Past Exam Questions Flashcards
Arguments for using semi-variance as a risk measure
Most investors do not dislike uncertainty of returns as such; rather they dislike the possibility of low returns.
One measure that seeks to quantify this view is downside semi-variance.
Arguments against using semi-variance as a risk measure
- not easy to handle mathematically
- takes no account of variability above the mean
- if returns are symmetrically distributed, semi-variance is proportional to variance - so it gives no extra information
- Semi-variance measures downside relative to the mean rather than another benchmark that might be more relevant to the investor
4 Assumptions of mean-variance portfolio theory
- Investors select their portfolios on the basis of the expected return and variance of that return over a single time horizon
- The expected returns, variance of returns and covariance of returns are known for all assets and pairs of assets.
- Investors are never satiated. At a given level of return, they will always prefer a portfolio with lower variance to one with higher variance.
8 Key arguments against modelling market returns using a Gaussian Random walk
- Market crashes appear more often than one would expect from a normal distribution
- While the random walk produces continuous price paths, jumps or discontinuities seem to be an important feature of real markets
- Days with no change, or very small change, also happen more often than the normal distribution suggests
- Assumption of independent increments is contradicted by empirical evidence of mean reversion and momentum effects
- Assumption of a constant volatility is contradicted by empirical evidence.
- Can be argued that expected returns on shares are likely to vary with bond yields, which contradicts the assumption of a constant mean
- Random walks have a fractal dimension of 1.5, whereas investigations of market returns often reveal a fractal dimension around 1.4
- Markets are often (negatively) skewed.
7 Properties of the one-factor Vasicek model
- incorporates mean reversion
- time homogenous, ie future dynamics of r(t) only depend upon the current value of r(t) rather than what the present time t actually is
- Arbitrage free
- Allows negative interest rates
- Easy to implement since the characteristic functions of all related quantities are available
- Constant volatility
7 Properties of the Cog-Ingersoll-Ross model
- Incorporates mean reversion
- Arbitrage free
- Time homogenous
- Volatility depends on the level of the rates (high when rates are high)
- does not allow negative interest rates
- More involving to implement than the Vasicek model as its linke to the chi-squared distribution
- one-factor model
State 12 limitations of CAPM
- Unrealistic assumptions
- Empirical evidence don’t support it
- Investors don’t always use the same “currency”
- Markets are not always perfect
- Investors don’t always have the same expectations
- Cannot borrow/lend unlimited amounts at the same risk-free rate
- Difficult to check as need to think about investment markets as well as capital markets
- Unrealistic to invest in the market portfolio in practice as so many stocks
Does not consider:
- multiple time periods
- or optimisation of consumption over time
Does not account for:
- taxes
- inflation
- situations in which no riskless asset exists
3 Forms of the Efficient Market Hypothesis
- Strong
- Semi-strong
- Weak
Strong form EMH
Market prices reflect all current information relevant to the stock, including information which is not public
Semi-strong form EMH
Market prices reflect all current, publicly available information relevant to the stockq
Weak form EMH
Market prices reflect all information available in the past history of the stock price
7 reasons why its hard to test any of the 3 EMH forms in practice
- need to make assumptions such as normality of returns / stationarity
- Transaction costs may prevent the exploitation of anomalies, so EMH might hold net of transaction costs
- Allowance for risk - EMH does not preclude higher returns as a reward for risk; however the EMH does not tell us how to price such risks
- Testing strong form EMH is problematic & requires access to info that’s not public
- It can be difficult to define “public information” or to determine exactly when information becomes public
- Impossible to test all of the possible trading rules that might be used by technical analysts
- Assumptions made about how security prices should react to new information may be invalid
4 Axioms of Expected Utility Theorem
- Comparability
- Transitivity
- Independence
- Certainty equivalence
Comparability
An investor can state a preference between all available certain outcomes
Transitivity
If a is preferred to B and B is preferred to C, then A is preferred to C.
Independence
If an investor is indifferent between two certain outcomes, A and B, then he is also indifferent between the following two gambles:
- A with probability p and C with probability (1-p)
- B with probability p and C with probability (1-p)
Certainty equivalence
Suppose A is preferred to B and B is preferred to C.
Then there is a unique probability, p, such that the investor is indifferent between B and a gamble giving a with probability p and C with probability (1-p).
B is known as the certainty equivalent of the gamble.
Non Satiation in terms of U(w)
U’(w) > 0
Risk-neutrality in terms of U(w)
U’‘(w) = 0
2 limitations of using Value at Risk to measure the downside risk in an investment portfolio
- VaR does not illustrate the size of the loss in the tail of the distribution, only the likelihood
- Usefulness of VaR may be limited by a lack of data to determine the tail of the distribution.
3 Main Assumptions of Mean-Variance portfolios
- Investors select their portfolios on the basis of the expected return and the variance of that return over a single time horizon
- The expected returns, variance of returns and covariance of returns are known for all assets and pairs of assets.
- Investors are never satiated. At a given level of risk, they will always prefer a portfolio with a higher returnn to one with a lower return.
3 types of credit risk model
- Structural model
- Reduced-form models
- Intensity-based models
Structural models
Explicit models of a corporate entity issuing both debt and equity.
aim to link default events explicitly to the fortunes of the issuer.
Reduced-form models
Statistical models which use market statistics (credit ratings) rather than specific data relating to the issuer, and give statistical models for their movement.