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.