Measuring & Managing Market Risk Flashcards
What is market risk?
- risk that arises from market movements (eg. Stock prices, interest rates, and etc.)
What is risk management?
- risk management: process of identifying and measuring risk and ensuring risk taken is in line with desired risk
What does 5% VaR of a portfolio is $2.2 Million over a one day period mean?
- 5% of the time losses would be at least $2.2 million
What percentage of VaR is equivalent to a 1 standard deviation move, 2.33 standard deviation move, and 1.65 standard deviation move?
- 1 standard deviation movement is equal to 16% VaR (below the mean)
- 2.33 standard deviation movement (below the mean) is equal to 1% VaR
- 1.65 standard deviation movement (below the mean) is equal to 5% VaR
What are 2 statements regarding VaR?
- VaR doesn’t not give a likelihood for losing a specific amount
- VaR is not expected loss it’s a minimum loss
What is Value at Risk (VaR)?
- minimum loss expected a certain percentage of time over a given time period
What are the 3 methods to estimate VaR?
- parametric method
- historical simulation method
- Monte Carlo simulation method
Regardless of the VaR method used what are three key steps in the estimation procedure?
- define risk factors with risk decomposition (factors such as equity risk, currency risk, etc.)
- gather historical data for each risk factor
- use data to estimate VaR using a preferred methodology
What are 2 other different names for the parametric method of VaR?
- analytical method
- variance - covariance
How can a normally distributed return be converted to a Z-distribution?
z = (R- U)/ O
R = return
M = mean
O = standard deviation
What is the formula for expected return of 2 assets in a portfolio?
E (Rp) = W1* R1 + W2* R2
What is the formula for standard deviation of a 2 asset portfolio?
O = sqrt ((W1^2* O1^2 + W2^2* O2^2) + (2 * W1 * W2 * P* O1 * O2)
W1 = weight of asset 1
O1 = standard deviation of asset 1
W2 = weight of asset 2
O2 = standard deviation of asset 2
P = correlation coefficient of asset 1 & 2
What is the formula for VaR under the parametric method?
(ERp - 1.65*Op) (-1) * portfolio value
ERp = expected return of portfolio
1.65 = standard deviation equivalent of VaR (eg. if VaR is 1% standard deviation would be 2.33 instead of 1.65)
Op = standard deviation of portfolio
How would you calculate VaR using the historical method?
- gather historical data and organize largest loss to largest gain
- if you want 5% VaR then you would find the bottom 5th percentile out of all the data
What is the Monte Carlo simulation method of VaR?
- Monte Carlo simulation method generates millions of random values or returns, then you use the historical simulation method to determine VaR (the historical method puts returns in largest loss to largest gain then you find the percentile)
What is conditional VaR?
- expected loss if VaR is exceeded (if returns are worse then expected then average returns of the worst losses would be conditional VaR)
What is incremental VaR?
- measures the impact of changing a positions size within a portfolio
What is marginal VaR?
- used to determine each individuals position contribution to overall VaR
What is relative VaR?
- indicates amount a portfolio deviates from its benchmark
What are sensitivity risk measures?
- sensitivity risk measures examine impact on performance from a change in just one underlying risk factor
What is equity exposure measure (sensitivity risk measure)?
- beta is primary measure to gauge exposure to equity risk. Use CAPM
What are the 2 fixed income exposure measures (sensitivity measures)?
- duration
- convexity
What is the duration fixed income sensitivity measure formula?
change in B/ B = -D (change in y / 1+y)
B = bond price
-D = duration
y = yield
- percentage change in bond price for a given change in yield
What is the convexity fixed income sensitivity measure formula?
change in B/ B = (-D (change in y / 1+y))+ (1/2 C) (change in y^2/(1+y)^2)
B = bond price
-D = duration
y = yield
C = convexity
What are 3 options risk measure (sensitivity risk measures)?
- delta
- gamma
- vega
What is delta and the formula for delta?
- delta: theoretical estimate of how much an option’s value may change given a $1 move UP or DOWN in the underlying security
Delta = change in value of option / change in value of underlying
What will a delta range from for call options and out options?
- call options: 0-1, 0 means option doesn’t change when value of underlying changes
- put options 0 to -1, 0 means option doesn’t change when value of underlying changes
What is gamma and the formula?
- gamma: rate of change between options delta and underlying asset prices
gamma = change in delta / change in value of underlying
What is Vega and formula?
- vega: measurement of an option’s price sensitivity to changes in the volatility of the underlying asset
vega = change in value of option/ change in volatility of underlying asset
What are the 3 second order formulas for delta, gamma, and vega to get a more accurate estimate for change in price of an option?
delta: option delta = change in option price * change in underlying price
gamma: option delta = change in option price * change in underlying price + (1/2*gamma of call * (change in value of underlying)^2)
vega: option delta = change in option price * change in underlying price + (1/2*gamma of call * (change in value of underlying)^2) + vega * (change in volatility)
What are the 2 types of scenario risk measures?
- historical scenarios: measure portfolio return if markets repeat themselves
- hypothetical scenarios: how what ifs would impact a portfolio
What is reverse stress testing?
- reverse stress testing: targeting a portfolios most significant exposures
What must managers seek to establish suitable risk limits?
- if constraints are too tight returns will likely decrease, if constraints are too loose there is a greater risk of incurring severe losses
What is risk budgeting?
- risk budgeting: sets risk limits for entire firm then allocates firms overall risk budget among sub activities
What are position limits?
- limits on market value of given investment or notional principal amount for derivatives
What are scenario limits?
- place limits on loss in a given scenario, if returns are not within limits corrective action should be taken
What are stop- loss limits?
- requires reduction in size of a portfolio, or its complete liquidation when a loss of a particular size occurs in a specified period
What are 3 factors that influence a market participants preference towards different risk measures?
- degree of leverage: high degree of leverage must have sufficient capital to avoid bankruptcy
- mix of risk factors to which business is exposed: fixed income concerned about interest rate, banks concerned about inflation & bank policies
- account or regulatory requirements:
What are glide path and liability hedge exposures versus generating exposures for pension fund risk measures?
- glide path: gradually moves overfunded or underfunded pension plan to its target funded level
- liability hedging exposures versus generating exposures: portion of assets that can be used to hedge liabilities, while another portion can be used to generate excess returns
What is the difference between ex ante tracking error and ex post tracking error?
- ex ante tracking error: uses current portfolio holdings exposed to the variability of historical markets
- ex post tracking error: measures the variability of historical portfolio holdings in historical markets.
