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risk management financial

Questions and Answers of Risk Management Financial

8. To properly value bonds, the rate on zero-coupon Treasury securities must be determined.
7. The proper approach values a bond as a package of cash flows, with each cash flow viewed as a zero-coupon instrument and each cash flow discounted at its own unique discount rate.
6. The traditional valuation methodology is to discount every cash flow of a bond by the same interest rate (discount rate), thereby incorrectly viewing each security as the same package of cash
5. The base interest rate in valuing bonds is the rate on default-free securities and U.S. Treasury securities are viewed as default-free securities.
4. The difficulty in determining the cash flow arises for bonds where either the issuer or the investor can alter the cash flow.
3. For any bond in which neither the issuer nor the investor can alter the repayment of the principal before its contractual due date, the cash flow can easily be determined assuming that the issuer
2. The fundamental principle of valuation is that the value of any financial asset is the present value of the expected cash flow, where the cash flow is the cash that is expected to be received each
1. Valuation is the process of determining the fair value of a financial asset.
12. Explain the Monte Carlo method for valuing mortgage-backed securities.
11. Explain the binomial method for valuation.
10. Explain why the volatility assumption is critical in the valuation of bonds with embedded options.
9. Describe what is meant by the option-adjusted spread.
8. Explain how to compute and interpret the zero-volatility spread.
7. Explain how to compute and interpret the nominal spread.
6. Explain how credit risk should be introduced into the term structure.
5. Demonstrate how the Treasury spot rate curve can be used to value any Treasury security.
4. Explain the difference between the Treasury yield curve and the Treasury spot rate curve and how the theoretical spot rate curve for Treasury securities can be constructed from the Treasury yield
3. Explain why a bond should be viewed as a package of zero-coupon securities.
2. Explain the situations in which determination of a bond’s cash flow is complex.
1. Discuss the process involved in valuing a bond.
32. Synthetic collateralized debt obligations and credit-linked notes can be used to manage a bank’s exposure to credit risk.
31. Credit derivatives can be used to control credit risk, the most popular credit derivative being credit default swaps.
30. Tracking error due to credit risk can be computed to measure the credit risk exposure of a bond portfolio relative to a benchmark.
29. Value-at-risk can be computed for credit risk and there are several vendors that provide credit VaR systems.
28. Rating transition tables produced by rating agencies can be used to gauge downgrade risk.
27. Credit rating can be used to gauge credit default risk.
26. Downgrade risk is related to credit spread risk.
25. Credit default risk and credit spread risk are forms of credit risk.
24. Once the appropriate risk control instrument (or instruments) is selected, the appropriate position (i.e., long or short) and the amount of the position must be determined.
23. A key factor in selecting the risk control instrument to employ is the correlation between the yield movements of the bond, whose risk is sought to be controlled, and the candidate risk control
22. Derivative instruments allow a risk manager to alter the interest rate sensitivity of a bond portfolio or position or an asset/liability position economically and quickly.
21. Risk control instruments include derivative instruments (futures, forwards, options, swaps, caps, and floors) and cash market instruments.
20. To control the interest rate risk of a position or portfolio, a position must be taken in one or more risk control instruments.
19. The control phase of risk management involves altering the risk exposure to an acceptable level.
18. Yield curve risk of a bond portfolio can be assessed by computing the tracking error due to the term structure risk factor.
17. Tracking error is the most common measure used by bond portfolio managers in assessing performance versus a bond market index.
16. Tracking error is the standard deviation of the difference between the return on a portfolio and return on a benchmark.
15. In the value-at-risk framework, risk is defined as the maximum estimated loss in market value of a given position that is expected to happen a certain percentage of times.
14. The value-at-risk framework ties together the price sensitivity of a bond position to rate changes and yield volatility.
13. Yield volatility is measured by the standard deviation of yield changes.
12. The greater the expected yield volatility, the greater the interest rate risk of a position for a given duration and current value of a position.
11. Measurement of the interest rate risk of a position must take into account expected yield volatility.
10. The duration approach to risk management is referred to as the parametric approach, while the full valuation approach is called the nonparametric approach.
9. A drawback of the duration approach is that duration is only a first approximation of how sensitive the value of a bond or bond portfolio is to rate changes.
8. The advantage of the duration approach over the full valuation approach is that it allows the manager to quickly estimate the effect of an adverse rate change on the potential dollar loss.
7. A good valuation model is needed to obtain the duration estimate.
6. The duration of a position is the approximate percentage change in the position’s value for a 100-basis-point change in rates.
5. The duration approach is an alternative approach for estimating the potential dollar loss for any adverse rate change.
4. Scenario analysis is used to estimate the dollar loss for various interest rate scenarios.
3. The full valuation approach to measuring the potential dollar loss of a position after the adverse rate change uses a valuation model.
2. The key to measuring the potential dollar loss of a position is having a good valuation model that can be used to determine what the value of a position is after an adverse rate change.
1. To control interest rate risk, a manager must be able to quantify the potential dollar loss of a position resulting from an adverse interest rate change.
8. Identify what credit derivatives can be used to control credit risk.
7. Briefly describe how credit ratings measure credit default risk and what downgrade risk is.
6. Explain the different forms of credit risk: credit default risk and credit spread risk.
5. Describe what is involved in controlling interest rate risk.
4. Briefly describe what the value at risk approach is.
3. Explain why the measurement of yield volatility is important in measuring interest rate risk.
2. Explain what is meant by the duration of a bond or bond portfolio.
1. Explain two approaches to measuring interest rate risk—the full valuation approach and the duration approach.
1. From the S&P 500 prices, calculate daily returns as Rt+1 = ln(St+1) − ln(St )where St+1 is the closing price on day t + 1, St is the closing price on day t , and ln is the natural logarithm.
2. Calculate the mean, standard deviation, skewness, and kurtosis of returns. Plot a histogram of the returns with the normal distribution imposed as well. (Excel Hints: You can either use the
3. Calculate the 1st through 100th lag autocorrelation. Plot the autocorrelations against the lag order. (Excel Hint: Use the function CORREL.) Compare your result with Figure 1.1.
4. Calculate the 1st through 100th lag autocorrelation of squared returns. Again, plot the autocorrelations against the lag order. Compare your result with Figure 1.3.
5. Set σ2 0 (i.e., the variance of the first observation) equal to the variance of the entire sequence of returns (you can square the standard deviation found in 2). Then calculate σ2 t+1= 0.94σ2
6. Compute standardized returns as zt =Rt/σt and calculate the mean, standard deviation, skewness, and kurtosis of the standardized returns. Compare them with those found in 2.
7. Calculate daily, 5-day, 10-day, and 15-day nonoverlapping log returns. Calculate the mean, standard deviation, skewness, and kurtosis for all four return horizons. Do the returns look more normal
1. Estimate the simple GARCH(1,1) model on the S&P500 daily log returns using the maximum likelihood estimation (MLE) technique. First estimateσ2 t+1= ω + αR2 t+ βσ2 t , with Rt = σt zt , and
2. Include a leverage effect in the variance equation. Estimateσ2 t+1= ω + α (Rt − θσt )2 + βσ2 t , with Rt = σt zt , and zt ∼ N(0, 1)Set starting values to α = 0.1, β = 0.85, ω =
3. Include the option implied volatility V IX series from the Chicago Board Options Exchange (CBOE) as an explanatory variable in the GARCH equation.Use MLE to estimateσ2 t+1= ω + α (Rt − θσt
4. Run a regression of daily squared returns on the variance forecast from the GARCH model with a leverage term. Include a constant term in the regression R2 t+1= b0 + b1σ2 t+1+ et+1(Excel Hint: Use
5. Run a regression using the range instead of the squared returns as proxies for observed variance—that is, regress 14 ln(2)D2 t+1= b0 + b1σ2 t+1+ et+1 Is the constant term significantly
1. Convert the TSE prices into US$ using the US$/CAD exchange rate. Normalize each time series of closing prices by the first observation and plot them.
2. Calculate daily log returns and plot them on the same scale. How different is the magnitude of variations across the different assets?
3. Construct the unconditional covariance and the correlation matrices for the returns of all assets. What are the determinant values?
4. Calculate the unconditional 1-day, 1% value at risk for a portfolio consisting of 20% in each asset. Calculate also the 1-day, 1% value at risk for each asset individually. Compare the
5. Estimate a Simple GARCH(1,1) model for the variance of the S&P 500, the US$/yen FX rate, and the TSE in US$. Set starting values to α = 0.06; β =0.93; ω = 0.00009.
6. Standardize each return using its GARCH standard deviation from question 5.Construct the unconditional correlation matrix for the standardized returns of the three assets. This is the constant
7. Use MLE to estimate λ in the exponential smoother version of the dynamic conditional correlation (DCC) model for the two bivariate systems consisting of the S&P500 and each of two other series
8. Estimate the GARCH DCC model for the bivariate systems from question 7.Set the starting values to α =0.05 and β =0.9. Plot the dynamic correlations.Calculate and plot the 1-day, 1% VaRs for the
1. Construct a QQ plot of the S&P 500 returns divided by the unconditional standard deviation. Use the normal distribution. Compare your result with the top panel of Figure 4.2. (Excel Hint: Use the
2. Copy and paste the estimated GARCH(1,1) volatilities from Chapter 2, question 2.
3. Standardize the returns using the volatilities from question 2. Construct a QQ plot for the standardized returns using the normal distribution. Compare your result with the bottom panel of Figure
4. Using QMLE, estimate the GARCH(1,1)-˜t(d) model. Fix the variance parameters at their values from question 3. Set the starting value of d equal to 10.(Excel Hint: Use the GAMMALN function for the
5. Estimate the GARCH(1.1)-˜t(d) model using MLE instead of QMLE. Set the starting values of all parameters equal to the final values from question 4. Skip this question if you are working on a slow
6. Estimate the EVT model on the standardized portfolio returns using the Hill estimator. Use the 5% largest losses to estimate EVT. (Excel Hint: Use the PERCENTILE function to calculate the pth
7. Construct the QQ plot using the EVT distribution for the 5% largest losses. Compare your result with Figure 4.4.
1. Assume you are long $1 of the S&P 500 index on each day. Calculate the 1-day, 1%VaRs on each day in October 1987 using historical simulation and weighted historical simulation. You can ignore the
2. Redo question 1, assuming instead that you are short $1 of the S&P 500 each day. Compare your result with Figure 5.3.
3. For each day in 2001, calculate the 1-day, 1%VaRs using the following methods:(a) RiskMetrics, that is, normal distribution with an exponential smoother on variance using the weight, λ = 0.94;
4. Estimate 10-day, 1% VaRs on December 29, 2000, using FHS (with 1000 simulations), RiskMetrics scaling the daily VaRs by√10 (although it is incorrect), and GARCH(1,1)-˜t(d) with parameters
1. Calculate the BSM price for each option using a standard deviation of 0.015 per day. Using Solver, find the volatility that minimizes the mean squared pricing error using 0.015 as a starting
2. Scatter plot the BSM pricing errors (actual price less model price) against moneyness defined as (S/X) for the different maturities.
3. Calculate the implied BSM volatility (standard deviation) for each of the options. You can use Excel’s Solver to do this. Scatter plot the implied volatilities against moneyness.
4. Fit the Gram-Charlier option price to the data. Estimate a model with skewness only. Use nonlinear least squares (NLS) again.
5. Regress implied volatility on a constant, moneyness, the time-to-maturity divided by 365, each variable squared, and their cross product. Calculate the fitted BSM volatility from the regression
6. Redo the IVF estimation using NLS to minimize the mean squared pricing error(MSE). Call this MIVF. Use the IVF regression coefficients as starting values.
7. Calculate the square root of the mean squared pricing error from the IVF and MIVF models and compare them to the square root of the MSE from the standard BSM model and the Gram-Charlier model.
8. Using GARCH parameters ω=0.00001524,α=0.1883, β=0.7162, θ =0, and a λ=0.007452, simulate the GARCH option price with a strike price of 100 and 20 days to maturity. Assume r =0.02/365 and
1. Assume a volatility of 0.015 per calendar day for option pricing and a volatility of 0.015 ∗√365/252 = 0.0181 per trading day for return volatility. Calculate the delta and gamma of a short

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