10. Portfolio Theory - Principles & Limitations Flashcards
A. Management of portfolio risk (page 2)
Modern Portfolio Theory (MPT):
- is concerned with the way in which portfolios can be constructed to maximise returns and minimise risks.=
- says that all assets need to be considered in respect of how they interact with each other
- assumes that investors are risk adverse, choosing a less risky investment if offered the choice
A1. Defining risk through standard deviation (pages 2 & 3)
Standard Deviation:
- the most commonly used measure of risk is the volatility of returns or Standard Deviation
- measures how widely the actual return on an investment varies around its average or expected return
- the higher the standard deviation the higher the risk
USALLY DESIGNATED BY THE GREEK LETTER SIGMA:
- an o with a high tail to the right
A1. Defining risk through standard deviation (pages 2 & 3)
CONTINUED
Example of Mean of 8% and Standard Deviation of 5%:
Returns can be expected to fall within 1 Standard Deviation 68% of the time:
- between 3% and 13% (Mean 8% +/- 5%)
Returns can be expected to fall within 2 Standard Deviations 95% of the time:
- between -2% and 18% (Mean 8% +/- 2 x 5%)
SKEWING
- POSITIVE SKEW (peak of curve to LEFT OF CENTRE)
- NEGATIVE SKEW (peak of curve to RIGHT of centre)
A2. Managing risk (page 3)
Normally buying low-risk assets will give a low-risk portfolio, but leads to low returns.
More attractive approach is to buy risky-assets and reduce the risk in two ways:
- hedging out risk
- diversifying portfolio holdings
A2A. Hedging (page 3)
Hedging means:
- protecting an existing investment position by taking another position that will increase in value
This can be acheived using derivatives:
- selling FTSE 100 futures contracts
- buying FTSE 100 put options
A2B. Diversification of risk (pages 3 & 4)
Holding a mixture of investment types, the portfolio is diversified and takes of advantage of the various assets when they perform well in certain market conditions.
A2C. Correlation (pages 4 & 5)
The effectiveness of diversification is dependant on the degree of correlation between the returns of different assets in the portfolio.
Correlation is a number between +1 and -1
- Closer to 1 is positive (move in same direction)
- Close to 0 is no relationship
- Closer to -1 is negative (move in opposite directions)
Most effective diversification comes from combining investments that are negatively correlated.
A2C. Correlation (pages 4 & 5)
CONTINUED
POSITIVE CORRELATION: the assets move up and down together. They are affected by the same things.
NEGATIVE CORRELATION: the assets move in opposite directions to each other.
NO CORRELATION: the shares/assets are not related to each other.
A2C. Correlation (pages 4 & 5)
CONTINUED
Diversification can be acheived by:
- HOLDING DIFFERENT ASSET CLASSES
- CHOOSING COMPANIES FROM DIFFERENT SECTORS
- INCLUDING OVERSEAS COMPANIES
B. The efficient frontier (page 5)
The relationship between the return that can be expected from a portfolio and the risk of the portfolio as measured by standard deviation.
B1. Constructing an efficient frontier (page 6)
Shows the best return that can be expected for a given level of risk.
Inputs to the models are:
- return of each asset class
- standard deviation of each asset’s returns
- correlation between each pair of assets’ returns
RISK - LEFT/RIGHT (standard deviation)
RETURN - UP/DOWN
B2. Limitations to using an efficient frontier (pages 6 & 7)
Limitations to using an efficient frontier:
- assumes that standard deviation is the correct measure of risk
- assets have normally distributed returns
- difficult to say which portfolio investors would prefer based solely on their attitude to risk
- inputs for risk and correlation between investors rely on historic data which may be unstable
- model does not include transaction costs
- assumes the underlying portfolios in each asset class are index funds
C. Capital asset pricing model (CAPM) (page 7)
C1. Systematic and non-systematic risk (pages 7 & 8)
SYSTEMATIC RISK (MARKET RISK)
- the risk that affects the market as a whole
- cannot be avoided
- measured by Beta (the volatility of stock relavant to the market)
NON-SYSTEMATIC RISK (INVESTMENT SPECIFIC)
- unique to a particular company or stock
- can be eliminated by holding a diversified portfolio
C2. Beta (page 8)
The Market has a Beta of 1.
The Beta of an individual security reflects the extent to which its return moves up or down relevant to the Market.
INDIVIDUAL SHARE’S BETA:
- Equal to 1: it’s return moves exactly the same as the Maket’s. Market goes up 10%, so does the share
- More than 1: exagerates the market’s movements, so more volatile. Market goes up, share goes up more
- Less than 1 (but more than 0): opposite to more than 1. Market goes down, share goes down but by less than the Market
C3. CAPM equation (pages 8 & 9)
CAPM derives the theoretical expected return for a security as a combination of the:
- return on a risk-free asset (such as a treasury gilt)
- risk premium (the compensation for holding a risky investment)
CAPM Equation:
E(Ri) = Rf + Bi (Rm - Rf)
E(Ri) = expected return on the risky investment
Rf = rate of return on risk-free asset
Rm - expected return of model portfolio
Bi = beta (sensitivity of investment to overall market)
(Rm - Rf) = market risk premium
Bi (Rm - Rf) = risk premium of the risky investment
Example:
- Share has beta of 1.4
- Treasury Bill expected return of 3.5%
- expected return on the portfolio Market of 8%
E(Ri) = 3.5 + 1.4 (8 - 3.5)
C4. Assumptions of CAPM (pages 9 & 10)
CAPM is based on a set of assumptions:
- investors are rational and risk adverse
- all investors have an identical holding period
- no one individual can affect the market price
- no taxes, transaction costs etc
- information is free and available to all investors
- all investors can borrow/lend unlimited money
- quantity of risky securities in the market is fixed
C5. Limitations of CAPM (page 10)
CAPM has limitations:
WHAT TO USE AS A RISK FREE RATE?
- difficult, but usually UK Government Treasury Bills
WHAT IS THE MARKET PORTFOLIO?
- usually a market index of shares relating to a particular national share market such as the FTSE 100
THE SUITABILITY OF BETA
- the beta of a security must be stable for CAPM to be useful
- however, historical data shows that betas are not stable
- therefore can they be used to estimate future risk?
D. Multifactor models (pages 10 & 11)
CAPM expresses a simple relationship between risk and return.
CAPM is often referred to as a single factor model, concerned with only one factor:
- security’s sensitivity to the market, as measured by Beta
Can be problems with this because the relationship between risk and return is too complex to describe using the relationship with a single market index.
D. Multifactor models (pages 10 & 11)
CONTINUED
FAMA-FRENCH THREE-FACTOR MODEL:
- expanded the CAPM
- added factors for company size and value
Fama-French identified two types of company securities that tended to do better than the market as a whole:
- small cap stocks (tended to outperform large cap)
- value stocks (tended to outperform growth)
The securities favoured by the Fama-French three-factor model tend to be more volatile than the stock market as a whole, and the higher reward should be considered as the compensation for taking on higher risk.
D1. Arbitrage pricing theory (pages 11 & 12)
Based on the idea that:
- a security’s returns can be predicted using the relationship between the security and a number of common risk factors
- and where sensitivity to changes in each factor is represented by a factor-specific beta
- the model derived return can then be used to correctly price the security
If the price diverges, arbitrage activities (taking advantage of security mispricing to make a risk-free profit) should bring it back in line, so that it is not possible for a security to yield better returns than indicated by its sensitivity to the various factors.
Like CAPM: it argues that returns are based on the systematic risk to which the security is exposed
UNLIKE CAPM: it views that asset prices are determined by more than just one type of market risk
D2. Application of multifactor models (page 12)
Factor models are also widely used in asset management business as follows:
- Active Management (allows managers to focus on forecasting factor premiums)
- Index-tracking Funds (sensitivity of a portfolio to all factors in the factor model can be set to match the overall market)
- Risk Management (the models allow a manager to analyse which factor exposures contributed to portfolio risk and adjust exposure to manage risk)
- Performance Attribution Analysis (models can be used to work out what contributed to a return)
E. Limitations of models (pages 12 & 13)
- Optimisation models based on efficient frontiers are used frequently for asset allocation
- CAPM is used to better understand the return from portfolios
- Jensen’s alpha is used to measure portfolio performance
- Multifactor models are used to forecast security and portfolio returns
E1. Models in a financial crisis (page 13)
- Security returns do not follow a normal distribution
- Therefore, models that use standard deviation as a risk measure do not work in a crisis
- Correlation not stable in extreme conditions
- Investors are irrational and become more so in extreme conditions
E2. Behavioural finance versus the efficient market hypothesis (page 13)
Behavioural finance is an area of research that explores how emotional and psychological factors affect investment decisions.
Attempts to explain market anomalies and other market activity that are not explained by traditional finance models like MPT and the EMH.
E2A. Efficient market hypothesis (pages 13 & 14)
In an open and efficient market, security prices reflect all available information and prices rapidly adjust to any new information.
For this reason market prices are always the correct prices for any given security.
Therefore not possible to outperform the market by picking undervalued securities because there are none.
EMH says that it is impossible to achieve consistent returns in excess of average market returns through stock selection or market timing.
Only way to achieve higher returns is through riskier investments.
E2A. Efficient market hypothesis (pages 13 & 14)
CONTINUED
Three forms of EMH:
- Weak-form efficiency (prices fully reflect past price data and future prices cannot be predicted by analysing this)
- Semi-strong efficiency (prices adjust to all publicly available data, which includes past prices and information reported in a company’s financial statements)
- Strong-form efficiency (prices reflect all information that any investor can acquire. This includes all public information plus private information typically held by corporate insiders)
E2B. Evidence to support the efficient market hypothesis (pages 14 & 15)
- Weak-form efficiency (generally, strong and consistent evidence supports this)
- so buying/selling shares based on past performance does not lead to outperformance - Semi-strong efficiency (strong factual support)
- markets are generally semi-strong - Strong-form efficiency (evidence to support that company directors and their advisers can outperform other investors, however, investment managers do not)
- market is therefore not strongly efficient
E2B. Evidence to support the efficient market hypothesis (pages 14 & 15)
CONTINUED
Critics of EMH see that the evidence shows that investors are affected by:
- tendency to make decisions based on what other investors are doing (the herd investor)
- tendency to ‘churn’ their portfolios
- tendency to under-react/over-react to news
- asymmetrical judgements about causes of previous profits and/or losses
E2C. Psychological factors or behavioural biases (page 15)
Principle theories within behavioural finance that often contradict the basic assumptions of traditional financial theory:
PROSPECT THEORY/LOSS AVERSION
- people do not always behave rationally, particularly in respect of their risk tolerance when they face a loss or make a profit
- people take losses harder than they do enjoy making gains on their investments
- loss aversion is taking risker decisions to reduce losses, such as holding onto an investment for longer than they should
REGRET
- avoid selling an investment because of the regret of having made an error of judgement
- avoid selling stocks that have gone down
OVERCONFIDENCE & OVER/UNDER REACTION
- people have a tendency to overestimate their own skills and predictions for success
- they also underestimate the likelihood of bad outcomes over which they have no control
E2D. Criticisms of behavioural finance (page 16)
- that it has little use in forecasting the markets, since the many factors of human behaviour cannot be quantified and so will not enable an individual investor to earn abnormal returns
- critics believe that behavioural finance is a collection of explanations and anomalies which will eventually be priced out of the market
Chapter 10 Key Points (pages 17 & 18)
MANAGEMENT OF PORTFOLIO RISK
- MPT suggests that portfolios can be constructed that maximise returns and minimise risk by carefully choosing different investments
- most commonly used measure of risk is volatility. This is measured by standard deviation
- the greater the SD the greater the risk (and visa versa)
- the overall risk of a portfolio can be reduced by diversification such as
1. combining different asset classes within a portfolio
2. holding a variety of investments in each asset class - the effectiveness of diversification in reducing a portfolio’s risk depends on the degree of correlation between the investments
- the risk for individual securities has two components:
1. systematic or market risk (can’t be diversified away)
2. non-systematic or investment specific risk - the sensitivity of an investment in relation to the market can be measured by Beta
Chapter 10 Key Points (pages 17 & 18)
CONTINUED
THE EFFICIENT FRONTIER
- represents a set of portfolios which have the maximum rates of return for each given risk level
CAPM
- is a model that derives the theoretical expected return for a security as a combination of the return on a risk-free asset and compensation for holding the risky asset
- CAPM is based on a number of assumption
MULTIFACTOR MODELS
- allow for different sensitivities to different macro-economic and fundamental factors and the identification of each factor’s contribution to the security’s return
- Arbitrage Pricing Theory (APT) is based on the assumption that there are a number of major macro-economic and fundamental factors that influence security prices
LIMITATIONS OF MODELS
- Models based on MPT have failed to explain investor and market behaviour, especially in extreme conditions
- according to the Efficient Market Hypothesis (EMH), in an open and efficient market, security prices fully reflect all available information and prices rapidly adjust to any new information
- if the EMH is correct, it makes sense to invest in tracker/index funds which mirror the performance of the market
- behavioural finance is an area of financial research that explores how emotional and psychological factors affect market decisions
- it attempts to explain market anomalies and other market activity that is not explained by the traditional finance models
- behavioural finance highlights certain inefficiencies caused by the irrational way in which investors react to new information as being causes of market trends, and in extreme cases, of speculative market bubbles and crashes
