminate or reduce this specific risk by adding other assets that perform dissimilarly to the investment basket.
The portfolio is constructed so that when some assets fall in value, other assets rise and balance is maintained. When markets in general rise, the investment portfolio gains in value. MPT uses mathematics to intelligently construct an investment portfolio. The steps involved include?
valuing the investments that could be included in the portfolio;
calculating the asset allocation (or number and type of investments);
optimising the portfolio to get the maximum amount of return for the minimum amount of risk; and
monitoring the portfolio to see if it meets performance expectations from both a risk and return perspective, making changes when market conditions warrant a change.
MPT was first introduced in 1952 in a paper titled Portfolio Selection, published by the Journal of Finance and written by Harry Markowitz, an American economist who was awarded Nobel Laureate status for his work. Markowitz's studies demonstrated that investing should not be about trying to pick future high-performing stocks, but that the combination of the investments chosen was more important in terms of reward for the level of risk taken. By adding assets that are uncorrelated or inversely correlated, the overall risk in a portfolio is what?
Diversified across all the different 'eggs in the basket' and risk is reduced
and can be quantified. This measuring of risk becomes extremely useful when considering purchases and sales within the investment basket.
In 1958 James Tobin added leverage to MPT by including an investment that pays a risk-free rate of return, which allowed the construction of portfolios whose risk-return profiles were capable of what?
Outperforming Markowitz's Efficient Frontier.
Define financial or capital markets
Where governments andcompanies raise financevia the sale and purchaseof fixed income securities,often called bonds orequities, more commonlyknown as shares via a stockmarket.
he market is used to trade new issues of either bonds or shares, which are known as primary, or already existing securities, known as the secondary market. Typical capital market instruments include what?
Equities, bonds, foreign exchange markets, derivatives (futures and options) as well as insurance contracts, mortgages and other tradable securities.
An efficient capital market is where the prices of these instruments reflect information accurately and in real time. New information about a company will be analysed and the future value of cash flow expected from the security will what?
Change the current share price to accommodate this change in fundamental value.
The prices of securities fluctuate and market participants, such as traders and stockbrokers, will trade them competitively to try to achieve maximum profit. Funds from savers and investors (corporate or individual) are expected to flow into the financial markets intent on seeking out the best places to invest and, therefore, you can see that information available and its ability to impact of share prices is of the utmost importance. If stocks are efficiently priced with all information about the underlying company known, investors can what?
Feel confident about the choices they make for their portfolios
Define diversification
How risk in a portfolio is reduced.
A portfolio which is constructed of a number of different asset classes suchas equities, bonds, cash, property and commodities will blend low-risk cash deposits and bonds with higher risk equities and commodities, for instance. The asset class could then be diversified further with what?
Different managers, industry sectors and geographies selected. The proportions allocated will depend upon the investor's risk preference and the prevailing market condition
Risk, in its simplest form, can be divided between systematic and unsystematic, or specific, risk. Specific risk is that associated with a particular individual investment. A specific risk is diversifiable by adding what?
Other diverse holdings to the portfolio, provided that the risks of the other holdings are not directly correlated.
Systematic risk is that of the portfolio or market and cannot be diversified away through the addition of other assets, and is due to outside factors such as what?
The economy performing poorly or international tensions, etc. Systematic risk affects the whole market or 'system'.
The risk for investors is that the return from an investment will be lower than expected. MPT is interested in the amount that this return deviates from the average return and quantifies this risk accordingly, measuring it as 'standard deviation'. Every holding has its own mean and therefore deviation from it can be measured specifically. MPT assesses the likely profitability of investments from a basis of weighting the expected returns on a 'normal' distribution, the familiar bell-shaped curve when drawn graphically. Therefore, risk is measured by what?
The standard deviation of returns and the expected portfolio return is measured by the weighted average of individual investments within it.
In considering risk, it is the effect that an investment will have on the overall risk of the portfolio that is important, not the risk of the investment in isolation. The amount of diversification of risk available will depend upon the degree to which returns from different investments move in line with each other or the degree to which they are 'correlated'. An investor can reduce the risk in a portfolio by holding several investments that are not perfectly (positively) correlated. Highly correlated shares for instance may occur from companies in the same industry or sector; if the oil price moves, oil companies' shares will tend to move in the same direction. Negative correlation is viewed when prices tend to what?
Move in opposite directions
If no discernible relationship can be observed with prices bearing no relationship to each other, there is no correlation between the assets. Correlation is measured on a scale of +1 to -1. A correlation coefficient of 1 between two assets (perfect) means whatever one asset does will predict the movement of the other. One asset's gain of 10% will be matched by the other asset's gain of 10%, therefore. Minus one is perfect inverse and is equally predictive but opposite. This means that if investment 'a' increases by 10%, investment 'b' will decrease by 10%. Ignoring the sign, the greater the number, the greater the strength of the relationship between the two. A correlation of zero means returns are completely independent and no relationship exists between the two. Anything less than 1 means that investors can what?
Diversify the risk in portfolios. Proportionate reduction of risk, relative to return is therefore available in almost all portfolios with two or more investments. Eggs (risk) will be in different baskets (investments).
The correlation between investments varies over time and reassessment of data leading to rebalancing of the investments in the portfolio may be necessary. This is a criticism levelled at MPT but the theory is often not what?
Perfectly replicable in practice
The expected return from a portfolio is therefore the weighted average of the expected returns of the two investments where the weights are the proportions of the available cash invested in each holding. Markowitz defined the proportionate risk of the two-asset portfolio as 'variance'. What is the calculation for this?
R(P) = xRa +(1-x)Rb
Where:R(P) is the expected return from the portfolio
X is the percentage invested
R(a) is the expected return from 'a'
R(b) is the expected return from 'b'
Define portfolio variance
A measurement of how the aggregate returns of a number of securities making up a portfolio fluctuate over time.
This portfolio variance is calculated using the standard deviations of each security in the portfolio as well as the correlations of each security pair in the portfolio. Portfolio variance looks at the covariance or correlation coefficients for the investments in the portfolio. Generally speaking, a lower correlation between securities in a portfolio results in a lower portfolio variance. MPT states that portfolio variance can be reduced how?
By choosing asset classes with a low or negative correlation, as we have seen from diversification
Portfolio variance is a weighted combination of the individual variances of each of the assets adjusted by their covariances. This means that the overall portfolio variance is lower than a simple weighted average of the individual variances of the stocks in the portfolio. Variance is often calculated using the standard deviation of the portfolio, which is simply the square root of variance. Variance measures the variability (or volatility) from an average or mean and volatility is a measure of risk; variance will help an investor determine what?
The risk they might take on when assessing a new investment.
A variance value of zero means that all values within a group of numbers are the same and that all variances that are non-zero will be positive numbers (because they have been squared). A large variance indicates that numbers in the set are far from the mean and each other (high volatility), while a small variance indicates what?
Little volatility
Covariance is used in portfolio theory to determine what assets to include in the portfolio. Covariance is a statistical measure of the directional relationship between two asset prices. Portfolio theory uses this statistical measurementto reduce the overall risk for a portfolio. A positive covariance means that assets generally move in the same direction. Negative covariance means assets generally move in opposite directions. Covariance is an important measurement in MPT. MPT attempts to determine an efficient frontier for a mix of assets in a portfolio. The efficient frontier seeks to optimise what?
The maximum return against the degree of risk for all the combined assets in the portfolio. The aim is to select investments for the portfolio that have a lower standard deviation than the standard deviation of the individual assets, thereby helping to reduce the volatility of the portfolio.
MPT tries to create an optimal blend of higher-volatility assets with lower-volatility assets and, by diversifying the assets in a portfolio, risk can be reduced but still achieve a positive return. In the construction of a portfolio, it is important to attempt to reduce overall risk by including assets that have a negative covariance with each other. Analysts use historical price data to determine the measure of covariance between different stocks. This assumes that the same statistical relationship between the asset prices will continue into the future, which is not always the case. By including assets that show a negative covariance, the risk of a portfolio is minimised. Covariance can be used to maximise diversification in a portfolio by adding investments with a negative covariance to a portfolio which reduces what?
The overall risk. Covariance provides a statistical measurement of the risk for a mix of different investments and is calculated by formulae.
Covariance only measures the directional relationship between two investments. It does not show the strength of the relationship between assets as the correlation coefficient does.Markowitz looked to achieve the optimum portfolio from the basis of two investments. The two investments generate differing returns in dissimilar environments or market conditions. Markowitz taught that there was an alternative strategy to selecting either investment because their returns do not move in unison (positive correlation) depending on the scenarios present. This relates once again to not putting all eggs in one basket, or all investment money in one holding and produces a portfolio with what?
The same overall return but reduces the risk taken to zero
The three significant conclusions that can be derived from Markowitz's two- asset portfolio, what are these?
Risky investments can be combined into a less risky (or even risk-free) portfolio. This can be viewed as putting 'eggs into different baskets', diversifying the specific risk of each investment.
Rational investors would not hold one investment exclusively as the return can be maintained but the risk reduced by holding both 'a' and 'b'.
The risk and return performance data for each individual holding should not be analysed in isolation due to the fact that when one is performing well, the other is performing badly - it can be said that they are inversely correlated.
There are two main formulae which allow intelligent combining of risks and returns, provided the correlation coefficient is known. From these formulae, it can be observed that the return is derived from the combination on a simple weighted average basis, and that the effect of combing risks is attributable to the correlation coefficient. What are these and how are they calculated?
Return of portfolio:
ra+b = Para + Pbrb
Risk of portfolio
σa+b2 = Pa2σa2 + Pb2σb2 + 2PaPbσaσbCorab
The correlation coefficient is the keyto the extent that a portfolio of two investments can achieve diversification of risk. To be able to calculate the proportionate allocation of multiple investments in a portfolio, the risk-return profiles of combinations of investments must be what?
Established, given the different correlation coefficients.
With perfect positive correlation, the two chosen investments move in unison and there is no benefit from diversification. The resulting risk and return performance are what?
The weighted average of the two investment risks and returns.
With perfect negative correlation, the two investments move in opposite directions to each other, there will be an asset allocation available that completely what?
Diversifies away the risk
It is highly improbable that the two investments are perfectly positively correlated (+1) or perfectly negatively correlated (-1). Imperfect correlation, somewhere between -1 and +1, is what?
The most likely situation
In efficient capital markets where returns from investments are normally distributed (symmetrical bell curve standard deviation), the rational, risk-averse investor can minimise their utility preferences by diversification. Most investors will look to diversify further than the two-asset combination will allow and include what?
Numerous investments within a portfolio
Given the universe of investments that could be included in a portfolio, technology is obviously very important in obtaining the possible combinations that could make up the efficient frontier. As mentioned before, Markowitz had proffered the theory in 1952 but the practical application was lengthy and based upon trial and error. Size will be a factor as a small portfolio will incur proportionately higher fees than a large portfolio, in practice. A diversified portfolio of 30 shares has been deemed to diversify away roughly 90% of the average shares' diversifiable risk. Large numbers of holdings do not need to be incorporated into a portfolio therefore and there is little risk reduction in holding 150 shares over a basket of only 50. In fact the costs associated with holding that many investments could what?
Start to outweigh the benefits [Show Less]