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principles of risk management

Questions and Answers of Principles Of Risk Management

A trader buys 200 shares of a stock on margin. The price of the stock is $20.The initial margin is 60% and the maintenance margin is 30%. How much money does the trader have to provide initially? For
Why didmortgage lenders frequently not check on information in the mortgage application during the 2000 to 2007 period?AppendixLO1
Why do you think the increase in house prices during the 2000 to 2007 period is referred to as a bubble?AppendixLO1
What are the numbers in Table 6.1 for a loss rate of (a) 5% and (b) 12%?AppendixLO1
In what ways are the risks in the tranche of an ABS different from the risks in a similarly rated bond?AppendixLO1
Explain the difference between (a) an ABS, and (b) an ABS CDO.AppendixLO1
How were the risks in ABS CDOs misjudged by the market?AppendixLO1
What is meant by the term “agency costs”?AppendixLO1
What is a waterfall in a securitization?AppendixLO1
How is an ABS CDO created? What was the motivation to create ABS CDOs?AppendixLO1
How did Mian and Sufi show that mortgage lenders relaxed their lending criteria during the 2000 to 2006 period?AppendixLO1
What is a mezzanine tranche?AppendixLO1
Explain the influence of an increase in default correlation on (a) the risks in the equity tranche of an ABS and (b) the risks in the senior tranches of an ABS.AppendixLO1
Explain why the end-of-year bonus is regarded as short-term compensation.AppendixLO1
Suppose that the principals assigned to the senior, mezzanine, and equity tranches for the ABSs and ABS CDO in Figure 6.4 are 70%, 20%, and 10%instead of 75%, 20% and 5%. How are the results in Table
Investigate what happens as the width of the mezzanine tranche of the ABS in Figure 6.4 is decreased, with the reduction in the mezzanine tranche principal being divided equally between the equity
The delta of a derivatives portfolio dependent on the S&P 500 index is –2,100.The S&P 500 index is currently 1,000. Estimate what happens to the value of the portfolio when the index increases to
The vega of a derivatives portfolio dependent on the dollar-sterling exchange rate is 200 ($ per %). Estimate the effect on the portfolio of an increase in the volatility of the exchange rate from
The gamma of a delta-neutral portfolio is 30 (per $). Estimate what happens to the value of the portfolio when the price of the underlying asset (a) suddenly increases by $2 and (b) suddenly
What does it mean to assert that the delta of a call option is 0.7? How can a short position in 1,000 options be made delta neutral when the delta of a long position in each option is 0.7?How Traders
What does it mean to assert that the theta of an option position is –100 per day? If a trader feels that neither a stock price nor its implied volatility will change, what type of option position
What is meant by the gamma of an option position? What are the risks in the situation where the gamma of a position is large and negative and the delta is zero?AppendixLO1
“The procedure for creating an option position synthetically is the reverse of the procedure for hedging the option position.” Explain this statement.AppendixLO1
A company uses delta hedging to hedge a portfolio of long positions in put and call options on a currency. Which of the following would lead to the most favorable result?(a) A virtually constant spot
A bank’s position in options on the dollar–euro exchange rate has a delta of 30,000 and a gamma of −80,000. Explain how these numbers can be interpreted.The exchange rate (dollars per euro) is
“Static options replication assumes that the volatility of the underlying asset will be constant.” Explain this statement.AppendixLO1
Suppose that a trader using the static options replication technique wants to match the value of a portfolio of exotic derivatives with the value of a portfolio of regular options at 10 points on a
Why is an Asian option easier to hedge than a regular option?AppendixLO1
Explain why there are economies of scale in hedging options.AppendixLO1
Consider a six-month American put option on a foreign currency when the exchange rate (domestic currency per foreign currency) is 0.75, the strike price is 0.74, the domestic risk-free rate is 5%,
The gamma and vega of a delta-neutral portfolio are 50 per $ and 25 per %, respectively. Estimate what happens to the value of the portfolio when there is a shock to the market causing the underlying
Consider a one-year European call option on a stock when the stock price is$30, the strike price is $30, the risk-free rate is 5%, and the volatility is 25% per annum. Use the DerivaGem software to
A financial institution has the following portfolio of over-the-counter options on sterling:Delta of Gamma of Vega of Type Position Option Option Option Call −1,000 0.50 2.2 1.8 Call −500 0.80
Consider again the situation in Problem 7.17. Suppose that a second traded option with a delta of 0.1, a gamma of 0.5, and a vega of 0.6 is available. How could the portfolio be made delta, gamma,
Reproduce Table 7.2. (In Table 7.2, the stock position is rounded to the nearest 100 shares.) Calculate the gamma and theta of the position each week. Using the DerivaGem Applications Builders to
Suppose that a bank has $5 billion of one-year loans and $20 billion of five-year loans. These are financed by $15 billion of one-year deposits and $10 billion of five-year deposits. Explain the
Explain why long-term rates are higher than short-term rates most of the time.Under what circumstances would you expect long-term rates to be lower than short-term rates?AppendixLO1
Why are U.S. Treasury rates significantly lower than other rates that are close to risk free?AppendixLO1
Explain how an overnight indexed swap works.AppendixLO1
Explain why the LIBOR-OIS spread is a measure of stress in financial markets.AppendixLO1
What does duration tell you about the sensitivity of a bond portfolio to interest rates? What are the limitations of the duration measure?AppendixLO1
A five-year bond with a yield of 11% (continuously compounded) pays an 8%coupon at the end of each year.(a) What is the bond’s price?(b) What is the bond’s duration?(c) Use the duration to
Repeat Problem 8.7 on the assumption that the yield is compounded annually.Use modified durations.AppendixLO1
A six-year bond with a continuously compounded yield of 4% provides a 5%coupon at the end of each year. Use duration and convexity to estimate the effect of a 1% increase in the yield on the price of
Explain three ways in which multiple deltas can be calculated to manage nonparallel yield curve shifts.AppendixLO1
Estimate the delta of the portfolio in Table 8.6 with respect to the first two factors in Table 8.7.AppendixLO1
Use the partial durations in Table 8.5 to calculate the impact of a shift in the yield curve on a $10 million portfolio where the 1-, 2-, 3-, 4-, 5-, 7-, and 10-year rates increase by 10, 8, 7, 6, 5,
How are “dollar duration” and “dollar convexity” defined?AppendixLO1
What is the relationship between (a) the duration, (b) the partial durations, and (c) the DV01 of a portfolio?AppendixLO1
Suppose that a bank has $10 billion of one-year loans and $30 billion of five-year loans. These are financed by $35 billion of one-year deposits and$5 billion of five-year deposits. The bank has
Portfolio A consists of a one-year zero-coupon bond with a face value of$2,000 and a 10-year zero-coupon bond with a face value of $6,000. Portfolio B consists of a 5.95-year zero-coupon bond with a
What are the convexities of the portfolios in Problem 8.16? To what extent does(a) duration and (b) convexity explain the difference between the percentage changes calculated in part (c) of Problem
When the partial durations are as in Table 8.5, estimate the effect of a shift in the yield curve where the ten-year rate stays the same, the one-year rate moves up by 9e, and the movements in
Suppose that the change in a portfolio value for a one-basis-point shift in the 1-, 2-, 3-, 4-, 5-, 7-, 10-, and 30-year rates are (in $ million) +5, –3, –1, +2, +5,+7, +8, and +1, respectively.
Consider a position consisting of a $100,000 investment in asset A and a$100,000 investment in asset B. Assume that the daily volatilities of both assets are 1% and that the coefficient of
Describe three ways of handling interest-rate-dependent instruments when the model-building approach is used to calculate VaR.AppendixLO1
Explain how an interest rate swap is mapped into a portfolio of zero-coupon bonds with standard maturities for the purposes of a VaR calculation.AppendixLO1
A financial institution owns a portfolio of options on the U.S. dollar–sterling exchange rate. The delta of the portfolio is 56.0. The current exchange rate is 1.5000. Derive an approximate linear
Suppose that you know the gamma of the portfolio in Problem 15.4 is 16.2.How does this change your estimate of the relationship between the change in the portfolio value and the percentage change in
Suppose that the five-year rate is 6%, the seven-year rate is7%(both expressed with annual compounding), the daily volatility of a five-year zero-coupon bond is 0.5%, and the daily volatility of a
Verify that the 0.3-year zero-coupon bond in the cash-flow mapping example in Table 15.9 is mapped into a $37,397 position in a three-month bond and a $11,793 position in a six-month bond.AppendixLO1
Suppose that the daily change in the value of a portfolio is, to a good approximation, linearly dependent on two factors, calculated from a principal components analysis. The delta of a portfolio
The text calculates a VaR estimate for the example in Table 15.10 assuming two factors. How does the estimate change if you assume (a) one factor and(b) three factors?AppendixLO1
A bank has a portfolio of options on an asset. The delta of the options is–30 and the gamma is –5. Explain how these numbers can be interpreted.The asset price is 20 and its volatility is 1% per
Suppose that in Problem 15.10 the vega of the portfolio is −2 per 1% change in the annual volatility. Derive a model relating the change in the portfolio value in one day to delta, gamma, and
Explain why the linear model can provide only approximate estimates of VaR for a portfolio containing options.AppendixLO1
Some time ago, a company entered into a forward contract to buy £1 million for $1.5 million. The contract now has six months to maturity. The daily volatility of a six-month zero-coupon sterling
The calculations in Section 15.3 assume that the investments in the DJIA, FTSE 100, CAC 40, and Nikkei 225 are $4 million, $3 million, $1 million, and $2 million, respectively. How does the VaR
What is the effect of changing from 0.94 to 0.97 in the EWMA calculations in Section 15.3? Use the spreadsheets on the author’s website.AppendixLO1
Consider a position consisting of a $300,000 investment in gold and a$500,000 investment in silver. Suppose that the daily volatilities of these two assets are 1.8% and 1.2% respectively, and that
Consider a portfolio of options on a single asset. Suppose that the delta of the portfolio is 12, the value of the asset is $10, and the daily volatility of the asset is 2%. Estimate the one-day 95%
Suppose that you know the gamma of the portfolio in Problem 15.17 is –2.6.Derive a quadratic relationship between the change in the portfolio value and the percentage change in the underlying asset
A company has a long position in a two-year bond and a three-year bond as well as a short position in a five-year bond. Each bond has a principal of $100 million and pays a 5% coupon annually.
A company has a position in bonds worth $6 million. The modified duration of the portfolio is 5.2 years. Assume that only parallel shifts in the yield curve can take place and that the standard
A bank has written a European call option on one stock and a European put option on another stock. For the first option, the stock price is 50, the strike price is 51, the volatility is 28% per
A common complaint of risk managers is that the model-building approach(either linear or quadratic) does not work well when delta is close to zero. Test what happens when delta is close to zero in
The calculations in Section 15.3 assume that the investments in the DJIA, FTSE 100, CAC 40, and Nikkei 225 are $4 million, $3 million, $1 million, and $2 million, respectively. How does the VaR
How many different ratings does Moody’s use for investment-grade companies?What are they?AppendixLO1
How many different ratings does S&P use for investment-grade companies?What are they?AppendixLO1
Calculate the average hazard rate for a B-rated company during the first year from the data in Table 16.1.AppendixLO1
Calculate the average hazard rate for a Ba-rated company during the third year from the data in Table 16.1.AppendixLO1
A credit default swap requires a semiannual payment at the rate of 60 basis points per year. The principal is $300 million and the credit default swap is settled in cash. A default occurs after four
Explain the two ways a credit default swap can be settled.AppendixLO1
Explain the difference between risk-neutral and real-world default probabilities.AppendixLO1
What is the formula relating the payoff on a CDS to the notional principal and the recovery rate?AppendixLO1
The spread between the yield on a three-year corporate bond and the yield on a similar risk-free bond is 50 basis points. The recovery rate is 30%. Estimate the average hazard rate per year over the
The spread between the yield on a five-year bond issued by a company and the yield on a similar risk-free bond is 80 basis points. Assuming a recovery rate of 40%, estimate the average hazard rate
Should researchers use real-world or risk-neutral default probabilities for (a)calculating credit value at risk and (b) adjusting the price of a derivative for defaults?AppendixLO1
How are recovery rates usually defined?AppendixLO1
Verify (a) that the numbers in the second column of Table 16.4 are consistent with the numbers in Table 16.1 and (b) that the numbers in the fourth column of Table 16.5 are consistent with the
A four-year corporate bond provides a coupon of 4% per year payable semiannually and has a yield of 5% expressed with continuous compounding. The risk-free yield curve is flat at 3% with continuous
A company has issued three- and five-year bonds, each of which has a coupon of 4% per annum payable semiannually. The yields on the bonds (expressed with continuous compounding are 4.5% and 4.75%,
Suppose that in an asset swap, B is the market price of the bond per dollar of principal, B∗ is the default-free value of the bond per dollar of principal, and V is the present value of the asset
Show that, under Merton’s model in Section 16.8, the credit spread on a T-year zero-coupon bond is −ln[N(d2) + N(−d1)/L]/T where L = De−rT/V0.Credit Risk: Estimating Default Probabilities 373
The value of a company’s equity is $2 million and the volatility of its equity is 50%. The debt that will have to be repaid in one year is $5 million. The risk-free interest rate is 4% per annum.
A five-year credit default swap entered into on June 20, 2013, requires quarterly payments at the rate of 400 basis points per year. The principal is $100 million. A default occurs after four years
“The position of a buyer of a credit default swap is similar to the position of someone who is long a risk-free bond and short a corporate bond.” Explain this statement.AppendixLO1
Why is there a potential asymmetric information problem in credit default swaps?AppendixLO1
Suppose that the LIBOR/swap curve is flat at 6% with continuous compounding and a five-year bond with a coupon of 5% (paid semiannually) sells for 90.00. How much would the bond be worth if it were a
Suppose that a three-year corporate bond provides a coupon of 7% per year payable semiannually and has a yield of 5% (expressed with semiannual compounding). The yields for all maturities on

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