Financial Risk Management summary
Week 1:
Slides:
• Key risk measures
o Value-at-risk and expected shortfall
o Credit risk
o Liquidity risk
• Nature of banking CHIEF INVESTMENT OFFICE AT JPM
o Commercial banking
The imbalance in deposits ($1.128 trillion) and loans
▪ Taking deposits, making loans (wholesale of retail) ($724 trillion) leads to excess deposits
▪ Money center banks operate in the wholesale market and often fund themselves JPMby borrowing
needed to profitably and safely invest these funds
o Investment banking Chief Investment Office (CIO) was responsible
▪ Investment
Raising debt and equity for companies, advise on m&a, restructurings, trading, fixed in Treasury bonds and other investment grade
etc. income securities
• A corporation is insolvent when it is not able to pay its debt
Additionally, CIO is responsible for reducing credit risk
o Two tests Default risk of borrowers (via loans or securities)
▪ Do liabilities exceed assets? Using credit default swaps (CDS)
▪ Can it raise new equity (from private investors)
CREDIT MARKETS RALLIED IN JAN 2012
• Equity is an example of Tier 1 capital
• Subordinated long term debt is an example of Tier 2 capital 17
• Debt financing is cheap, deposits → low interest
o Moreover, debt financing is subsidized by the government → deposit insurance
• Fortress Balance Sheet
o 8% equity ratio
o Large share of short-term debt
CDSS AT JPM
o Small share of loans, less than 1/3 of assets
Credit default swaps
▪ Increasing focus on trading assets
Insurance contract protecting against a borrower’s default
• Differences in accounting standards (IFRS vs GAAP) are mostly due to the treatment of derivatives Buyer (long protection, short credit risk) pays premiums,
o Extensive netting allowance under GAAP CIO aggregate longsum
receives a lump in protection losses
at a default event
• The Chief Investment Officer is responsible for reducing credit Seller (short protection, long credit risk) receives
premiums, pays a lump sum at a default event
21
o Default risk of borrowers (via loans or securities) Could be used for hedging (if the buyer is exposed to the
o Using credit default swaps (CDS) credit risk) or speculation on changes in creditworthiness
• Credit Default Swap
o Insurance contract protecting against a borrower’s default
o Buyer (long protection, short credit risk) pays premiums, receives a lump sum at a REACTION PLAN
Overall strategy: buy INmore
JANprotection
2012 if the economic
default event outlook worsens, buy less if the outlook improves
o Seller (short protection, long credit risk) receives premiums, pays a lump sum at a default Toevent
stop losses, in view of improving economy, take 18
o Could be used for hedging (if the buyer is exposed to the credit risk) or speculation on changes
more creditin creditworthiness
risk. Either of:
o Overall strategy 1. Allow CDSs to expire (but typically long-term, 10 yrs)
▪ Buy more protection if the economic outlook worsens, less if the outlook improves
2. Sell the same protection that was bought before (costly)
• Three types of traders
3. Add credit risk of other indices/tranches
o Hedgers
o Speculators Credit rating Protection Risk Exposure Premiums
o Arbitrageurs High yield Buy Short Pay
Investment Grade Sell Long Receive
• To stop losses, in view of improving the economy, take more credit risk. Either of:
o Allow CDSs to expire (but typically long-term, 10 yrs) Credit
o Sell the same protection that was bought before (costly) 22
o Add credit risk of other indices/tranches
• With rallying credit market, gains on investment grade securities were below losses on high-yield assets
o Sell more protection, take more credit risk
1
, • Other financial institutions
o Insurance companies
▪ Longevity and mortality risk, catastrophe risk
o Pension funds
▪ Defined-benefit plans, defined-contributions plans
o Hedge and mutual funds
▪ Constraints on investment, fees
Book week 1, chapter 2 and 5
• Net interest income
o The excess of the interest earned over the interest paid (income statement)
o For banks it is important that net interest income remains roughly constant regardless of movements in interest
rates of different maturities
• Loan losses
o Loans that have default, and this amount tends to fluctuate from year to year with economic conditions
• Non-interest income
o Consists of income from all the activities of the bank other than lending money
▪ This includes fees for the services the bank provides for its clients
• Non-interest expense
o This consists of all expenses other than interest paid
▪ It includes salaries, technology-related costs, and other overheads
o Non-interest expenses tend to increase over time in case of large businesses, unless they are managed carefully
• One measure of the performance of a bank is return on equity (ROE)
o When ROE is too low, the company can choose to buy back shares and replacing them with deposits so that equity
financing is lower and ROE is higher
2
,• Operational risk
o Large company losses due to litigation, business disruption, employee fraud, etc
• Equity provides the best protection against adverse events
• Subordinated long-term debt-holders rank below depositors in the event of default, but subordinated debt does not provide a
good cushion for the bank as equity because it does not prevent the bank’s insolvency
• The united states is particularly prone to bank failures with its large number of small banks
• The deposit insurance program, founded in 1933, did a good job until the 80’s. Bank runs took place, because of the way
interest rate risk was managed, and because of a reduction in oil and other commodity prices, which led to many loans to oil,
gas, and agricultural companies not being repaid
o Another reason, banks took more risk due to the deposit insurance → moral hazard
▪ Moral hazard: the possibility that the existence of insurance changes the behaviour of the insured party
• The main activity of investment banking is raising debt and equity financing for corporations and governments
o Originating the securities, underwriting them, and then placing them with investors
• Hybrid security/instrument → convertible bond
• Two types of arrangement between company and investment bank to issue shares
o Best efforts (IPOs are mostly on best efforts basis)
▪ The investment bank does as well as it can to place the securities with investors and is paid a fee that
depends, to some extent, on its success
o Firm commitment basis
▪ The investment bank agrees to buy the securities from the issuer at a particular price and then attempts
to sell them in the market for a slightly higher price
• Investment banks also advise companies on M&A related topics
• Investment banks also suggest steps their clients should take to avoid a merger or takeover, so called poison pills
o A potential target adds to its charter a provision where, if another company acquires one third of the shares, other
shareholders have the right to sell their shares to that company for twice the recent average share price.
o A potential target grants to its key employees stock options that vest (i.e., can be exercised) in the event of a
takeover. This is liable to create an exodus of key employees immediately after a takeover, leaving an empty shell
for the new owner.
o A potential target adds to its charter provisions making it impossible for a new owner to get rid of existing directors
for one or two years after an acquisition.
o A potential target issues preferred shares that automatically get converted to regular shares when there is a change
in control.
o A potential target adds a provision where existing shareholders have the right to purchase shares at a discounted
price during or after a takeover.
o A potential target changes the voting structure so that shares owned by management have more votes than those
owned by others.
• There is a potential conflict of interest between investment banking and commercial banking, the reason they were split
o For example
▪ A bank, when it lends money to a company, often obtains confidential information about the company. It
might be tempted to pass that information to the M&A department of the investment bank to help it
provide advice to one of its clients on potential takeover strategies
o The department within the bank are split through internal barriers known as Chinese Walls
▪ These internal barriers prohibit the transfer of information from one part of the bank to another when
this is not in the best interest of one or more of the bank’s clients
• The Originate to Distribute model – or Securitization
o This involves the bank originating but not keeping loans. Portfolios of loans are packaged into tranches that are then
sold to investors
o By securitization of the bank’s loans it gets them off the balance sheet and frees up funds to enable it to make more
loans. It also frees up capital that can be used to cover risks being taken elsewhere in the bank
o A bank earns a fee for originating a loan, and a further fee if it services the loan after it has been sold
• Central bank regulators require banks to hold capital for the risk they are bearing, namely
o Credit risk
▪ The risk that counterparties in loan transactions and derivative transactions will default
o Market risk
▪ Arises primarily from the bank’s trading operations. It is the risk relating to the possibility that
instruments in the bank’s trading book will decline in value
o Operational risk
▪ Often considered to be the biggest risk facing banks, is the risk that losses are created because internal
systems fail to work as they are supposed to or because of external events
• Economic capital
o The capital the bank thinks it needs based on own models rather than prescribed by regulators
3
,Chapter 5 Trading in Financial Markets
• Margin
o Collateral (usually in the form of cash) that an exchange requires from traders to guarantee that they will not walk
away from their obligations
o It has become an important feature of over-the-counter (OTC) markets
• There are two markets for trading financial instruments
o Exchange traded markets
▪ The role of the exchange markets is to define the contracts that trade and organize trading so that
market participants can be sure that the trades they agree to will be honoured
o OTC
▪ The OTC market is a huge network of traders who work for financial institutions, large corporations, or
fund managers
▪ It is used for trading many different products including bonds, foreign currencies, and derivatives
▪ Key advantage of OTC
• The terms of a contract do not have to be those specified by an exchange, market participants
are free to negotiate any mutually attractive deal
▪ Trades in OTC are typically much larger than trades in the Exchange traded markets
• Clearing houses
o Exchange-traded contracts are administered by a clearing house
o The clearing house in effect stand between the two traders so that Trader X is selling the contracts to the clearing
house and Trader Y is buying the contract from the clearing house
▪ Advantage
• Trader X does not need to worry about the creditworthiness of trader Y, and vice versa
o The clearing houses make use of the Margin requirement, and failures by clearing houses are rare
• Derivative
o A derivative is an instrument whose value depends on (or derives from) other more basic market variables
▪ A stock option for example, is a derivative whose value is dependent on the price of a stock
o Derivatives trade in both the exchange-traded and OTC markets
• Compression
o This is a procedure where two or more counterparties restructure transactions with each other with the result that
the underlying principal is reduced
• Plain vanilla products
o Standard, or commonly traded, contracts in derivatives markets
▪ Forwards, futures, swaps and options
• Forward contract
o An agreement to buy an asset in the future for a certain price
o Traded in the OTC market
o One of the parties to a forward contract assumes a long position and agrees to buy the underlying asset on a certain
specified date in the future for a certain specified price, the other party assumes a short position and agrees to sell
the asset on the same date for the same price
o Forward contracts are used to hedge foreign currency risk
o A long forward contract can lead to a payoff that is a gain or a loss
▪ The payoff is the spot price of the assets underlying the forward contract minus the agreed delivery price
for the assets
• Futures contract
o Like forward contracts, are agreements to buy an asset at a future time
o Unlike forward contracts, futures are traded on an exchange, which means that the contracts that trade are
standardized
▪ The exchange defines the amount of the asset underlying one contract, when delivery can be made,
exactly what can be delivered, and so on.
o Price is determined by supply & demand
o An advantage of a futures contract, or other contracts traded on an exchange market, is that it is easy to close out a
position.
▪ Go long and short
o This is the reason that futures contracts are usually closed out before the delivery month is reached, un like forward
contracts which lead to an actual delivery
o Cleared on an exchange clearing house
• The futures price is usually very similar to the forward price
• Difference between the two contracts
o A futures contract is settled daily, whereas a forward is settled at the end of its life
• Swaps
o An agreement between two companies to exchange cashflows in the future
• Options
o Are traded both on exchanges and in the OTC market
o Two types
▪ Call options
• Give the holder the right to buy the underlying asset by a certain date for a certain price
▪ Put options
4
, o Four types of trades in the option market
▪ Buying a call
▪ Selling/writing a call
▪ Buying a put
▪ Selling/writing a put
o Buyers are referred to as having long positions, sellers are referred to as having short positions
• Important interest rate options that trade in the OTC market are
o Caps
▪ Call option series on floating rates
o Floors
▪ Put option series on floating rates
o Swap options
• Instruments such as futures, forwards, swaps, and options, can be used for
o Hedging
▪ Reducing risks
o Speculation
▪ Taking risks
o Arbitrage
▪ Attempting to lock in a profit
Slides week 2:
• Financial institutions manage risk in the following way
o Risk decomposition
▪ Tackles risk one by one
o Risk aggregation
▪ Aims to get rid off non-systematic risks with diversification
• The whole portfolio
o Note
▪ In practice financial institutions use both approaches
• Question asked in VAR
o What loss level is such that we are X% confident it will not be exceeded in N business days
• Market risk is calculated on a 10-day VAR of 99%
• Credit risk and operational risk are based on a one-year 99.9 % VAR
• Advantages of VAR
o It captures an important aspect of risk in a single number
o It is easy to understand
o Is asks the simple question ‘how bad can things get’
• The question asked in Value At Risk
o What loss level is such that we are X% confident it will not be exceeded in N Business days?
• In the distribution scheme, gains are notated as negative numbers
• VAR importance
o Regulators base the capital they require banks to keep on VaR
o The market-risk capital has traditionally been calculated from a 10-day VaR estimated where the confidence level is
99%
o Credit risk and operational risk capital are based on a one-year 99.9% VaR
• VaR formula under normal distribution of gains
o 𝑉𝑎𝑅 = −(𝜇 + 𝜎𝑁 −1 ( 1− 𝑋) )
• VaR formula under normal distribution of losses
o 𝑉𝑎𝑅 = 𝜇 + 𝜎𝑁 −1( 1 − 𝑋)
• VaR is the loss level that will not be exceeded with a specified probability (how bad things can go)
• ES is the expected loss given that the loss is greater than the VaR level (also called C-VaR and Tail Loss) → if things go bad, what
is the expected loss?
• Two portfolios with the same VaR can have very different expected shortfalls
• Coherent risk measures
o R(L) denotes risk associated with loss L
▪ Properties of coherent risk measure
• Monotonicity
o If one portfolio always produces a worse outcome than another, its risk measure
should be greater
▪ 𝑅 𝐿1 <𝑅 𝐿2 if𝐿1 <𝐿2
• Translation invariance
o If we add an amount of cash K to a portfolio its risk measure should go down by K,
since you still have the money (cash)
▪ 𝑅𝐿+𝐾=𝑅𝐿−𝐾
5
, • Homogeneity
o Changing the size of a portfolio by , should result in the risk measure being
multiplied by
▪ 𝑅 𝜆𝐿 =𝜆𝑅 𝐿 for every 𝜆 > 0
• Subadditivity
o The risk measures for two portfolios after they have been merged should be no
greater than the sum of their risk measures before they were merged, due to
diversification for example
▪ 𝑅𝐿1 +𝐿2 ≤𝑅𝐿1 +𝑅(𝐿2 )
o VaR satisfies the first three conditions, but not the fourth
o VaR is not a coherent measure because it may violate the subadditivity criterion which reflects the idea that risk can
be reduced by diversification
o If a regulator uses a non-subadditive risk measure in determining the regulatory capital for a financial institution,
that institution has an incentive to legally break up into various subsidiaries in order to reduce its regulato ry capital
requirements
o Expected Shortfall satisfies all four conditions
• There is no advantage of ES over VaR in the real world, with the same distribution
• Rest of summary is in slides below
6
,7
,Book week 2 & 3
Chapter 12 Value at Risk and Expected Shortfall
• The Value at Risk (VAR) and Expected Shortfall (ES) are attempts to provide a singl e number that summarizes the total risk in a
portfolio
o Used for the setting of capital requirements for market risk, credit risk, and operational risk
• When using the value at risk measure, we are interested in making a statement of the following form
o We are X percent certain that we will not lose more than V dollars in time T
▪ Variable V, is the Var of the portfolio
• Two parameters
o Time horizon T
o Confidence level X percent
o It is the loss level during a time period of length T that we are X% certain wi ll not be exceeded
• VAR can be calculated from either the probability distribution of gains during time T or the probability distribution of losses
during time T
o Losses are negative gains, gains are negative losses
• VAR is equal to the loss at the Xth percentile of the distribution
• X% VaR is the amount we do not expect to lose in (1-x)% of the time
o Only the x% at the left hand side → negative influences (loss) to the security
• Purpose of Value at Risk
o Information reporting
o Resource allocation
o Performance evaluation
o Informative calculation
• Banks have capital reserves based on VaR
o Liquid assets are held to back the VaR in case of losses
• Relevance of VaR
o Information hedging positions
o Capital risk can be analysed → easy to cross section
▪ On portfolio
▪ By asset class
▪ By individual manager
• Drawback of VaR
o When VaR is used in an attempt to limit the risks taken by a trader, it can lead to undesirable results
• Expected Shortfall is also known as conditional value at risk, conditional tail expectation or expected tail loss
• To calculate ES it is necessary to calculate VaR first
o ES is the expected loss during time T conditional on the loss being greater than the VaR
• Expected Shortfall is the expected loss during time T conditional on the loss being greater than the VaR
o It ALWAYS recognizes the benefits of diversification
▪ Although it doesn’t have the simplicity the VaR has, it is more difficult to understand, and back-testing Is
more difficult
• Back-testing
o A way of looking at historical data to test the reliability of a particular methodology
for calculating a measure
• The coherent properties a risk measure should have
o Monotonicity
▪ If a portfolio produces a worse result than another portfolio for every state of the world, its risk measure
should be greater
• If one portfolio always performs worse than another portfolio, it clearly should be viewed as
more risky and require more capital
o Translation invariance
▪ If an amount of cash K is added to a portfolio, its risk measure should go down by K
• The cash provides a buffer against losses and should reduce the capital requirements by K
o Homogeneity
▪ Changing the size of a portfolio by factor labda while keeping the relative amounts of different items in
the portfolio the same should result in the risk measure being multiplied by labda
• If we double the size of a portfolio, presumably we should require twice as much capital
o Subadditivity
▪ The risk measure for two portfolios after they have been merged should be no greater than the sum of
their risk measures before they were merged
• When we aggregate two portfolios, the total risk measure should either decrease or stay the
same
8
, • Var satisfies the first three condition
• Risk measures satisfying all four conditions are said to be coherent
• A risk measure can be characterised by the weights it assigns to percentiles of the loss distribution
o VAR gives a 100% weighting to the Xth percentiles and zero to other percentiles
o ES gives equal weight to all percentiles greater than the Xth percentile and zero weight to all percentiles below the
Xth percentile
• For VaR and ES, a user must choose two parameters
o The time horizon
o The confidence level
• 𝑉𝑎𝑅 = 𝜇 + 𝜎𝑁 −1(𝑋)
o X is the confidence level
o N-1 is the inverse cumulative normal distribution
𝑌2
(− )
• 𝐸𝑆 = 𝜇 + 𝜎( (𝑒 2 /(√2𝜋(1− 𝑋) )
o Y is the Xth percentile point of the standard normal distribution
▪ This shows that when is assumed to be zero, ES, like VaR, is proportional to
• When positions are very liquid and actively traded, it makes sense to use a short time horizon
• A longer timer horizon might not be meaningful because of changes in the composition of the portfolio
• Whatever the application, when market risks are being considered, analysts often start by calculating VaR or ES for a time
horizon of one day
• 𝑇 − 𝑑𝑎𝑦 𝑉𝑎𝑅 = 1 − 𝑑𝑎𝑦 𝑉𝑎𝑅 ∗ √𝑇
• 𝑇 − 𝑑𝑎𝑦 𝐸𝑆 = 1 − 𝑑𝑎𝑦 𝐸𝑆 ∗ √𝑇
o These formulas are exactly true when the changes in the value of the portfolio on successive days have independent
identical normal distributions with mean zero
o The standard deviation of the sum on T independent identical distributions is SQRT(T) times the standard deviation
of each distribution
o The sum of the independent normal distributions is normal
Chapter 13
• Historical simulation
o It involves using the day-to-day changes in the values of market variables that have been observed in the past in a
direct way to estimate the probability distribution of the change in the value of the current portfolio between today
and tomorrow
o Steps
▪ Identify market variables affecting the portfolio
• Also called ‘risk factors’
o Such as exchange rates, interest rates, stock indices, volatilities and so on
▪ Collect the data of the last 501 days
• Providing 500 alternative scenarios, of what can happen between today and tomorrow
• Denote the first day for which we have data, Day 0, the second day as Day 1, and so on
• Scenario 1 is where the percentage changes in the values of all variables are the same as they
were between Day 0 and Day 1
o Scenario 2 is where they are the same as between Day 1 and Day 2, and so on
▪ For each scenario, the dollar-change in the value of the portfolio between today and tomorrow is
calculated
• This defines the probability distribution for daily loss (with gains counted as negative losses) in
the value of the portfolio
o The 99-percentile of this distribution can be estimated as the fifth worst outcome
(1/500)
▪ We are 99% certain that we will not take a loss greater than the VaR
estimate if the percentage changes in the market variables in the past
500 days are representative of what will happen between today and
tomorrow
▪ ES is the average loss conditional that we are in the 1% tail of the loss distribution
• VaR is estimated as the fifth worst loss
• ES can be estimated by averaging the losses that are worse than VaR, that is, the four worst
losses
o Algebraically:
• Vi
o Value of a market variable on Day i and suppose that today is Day n
• The i-th scenario in the historical simulation approach assumes that the value of the market
variable tomorrow will be
𝑣
▪ 𝑉𝑎𝑙𝑢𝑒 𝑢𝑛𝑑𝑒𝑟 𝑖th Scenario = 𝑣𝑛 𝑖
𝑣𝑖 −1
• For some variables such as interest rates, credit spreads, and volatilities, actual rather than
percentage changes in market variables are considered. It is then the case that the equation
becomes:
▪ 𝑉𝑎𝑙𝑢𝑒 𝑢𝑛𝑑𝑒𝑟 𝑖th Scenario = 𝑣𝑛 + 𝑣𝑖 − 𝑣𝑖−1
9
, • Do not forget to rank the outcomes from highest loss to lowest, and gains are negative losses
▪ To arrive at the 10-day 99% VaR, it is often calculated as SQRT (10) times the one-day 99% VaR, which is
the 1% place in the ranking, if 500, number 5
• The VaR on any given day is calculated on the assumption that the portfolio will remain unchanged over the next business day
• The market variables (or risk factors) that have to be considered in a VaR calculation include exchange rates, commodity prices,
and interest rates.
o In the case of interest rates, a financial institution typically needs term structures describing zero-coupon LIBOR,
Treasury, and OIS interest rates in each of a number of different currencies in order to value its portfolio
• Expected Shortfall
o To calculate expected shortfall using historical simulation, we average the losses that are worse than VaR, so the top
4 (with 99% of 500 scenarios)
• Stressed VaR and stressed ES
o The calculations given so far assume that the most recent data are used for the historical simulation on any given
day
▪ For example, when calculating VaR and ES for the four-index example we used data from the
immediately preceding 501 days
• Referred to as current VaR and current ES
o For the stress test
▪ A financial institution searches for the 251-day period that would be particularly stressful for its current
portfolio
• The data for that 251-day period then play the same role as the 501-day period in the
example above.
• Accuracy of VaR
o The historical simulation approach estimates the distribution of portfolio changes from a finite number of
observations
▪ As a result, the estimates of percentiles of the distribution are subject to error
• The standard error of the estimate is
1
o √(1− 𝑞)𝑞
𝑓 (𝑥) 𝑛
▪ Where n is the number of observations and f(x) is an estimate of the
probability density function of the loss evaluated at x
• Extreme value theory
o The extreme value theory (EVT) is the term used to describe the science of estimating the tails of a distribution.
▪ EVT can be used to improve VaR or ES estimates and to help in situations where analysts want to
estimate VaR with a very high confidence level.
• It is a way of smoothing and extrapolating the tails of an empirical distribution
o Key result in EVT shows that the tails of a wide range of different probability distributions share common properties
o Generalized Pareto (cumulative) distribution
−1
𝑦
▪ 𝐺𝜉,𝛽 (𝑦) = 1 − [1 + 𝜉 ] 𝜉
𝛽
• The distribution has to parameters that have to be estimated from the data
o These are Xi and Beta
▪ XI is the shape parameter and determines the heaviness of the tail of
the distribution
▪ Beta is a scale parameter
o When the underlying variable v has a normal distribution, Xi=0
▪ As the tails of the distribution becomes heavier, the value of Xi
increases.
• For most financial data, Xi is positive and in the range of 0.1
to 0.4
o How to estimate Xi and Beta?
▪ They can be estimated using maximum likelihood methods
• The standard error for a VaR that is estimated using historical simulation tends to be quite high. The higher the VaR confidence
level required, the higher the standard error.
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