量化金融面试知识点: Market Risk

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问题来源于一份Top 50 Questions related to Market Risk. 试着回答了一部分问题，希望对准备面试有所帮助。

Risk Measures

  1. How would you calculate Value at Risk (VaR)?

    There are three methods to calculate VaR.

    1. Delta-Normal Method (Parametric Method)

      • Assume the distribution of underlying asset returns.
      • Go back on time for over N years and collect asset returns’ data.
      • Fit the data into the assumed distribution and calculate the VaR as the Xth percentile.
      • For example, a one-day 5% VaR is just the 5th percentile of the underlying return’s distribution.

    2. Historical-Simulation Method

      • Assume historical path will be a guidence of what will happen in the future
      • Go back on time for over N years and collect portfolio’s data (close price).
        • Each historical period is considered a scenario
      • Given current portfolio’s value, forecast the next period’s value based on each scenario
      • Once portfolio’s value is calculated for each period, calculate the sample Nth percentile as the VaR

    3. Monte-Carlo Method

      • Assume a stochastic process for each market variable (distribution and parameters)
        • parameters can be estimated from historical data
      • Simulate the data path for all variables of interest
      • Revalue the portfolio by the new market variables and calculate the value difference

      • Calculate the Nth percentile as the VaR value.

      • For example, we can assume all market variables changes are generated from a multivariate normal distribution

      • Then each step will involve generating data from the multivariate distribution and revalue the portfolio based on that

  2. What’s wrong with VaR as a measurement of risk?

    • It does not describe the loss on the left tail. When the return distribution is far from a normal distribution, it does not face real risk
      • Example: short CDS of a 3% default rate with 0 recovery rate bond, 95% VaR is 0 (which doesn’t reflect the risk at all)
    • It is not a coherent measure and is not sub-additive.
      • It means when we combine two positions, we do not always have VaR(C) <= VaR(A) + VaR(B)
      • Example: two short CDS positions with 3% default rate and 0 recovery rate bond:
        one of the bond default rate is 1 - (1 - 3%)*(1 - 3%) = 5.9%, so VaR(C) > Var(A) + VaR(B)
        This contradicts the idea that diversification reduces risks.

  3. What is non-Linear VaR? How would you calculate it?
    Non-linear VaR reflects that the portfolio contains nonlinear derivatives which the payoff or the response to the risk factor is non-linear.
    It is often calculate by using the monte carlo simulation of pricing model.

  4. What is the parametric method of calculating VaR? What are its advantages?
    The parametric method is the delta-normal method described in Q1.
    The advantage is it is simple to calculate. It just need to estimate the joint distribution and
    calculate the portfolio return’s distribution using either linear or nonlinear model.

    • Non-linear model is called: Cornish-Fisher expansion (P448 on John Hull)

  5. What is the historical method of calculating VaR? What are its advantages?
    Second Method described in Q1.
    Advantage is it is a nonparametric method and the historical data determines the joint probability distribution of market variables.

  6. Why would you calculate VaR using Monte Carlo simulations?
    If the portfolio is consisting nonlinear derivatives, such as options, the return profile of the portfolio is non symmetric.
    VaR is very sensitive to the left tail of the distribution so in this case we need to use monte carlo simulation to better model the nonlinear characterics.

  7. What are the challenges in calculating VaR for a mixed portfolio?
    Nonlinearity? [NOT finished yet]

  8. What’s GVAR? How can you calculate it?
    GVAR = Global vector autoregression Model

  9. What is the one-day VaR of a $50m portfolio with a daily standard deviation of 2% at a 95% confidence level? What is the annualized VaR?

    • One day VaR = 50m * 0.02 * 1.96 ~= 2m
    • Annualized VaR = sqrt(252) * 2m = 16 * 2m = 32m

  10. What do you know about extreme value theory?

  11. What is Expected Shortfall? How is it calculated? Why is it considered better than VaR? What are the disadvantages?

    • Expected shortfall is also called conditional value at risk
    • It measures the expected loss under a certain amount.
    • It can be calculated by a list of scenarios.
      • Each scenarios has the probability of occurrence and the return
      • Given a threshold, calculate the probablity of each scenario that happen with odds less than the threshold
      • Cacluate the expected (averaged) loss.
    • Advantage：
      1. It is a coherent measure and a more complete measure of downside risk
        • Reflect the sknewness (asymmetry) and kurtosis (fat tail)
    • Disadvantage:
      1. It treats a large probability of small loss as equivalent to a small probability of large loss
      2. Difficult to forecast

  12. What is incremental default risk?
    Default risk incremental to what is calculated through the Value-at-risk model,
    which often does not adequately capture the risk associated with illiquid products.

Yield Curve

  1. What are the uses of the yield curve?
    Yield curve depicts the relationship between bond yield and its maturities. It is used to:

    1. Forecasting interest rate
    2. Pricing bond
    3. Create strategies to boost total returns

  2. What’s the riskiest part of the yield curve?
    The riskiest part is either a flattening or steepening of the yield curve.
    It reflects yield changing among comparable bonds with different maturities.

  3. What does it mean for risk when the yield curve is inverted?
    When the yield curve is inverted, it is often viewed as an pending economic recession.
    In this case, people tend to have negative view in long term so the price of long term bond is bidding up.

  4. What is the discount factor? How would you calculate it?
    Discount factor is the present value of a unit of currency delivered at a future time T.

  5. What is convexity? How would you calculate it? Why is it important?
    Convexity is the second derivatives of bond price relative to the interest rate.
    Convexity measures the curvature of price-yield curve. It is a key aspect when measure interest rate risk.

  6. What’s the relationship between coupon rate and convexity?
    convexity decrease as coupon rate increase.
    Zero-coupon bond have the highest convexity compared to other bond with the same duration and yield to maturity.

  7. What’s the meaning of duration? Is it constant for all yields?
    Duration is the sentivity of bond price relative to interest rate. (First derivative)
    It is not constant for all yield since price-yield curve has curvature.

  8. What’s the meaning of partial duration?
    It’s also called key rate duration. It measures the bond price change relative to a set of rates with specific maturities.
    It does not assume parallel shift in yield curve.

  9. What are the limits of duration as a risk measure?
    It assumes the parallel shift in yield curve and it ignores the curvature.

  10. How would you decide which discount curve to use to value future cash flows from interest rate swaps?

Questions on quantitative concepts:

  1. Can you explain the assumptions behind Black Scholes?

  2. What’s a volatility smile? Why does it occur? What are the implications for Black Scholes?

  3. What are the Greeks?

  4. How are the main Greeks derived?

  5. What do you know about jump processes?

  6. Should you use implied standard deviation or historical deviation to forecast volatility? Explain your choice.

Hedging

  1. What is delta hedging?

  2. How would you hedge against a particular equity/bond under current market conditions?

  3. When can hedging an options position mean that you take on more risk?

  4. An option is at the money. How many shares of stock should you hold to hedge it?

Questions on particular products:

  1. What is interest rate risk?
    The effect on your portfolio value when interest rate changes.

  2. What is reinvestment risk?
    If you have cash flow generated from your portfolio and the market interest rate is changing, you have the reinvestment risk.
    That means you may have to reinvest your proceedings at a lower/higher market preceding rate.

  3. How do interest rate risk and reinvestment risk interact?
    Reinvestment risk is more likely when interest rates are declining.
    Reinvestment risk affects the yield-to-maturity of a bond,
    which is calculated on the premise that all future coupon payments will be reinvested at the interest rate in effect when the bond was first purchased.

  4. Which bond has the greatest associated interest rate risk? A five year zero coupon bond? Or a five year bond that pays coupons?
    zero coupon bond has the highest duration and thus has the greatest interest rate risk.

  5. Which is more volatile, a 20-year zero coupon bond or a 20-year 4.5% coupon bond?
    20-year zero coupon bond.

  6. What are the risks inherent in an interest rate swap?

Regulation

  1. How has Basel III changed the treatment of market risk?

  2. What the implications of Basel IIIs new trading book rules for market risk professionals?

  3. How could the Basel III treatment of trading books be improved?

  4. How will trading businesses change as a result of Basel III capital rules for banks’ trading books?

  5. What are the key requirements of the Basel stress testing framework? Are they sufficiently stringent?

  6. Which extreme events should stress tests be taking into consideration now?

  7. Why is Basel II blamed for precipitating the 2008 financial crisis?