Topic 1: Context and Overview Flashcards
Define Global Risk Management
- Monitoring of overall market risk of the firm
- Aggregate the risks of all the desks and look at these risks broadly
Key points for Global Risk Management
- Zero exposure is not zero risk
- Markets are not normal
- Correlations between markets during market events increase dramatically
- When it really matters, diversification does not work
- Local measures miss the global risk
- Catastrophic risks are not complex
- The material risks are not always the easiest to explore
Zero exposure is not zero risk
- A hedged portfolio still has residual risks
- Inventory size is correlated to residual risk, because inventory risk is subject to hedging error
- risks unaccountable for will be larger with larger inventory size
Markets are not normal
- Leptokurtosis: fat tails
- general rule of thumb: every financial market experiences one or more daily price moves of 4 SD or more each year.
Correlations between markets during market events increase dramatically
- correlations are relied on for VaR.
- correlations change markedly during major market events.
- scenario analysis can help - postulate a particular market event and its market implications
When it matters diversification does not work
- large market moves are contagious
- correlation between markets is compounded by an increase in volatility across markets
Local measures miss the global risk
- Non linear exposures: exposures that are small at current level of risk factor but grow more than proportionately with changes in risk factor. ie GAMMA
- negative gamma: loss that grows more than proportionately with change in risk factor.
- P/L: make a little, make a little, lose a lot
Catastrophic risks are not complex
- failure of organisational structure
-
Why is recognising the differences between theoretical utility functions important?
An investor with a different degree of risk aversion will see the same investment as having a different required rate of return
The degree of bending in the concave U curve is greater the higher the level of risk aversion
Differences of opinion and risk aversion drive trading activity
Stylised facts and properties of U(W)
1. More Wealth is Better
U(W) property = ?
Words = ?
U’(W) > 0
The utility function slopes upwards
Stylised facts and properties of U(W)
2. You can never have too much wealth (= ‘non satiation’)
U(W) property = ?
Words = ?
U(W) is monotone +ve for all levels of W
The utility function has no maximum, no turning point, never slopes downwards
Stylised facts and properties of U(W)
3. The richer you are the less you care about having more wealth
U(W) property = ?
Words = ?
U’‘(W) < 0
The +ve slope gets smaller as W gets bigger
Stylised facts and properties of U(W)
4. The poorer you are the more you care about having less wealth
U(W) property = ?
Words = ?
U’‘(W) < 0
The +ve slope gets larger as W gets smaller.
Difference between certainty equivalent and E(W):
Certainty equivalent: for sure, definite utility cost
E(W) has risk associated with it. Expectation might not be the actual outcome
The difference between CE & E(W) = investor’s risk premium expressed in dollar terms not percentage (spreadsheet)
Compare certainty equivalent to E(W) for the following:
- risk averse investor
- risk neutral
- risk loving
- risk averse: FV of CE < E(W)
- risk neutral: FV of CE = E(W)
- risk loving: FV of CE > E(W)
certainty equivalent =
W - CE = ?
certainty equivalent =
price that would entice risk averse player to partake
rate that risk free investments would need to offer to provide the same utility score as the risky portfolio
Portfolio is desirable if CE > risk free alternative
CE < W IF you are risk averse.
W - CE = pay to play amount
on a chart of utility, what is described by the degree of bending
bending describes the degree of risk aversion. The greater the degree of bending, the greater the risk aversion
The higher the risk aversion, the higher the required return
A straight line would imply a risk neutral investor
Risk neutrality
- Investor’s utility function is linear
- the investor does not seek risk, and does not exhibit risk aversion
- requires no risk premium for bearing risk
Certainty equivalent
- price that a risk averse player would partake, rate that risk free investments would need to offer to provide the same utility score as the risky portfolio. For sure, definite utility cost
- portfolio will be desirable if CE> risk free alternative.
What is the difference between an investor’s CE and the expected outcome of the bet, E(W)
CE - E(W) = investor’s risk premium expressed in $ terms
Certainty Equivalent vs E(W)
CE < E(W):
CE = E(W):
CE > E(W):
If
CE < E(W): investor is risk averse
CE = E(W): investor is risk neutral
CE > E(W): investor is risk seeking
Law of one price,
Positions that have the same payoff should have the same price
Replicating portfolio for call options
- Delta shares: delta is also sensitivity of the option to a change in share prie
- B (ie dollar amount, representing lending
Dividend yield substitutions in binomial tree:
Stock index: Currency: futures contract: commodity: coupon bond:
Stock index: div yld Currency: foreign risk free rate futures contract: domestic risk free rate commodity: commodity lease rate coupon bond: yield on the bond.
Certainty Equivalent
Definition
Risk seeking, neutral and averse definitions
Definition: the certain amount that is equally preferred to the alternative.
- If CE < expected profits; you are risk averse
- If CE = expected profits; you are risk neutral
- If CE > expected profits, you are risk seeking
Certainty Equivalent calculation
- Convert outcomes to utilities using the utility function
- Calculate the expected outcome E(U)
- Calculate the certainty equivalent,. Use the E(U) result above, to work out what value of W will deliver the same result. This is the CE. eg ln(CE) = ln(W). To find W: EXP(gamble result).
Certainty Equivalent
Definition
Risk seeking, neutral and averse definitions
Definition: the certain amount that is equally preferred to the alternative.
- If CE < expected profits; you are risk averse
- If CE = expected profits; you are risk neutral
- If CE > expected profits, you are risk seeking
