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principles of risk management

Questions and Answers of Principles Of Risk Management

Equation (12.9) gives the formula for the capital required under Basel II. It involves four terms being multiplied together. Explain each of these terms.AppendixLO1
Banks sometimes use what is referred to as regulatory arbitrage to reduce their capital. What do you think this means?AppendixLO1
Under Basel I, banks do not like lending to highly creditworthy companies and prefer to help them issue debt securities. Why is this? Do you expect the banks’ attitude to this type of lending to
What is the difference between the trading book and the banking book for a bank? A bank currently has a loan of $10 million dollars to a corporate client.At the end of the life of the loan, the
Explain why the final stage in the Basel II calculations for credit risk (IRB), market risk, and operational risk is to multiply by 12.5.AppendixLO1
All the transactions a bank has with a corporate client are loans to the client.What is the value to the bank of netting provisions in its master agreement with the client?AppendixLO1
What is the capital required in Problem 12.6 under Basel I assuming that the 1995 netting amendment applies?AppendixLO1
Estimate the capital required under Basel I for a bank that has the following transactions with a corporation. Assume no netting.(a) A nine-year interest rate swap with a notional principal of $250
A four-year interest rate swap currently has a negative value to a financial institution. Is the financial institution exposed to credit risk on the transaction?Explain your answer. How would the
In a currency swap, interest on a principal in one currency is exchanged for interest on a principal in another currency. The principals in the two currencies are exchanged at the end of the life of
An interest rate swap involves the exchange of a fixed rate of interest for a floating rate of interest with both being applied to the same principal. The principals are not exchanged. What is the
“The existence of deposit insurance makes it particularly important for there to be regulations on the amount of capital banks hold.” Explain this statement.AppendixLO1
“When a steel company goes bankrupt, other companies in the same industry benefit because they have one less competitor. But when a bank goes bankrupt other banks do not necessarily benefit.”
The default rates in the last 15 years for a certain category of loans is 2%, 4%, 7%, 12%, 6%, 5%, 8%, 14%, 10%, 2%, 3%, 2%, 6%, 7%, 9%. Use the maximum likelihood method to calculate the best fit
Suppose that a bank has made a large number loans of a certain type. The oneyear probability of default on each loan is 1.2%. The bank uses a Gaussian copula for time to default. It is interested in
Create an Excel spreadsheet to produce a chart similar to Figure 11.5 showing samples from a bivariate Student t-distribution with four degrees of freedom where the correlation is 0.5. Next suppose
The probability density function for an exponential distribution is e−x where x is the value of the variable and is a parameter. The cumulative probability distribution is 1 − e−x. Suppose
Suppose that the price of Asset X at close of trading yesterday was $300 and its volatility was estimated as 1.3% per day. The price of X at the close of trading today is $298. Suppose further that
Suppose that the default rate for a portfolio of consumer loans over the last 10 years has been 1%, 9%, 2%, 3%, 5%, 1%, 6%, 7%, 4%, and 1%. What are the maximum likelihood estimates of the parameters
Suppose that a bank has made a large number of loans of a certain type. The total amount lent is $500 million. The one-year probability of default on each loan is 1.5% and the recovery rate is 30%.
What is the median of the distribution of V2 when V1 equals 0.2 in the example in Tables 11.1 and 11.2?AppendixLO1
In Table 11.3, what is the probability density function of V2 conditional on V1 0.1? Compare it with the unconditional distribution of V2.AppendixLO1
Suppose that the marginal distributions of V1 and V2 are standard normal distributions but that a Student t-copula with four degrees of freedom and a correlation parameter of 0.5 is used to define
Explain what is meant by tail dependence. How can you vary tail dependence by the choice of copula?AppendixLO1
Assume that you have independent random samples z1, z2, and z3 from a standard normal distribution and want to convert them to samples ε1, ε2, andε3 from a trivariate normal distribution using the
Suppose that two variables V1 and V2 have uniform distributions where all values between 0 and 1 are equally likely. Use a Gaussian copula to define the correlation structure between V1 and V2 with a
Suppose that in Problem 10.15 the correlation between the S&P 500 index(measured in dollars) and the FTSE 100 index (measured in sterling) is 0.7, the correlation between the S&P 500 index (measured
Suppose that the current daily volatilities of asset X and asset Y are 1.0% and 1.2%, respectively. The prices of the assets at close of trading yesterday were$30 and $50 and the estimate of the
Suppose that the current daily volatilities of asset A and asset B are 1.6% and 2.5%, respectively. The prices of the assets at close of trading yesterday were$20 and $40 and the estimate of the
What is meant by a positive-semidefinite matrix? What are the implications of a correlation matrix not being positive-semidefinite?AppendixLO1
What is a factor model? Why are factor models useful when defining a correlation structure between large numbers of variables?AppendixLO1
What is the difference between correlation and dependence? Suppose that y = x2 and x is normally distributed with mean zero and standard deviation one. What is the correlation between x and y
If you know the correlation between two variables, what extra information do you need to calculate the covariance?AppendixLO1
The probability that the loss from a portfolio will be greater than $10 million in one month is estimated to be 5%.(a) What is the one-month 99% VaR assuming the change in value of the portfolio is
Estimate parameters for the EWMA and GARCH(1,1) model on the euro-USD exchange rate data between July 27, 2005, and July 27, 2010. This data can be found on the author’s
Suppose that the parameters in a GARCH(1,1) model are = 0.03, = 0.95 and = 0.000002.(a) What is the long-run average volatility?(b) If the current volatility is 1.5% per day, what is your
An Excel spreadsheet containing over 900 days of daily data on a number of different exchange rates and stock indices can be downloaded from the author’s website:
Suppose that the price of an asset at close of trading yesterday was $300 and its volatility was estimated as 1.3% per day. The price at the close of trading today is $298. Update the volatility
Suppose that observations on a stock price (in dollars) at the end of each of 15 consecutive days are as follows:30.2, 32.0, 31.1, 30.1, 30.2, 30.3, 30.6, 30.9, 30.5, 31.1, 31.3, 30.8, 30.3, 29.9,
Suppose that GARCH(1,1) parameters have been estimated as = 0.000002, = 0.04, and = 0.94. The current daily volatility is estimated to be 1.3%.Estimate the volatility per annum that should be used
Suppose that GARCH(1,1) parameters have been estimated as = 0.000003, = 0.04, and = 0.94. The current daily volatility is estimated to be 1%.Estimate the daily volatility in 30 days.AppendixLO1
Suppose that the daily volatility of the FTSE 100 stock index (measured in pounds sterling) is 1.8% and the daily volatility of the dollar–sterling exchange rate is 0.9%. Suppose further that the
The parameters of a GARCH(1,1) model are estimated as = 0.000004, = 0.05, and = 0.92. What is the long-run average volatility and what is the equation describing the way that the variance rate
A company uses the GARCH(1,1) model for updating volatility. The three parameters are , , and . Describe the impact of making a small increase in each of the parameters while keeping the others
The most recent estimate of the daily volatility of the dollar–sterling exchange rate is 0.6% and the exchange rate at 4:00 P.M. yesterday was 1.5000. The parameter in the EWMA model is 0.9.
Assume that the S&P 500 at close of trading yesterday was 1,040 and the daily volatility of the index was estimated as 1% per day at that time. The parameters in a GARCH(1,1) model are = 0.000002,
A company uses an EWMA model for forecasting volatility. It decides to change the parameter from 0.95 to 0.85. Explain the likely impact on the forecasts.AppendixLO1
The most recent estimate of the daily volatility of an asset is 1.5% and the price of the asset at the close of trading yesterday was $30.00. The parameter Volatility 231 in the EWMA model is 0.94.
What is the difference between the exponentially weighted moving average model and the GARCH(1,1) model for updating volatilities?AppendixLO1
Explain the exponentially weighted moving average (EWMA) model for estimating volatility from historical data.AppendixLO1
The number of visitors to websites follows the power law in equation (10.1)with = 2. Suppose that 1% of sites get 500 or more visitors per day. What percentage of sites get (a) 1,000 and (b) 2,000
Suppose that observations on an exchange rate at the end of the last 11 days have been 0.7000, 0.7010, 0.7070, 0.6999, 0.6970, 0.7003, 0.6951, 0.6953, 0.6934, 0.6923, 0.6922. Estimate the daily
What is implied volatility? What does it mean if different options on the same asset have different implied volatilities?AppendixLO1
Why do traders assume 252 rather than 365 days in a year when using volatilities?AppendixLO1
The volatility of an asset is 25% per annum. What is the standard deviation of the percentage price change in one trading day? Assuming a normal distribution with zero mean, estimate 95% confidence
The volatility of an asset is 2%per day. What is the standard deviation of the percentage price change in three days?AppendixLO1
Suppose that we back-test a VaR model using 1,000 days of data. The VaR confidence level is 99% and we observe 15 exceptions. Should we reject the model at the 5% confidence level? Use Kupiec’s
Suppose that daily changes for a portfolio have first-order correlation with correlation parameter 0.12. The 10-day VaR, calculated by multiplying the one-day VaR by√10, is $2 million. What is a
Suppose that each of two investments has a 4%chance of a loss of $10 million, a 2%chance of a loss of $1 million, and a 94% chance of a profit of $1 million.They are independent of each other.(a)
Prove equation 9.3.AppendixLO1
Explain what is meant by bunching.AppendixLO1
Suppose that we back-test a VaR model using 1,000 days of data. The VaR confidence level is 99% and we observe 17 exceptions. Should we reject the model at the 5% confidence level? Use a one-tailed
Explain carefully the differences between marginal VaR, incremental VaR, and component VaR for a portfolio consisting of a number of assets.AppendixLO1
What difference does it make to your answer to Problem 9.6 if there is firstorder daily autocorrelation with a correlation parameter equal to 0.16?AppendixLO1
Suppose that the change in the value of a portfolio over a one-day time period is normal with a mean of zero and a standard deviation of $2 million, what is(a) the one-day 97.5% VaR, (b) the five-day
Suppose that each of two investments has a 0.9% chance of a loss of $10 million, a 99.1% of a loss of $1 million. The investments are independent of each other.(a) What is the VaR for one of the
A fund manager announces that the fund’s one-month 95% expected shortfall is 6% of the size of the portfolio being managed. You have an investment of$100,000 in the fund. How do you interpret the
A fund manager announces that the fund’s one-month 95% VaR is 6% of the size of the portfolio being managed. You have an investment of $100,000 in the fund. How do you interpret the portfolio
What is a spectral risk measure? What conditions must be satisfied by a spectral risk measure for the subadditivity condition in Section 9.4 to be satisfied?AppendixLO1
What is the difference between expected shortfall and VaR? What is the theoretical advantage of expected shortfall over VaR?AppendixLO1
What is the difference between an open-end and closed-end mutual fund?AppendixLO1
How is the NAV of an open-end mutual fund calculated? When is it calculated?AppendixLO1
An investor buys 100 shares in a mutual fund on January 1, 2012, for $30 each. The fund makes capital gains in 2012 and 2013 of $3 per share and $1 per share, respectively, and earns no dividends.
What is an index fund? How is it created?AppendixLO1
What is a mutual fund’s (a) front-end load and (b) back-end load?AppendixLO1
Explain how an exchange-traded fund that tracks an index works. What is the advantage of an exchange-traded fund (a) over an open-end mutual fund and(b) a closed-end mutual fund?AppendixLO1
What is the difference between the geometric mean and the arithmetic mean of a set of numbers? Why is the difference relevant to the reporting of mutual fund returns?AppendixLO1
Explain the meaning of (a) late trading, (b) market timing, (c) front running, and (d) directed brokerage.AppendixLO1
Give three examples of the rules that apply to mutual funds, but not to hedge funds.AppendixLO1
“If 70% of convertible bond trading is by hedge funds, I would expect the profitability of that strategy to decline.” Discuss this viewpoint.AppendixLO1
Explain the meanings of the terms hurdle rate, high-water mark clause, and clawback clause when used in connection with the incentive fees of hedge funds.AppendixLO1
A hedge fund charges 2 plus 20%. Investors want a return after fees of 20%.How much does the hedge fund have to earn, before fees, to provide investors with this return? Assume that the incentive fee
“It is important for a hedge fund to be right in the long term. Short-term gains and losses do not matter.” Discuss this statement.AppendixLO1
“The risks that hedge funds take are regulated by their prime brokers.” Discuss this statement.AppendixLO1
An investor buys 100 shares in a mutual fund on January 1, 2012, for $50 each. The fund earns dividends of $2 and $3 per share during 2012 and 2013.These are reinvested in the fund. Its realized
Good years are followed by equally bad years for a mutual fund. It earns +8%,–8%, +12%, –12% in successive years. What is the investor’s overall return for the four years?AppendixLO1
A fund of funds divides its money between five hedge funds that earn –5%, 1%, 10%, 15%, and 20% before fees in a particular year. The fund of funds charges 1 plus 10% and the hedge funds charge 2
A hedge fund charges 2 plus 20%. A pension fund invests in the hedge fund.Plot the return to the pension fund as a function of the return to the hedge fund.AppendixLO1
An investment has probabilities of 0.1, 0.2, 0.35, 0.25, and 0.1 for giving returns equal to 40%, 30%, 15%, −5%, and −15%. What is the expected return and the standard deviation of
Suppose that there are two investments with the same probability distribution of returns as in Problem 1.1. The correlation between the returns is 0.15. What is the expected return and standard
For the two investments considered in Figure 1.2 and Table 1.2, what are the alternative risk-return combinations if the correlation is (a) 0.3, (b) 1.0, and(c) −1.0?AppendixLO1
What is the difference between systematic and nonsystematic risk? Which is more important to an equity investor? Which can lead to the bankruptcy of a corporation?AppendixLO1
Outline the arguments leading to the conclusion that all investors should choose the same portfolio of risky investments. What are the key assumptions?AppendixLO1
The expected return on the market portfolio is 12% and the risk-free rate is 6%. What is the expected return on an investment with a beta of (a) 0.2, (b)0.5, (c) 1.4?AppendixLO1
“Arbitrage pricing theory is an extension of the capital asset pricing model.”Explain this statement.AppendixLO1
“The capital structure decision of a company is a trade-off between bankruptcy costs and the tax advantages of debt.” Explain this statement.AppendixLO1
What is meant by risk aggregation and risk decomposition? Which requires an in-depth understanding of individual risks? Which requires a detailed knowledge of the correlations between
A bank’s operational risk includes the risk of very large losses because of employee fraud, natural disasters, litigation, etc. Do you think operational risk best handled by risk decomposition or
A bank’s profit next year will be normally distributed with a mean of 0.6% of assets and a standard deviation of 1.5% of assets. The bank’s equity is 4% of assets. What is the probability that
Why do you think that banks are regulated to ensure that they do not take too much risk but most other companies (for example, those in manufacturing and retailing) are not?AppendixLO1

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