Measurements of investment risk Flashcards
1
Q
How do you calculate Beta?
A
A stocks beta equals covariance over variance
Variance is STDEV squared
=0.005 / (0.05^2)
2
Q
A
Beta = (0.4 * 0.45) / 0.16 = 1.125
3
Q
What is the covariances of a stock?
A
Covariances of a stock = correlation of stock to market * standard deviation of stock
4
Q
How do you find the monthly beta?
A
Monthly beta = (monthly STEV of stock / monthly STDEV of market)
Beta is 0.60 x (6% / 3.2%) = 1.125
5
Q
What is unlevered beta?
A
- Unlevered beta removes the financial effects of leverage.
- BU = BL / (1+D/E)
- BL is the firm’s beta with leverage, D/E is the company’s debt/equity ratio, BU is the unlevered beta; i.e. a company without any debt.
- BU = 1.4 / (1+0.6) = 0.875
- Now we add 15% leverage
- BL = BU X 1.15 = 1
6
Q
What are the main risk of asset classes and strategies?
A
- Liqudity:
- The corporate bond market is not as liquid as the gilt market. Difficult economic conditions can suppress the market more. Less liquidity can mean higher transaction costs.
- Credit risk:
- There is greater risk that the company might not be in a position to repay the loan, leading to a credit downgrade, or in the extreme that the issuer defaults on its debt obligations. Yields tend to be higher in recognition of this increased risk.
- Re-investment risk:
- Corporate bonds are oftern issued with a shorter maturity than gilts. There is the risk that yieldsare not as high when reinvesting the proceeds into other corporate bonds. Shorter maturities can also mean more portfolio turnover.
- Duration risk:
- How much a change in the interest rate will change the price and return of a bond.
- Call risk:
- If a corporate bond is callable, then the issuing company has the right to buy the bond back after a time period. If an investor holds a high yielding bond and interest rates decline, a company with a call option will want to call the bond in order to issue new bonds at lower interest rates.
- Bond Covenant risk:
- A bond covenant is the legally binding term to the agreement between a bond issuer and a bond holder that sets out the deal for bond holders when, for example, there is a change in company ownership, a major change in capital structure, or governance.
- Event risk:
- Risk that a natural disaster or regulatory change will cause an abrupt downgrade in a corporate bond. Event risk tends to very by industry sector.
7
Q
What is the Portfolio Variance and STDEV?
A
Portfolio Variance =
Covariance =
Portfolio STDEV = square root of variance
8
Q
How do you find the annualised STDEV?
A
When annualising a standard deviation take the square root of the number of observations per year. In the case of quarterly then we use for. Eq if you have quarterly standard deviation of returns of 0.05999*sqrt4 = 12%.
9
Q
What is Kurtosis?
A
- Implies that for much of the time the market moves very little, must less predicted by a normal distribution.
- So a perfectly normal distribution would have kurtosis of 0.
- A postive kurtosis shows that there is a greater severity of large negative returns than predicted by a normal distribution.
10
Q
What is Skewness?
A
- Perfect normal distribution would have a skewness of 0
- Negative skewness shows that the mean is to the left of the median.
- Negative implies that large negative returns occur more freuent and the severity of negative returns are larger than predicted by normal distribution.
11
Q
What is value at risk?
Annual standard deviation of returns on a portfolio is 9.5% what is the 95% VAR.
And what would you say if the annualised return exceeds the 99.5% VAR level
A
- VAR is the variability of loss of a portfolio and takes a probabilistc approach to how much may be lost on a bad day.
- So it is the % probability that losses will be larger than a given amount given the distribution of returns over a past period.
- Oftern VAR is expressed as a maximum % loss in the value of a portfolio that occurs on 95% of loss occasions.
- Answer:
- The worst 5% of returns is the 90% level under the 2-tail normal distribution, split 5% worst and 5% best.
- VAR = 1.645 x SD
- = 1.645 X 9.5 = 15.63 below the mean
- If the annualised return exceeds 99.5% VAR this is a 1 in 200 quarter even that is statistically highly unlikely and may be caused by poor management.
12
Q
What is CVaR
A
- CVaR asks if i do end up in the tail of say 5% what is the average loss I will incur.
- Adding up all the possible losses in the bottom 5% and took the average, this is CVaR.
- It is the expected probability fall below a certain level.
- Also expressed as the expected return on the portfolio in the worst 5% of the cases.
- It is a measure of tail loss.
- CVaR is the average of mean loss of the 5% of worst outcomes.
13
Q
What is semi-deviation
A
- Take absolute value of below zero return and sqaure.
- Then sum the square and divide it by number of observations.
- This is the variance.
- Take the square root of the variance to find the semi-deviation.
14
Q
What is the difference between STDEV and Beta?
A
- STDEV is a measure of total risk, it measures the volatility of an investment returns and reflects the volatility of the underlying markets plus the risk the manager has taken against the market by making active decisions.
- STDEV indicates the probability, if we assume normally distributed returns, of a return falling in a specifc range. For instance, approx 68.3% of the returns will fall between the average return plus or minus one STDEV. There is a 95.5% probability that returns will lie between two standard deviation of the average return.
- Beta measures a component of total risk. It measures the systemic risk or market risk of the stock as opposed to the specfic or unsystematic risk. The average beta of stocks in the market is one, so if a stock has a beta significantly higher than one, it is sensitive to the market. A stock with a beta of less than one will tend to dampen market moves.
