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Financial Risk Manager Handbook 6th Edition Philippe Jorion - Solutions

The yield curve is upward sloping. You have a short T-bond futures position.The following bonds are eligible for delivery:Bond A BC Spot price 102-14/32 106-19/32 98-12/32 Coupon 4% 5% 3%Conversion factor 0.98 1.03 0.952
Consider the buyer of a 6 × 9 FRA. The contract rate is 6.35% on a notional amount of $10 million. Calculate the settlement amount of the seller if the settlement rate is 6.85%. Assume a 30/360-day count basis.a. −12,500b. −12,290c. +12,500d. +12,290
ABC, Inc., entered a forward rate agreement (FRA) to receive a rate of 3.75%with continuous compounding on a principal of USD 1 million between the end of year 1 and the end of year 2. The zero rates are 3.25% and 3.50%for one and two years. What is the value of the FRA when the deal is just
A long position in a 2 × 5 FRA is equivalent to the following positions in the spot market:a. Borrowing in two months to finance a five-month investmentb. Borrowing in five months to finance a two-month investmentc. Borrowing half a loan amount at two months and the remainder at five monthsd.
Which of the following would not cause an upward-sloping yield curve?a. An investor preference for short-term instrumentsb. An expected decline in interest ratesc. An improving credit risk outlookd. An expected increase in the inflation rate
During 2002, an Argentinean pension fund with 80% of its assets in dollardenominated debt lost more than 40% of its value. Which of the following reasons could explain all of the 40% loss?a. The assets were invested in a diversified portfolio of AAA firms in the United States.b. The assets invested
A portfolio consists of two zero-coupon bonds, each with a current value of$10. The first bond has a modified duration of one year and the second has a modified duration of nine years. The yield curve is flat, and all yields are 5%. Assume all moves of the yield curve are parallel shifts. Given
According to the pure expectations hypothesis, which of the following statements is correct concerning the expectations of market participants in an upward-sloping yield curve environment?a. Interest rates will increase and the yield curve will flatten.b. Interest rates will increase and the yield
Suppose that the yield curve is upward sloping. Which of the following statements is true?a. The forward rate yield curve is above the zero-coupon yield curve, which is above the coupon-bearing bond yield curve.b. The forward rate yield curve is above the coupon-bearing bond yield curve, which is
The term structure of swap rates is: 1-year, 2.50%; 2-year, 3.00%; 3-year, 3.50%; 4-year, 4.00%; 5-year, 4.50%. The two-year forward swap rate starting in three years is closest toa. 3.50%b. 4.50%c. 5.51%d. 6.02%
The price of a three-year zero-coupon government bond is $85.16. The price of a similar four-year bond is $79.81. What is the one-year implied forward rate from year 3 to year 4?a. 5.4%b. 5.5%c. 5.8%d. 6.7%
Consider a bond with par value of EUR 1,000 and maturity in three years, and that pays a coupon of 5% annually. The spot rate curve is as follows:1-year, 6%; 2-year, 7%; and 3-year, 8%. The value of the bond is closest to:a. 904b. 924c. 930d. 950
Your boss wants to devise a fixed-income strategy such that there is no reinvestment risk over five years. Reinvestment risk will not occur if:I. Interest rates remain constant over the time period the bonds are held.II. The bonds purchased are callable.III. The bonds purchased are issued at
From the time of issuance until the bond matures, which of the following bonds is most likely to exhibit negative convexity?a. A puttable bondb. A callable bondc. An option-free bond selling at a discountd. A zero-coupon bond
A money markets desk holds a floating-rate note with an eight-year maturity.The interest rate is floating at the three-month LIBOR rate, reset quarterly.The next reset is in one week. What is the approximate duration of the floating-rate note?a. 8 yearsb. 4 yearsc. 3 monthsd. 1 week
A 10-year zero-coupon bond is callable annually at par (its face value) starting at the beginning of year 6. Assume a flat yield curve of 10%. What is the bond duration?a. 5 yearsb. 7.5 yearsc. 10 yearsd. Cannot be determined based on the data given
With any other factors remaining unchanged, which of the following statements regarding bonds is not valid?a. The price of a callable bond increases when interest rates increase.b. Issuance of a callable bond is equivalent to a short position in a straight bond plus a long call option on the bond
Which one of the following statements about American options is incorrect?a. American options can be exercised at any time until maturity.b. American options are always worth at least as much as European options.c. American options can easily be valued with Monte Carlo simulation.d. American
Of the following options, which one does not benefit from an increase in the stock price when the current stock price is $100 and the barrier has not yet been crossed?a. A down-and-out call with barrier at $90 and strike at $110b. A down-and-in call with barrier at $90 and strike at $110c. An
All else being equal, which of the following options would cost more than plain-vanilla options that are currently at-the-money?I. Lookback options II. Barrier options III. Asian options IV. Chooser optiona. I onlyb. I and IVc. II and IIId. I, III, and IV
Which of the following options is strongly path-dependent?a. An Asian optionb. A binary optionc. An American optiond. A European call option
In the Black-Scholes expression for a European call option, the term used to compute option probability of exercise isa. d1b. d2c. N(d1)d. N(d2)
Using the Black-Scholes model, calculate the value of a European call option given the following information: spot rate = 100; strike price = 110; riskfree rate = 10%; time to expiry = 0.5 years; N(d1) = 0.457185; N(d2) =0.374163.a. $10.90b. $9.51c. $6.57d. $4.92
Which two of the following four statements are correct about the early exercise of American options on non-dividend-paying stocks?I. It is never optimal to exercise an American call option early.II. It can be optimal to exercise an American put option early.III. It can be optimal to exercise an
You have been asked to verify the pricing of a two-year European call option with a strike price of USD 45. You know that the initial stock price is USD 50, and the continuous risk-free rate is 3%. To verify the possible price range of this call, you consider using price bounds. What is the
Given strictly positive interest rates, the best way to close out a long American call option position early (on a stock that pays no dividends) would be toa. Exercise the callb. Sell the callc. Deliver the calld. Do none of the above
According to an in-house research report, it is expected that USDJPY (quoted as JPY/USD) will trade near 97 at the end of March. Frankie Shiller, the investment director of a house fund, decides to use an option strategy to capture this opportunity. The current level of the USDJPY exchange rate is
Consider a bearish option strategy of buying one $50 strike put for $7, selling two $42 strike puts for $4 each, and buying one $37 put for $2. All options have the same maturity. Calculate the final profit per share of the strategy if the underlying is trading at $33 at expiration.a. $1 per
A portfolio manager wants to hedge his bond portfolio against changes in interest rates. He intends to buy a put option with a strike price below the portfolio’s current price in order to protect against rising interest rates. He also wants to sell a call option with a strike price above the
An investor sells a June 2008 call of ABC Limited with a strike price of USD 45 for USD 3 and buys a June 2008 call of ABC Limited with a strike price of USD 40 for USD 5. What is the name of this strategy and the maximum profit and loss the investor could incur?a. Bear spread, maximum loss USD 2,
Which of the following is the riskiest form of speculation using option contracts?a. Setting up a spread using call optionsb. Buying put optionsc. Writing naked call optionsd. Writing naked put options
Jeff is an arbitrage trader, who wants to calculate the implied dividend yield on a stock while looking at the over-the-counter price of a five-year European put and call on that stock. He has the following data: S = $85, K = $90, r = 5%, c = $10, p = $15. What is the continuous implied dividend
The current price of stock ABC is $42 and the call option with a strike at$44 is trading at $3. Expiration is in one year. The corresponding put is priced at $2. Which of the following trading strategies will result in arbitrage profits? Assume that the risk-free rate is 10% and that the risk-free
A one-year European put option on a non-dividend-paying stock with strike at EUR 25 currently trades at EUR 3.19. The current stock price is EUR 23 and its annual volatility is 30%. The annual risk-free interest rate is 5%.What is the price of a European call option on the same stock with the same
Which one of the following statements is incorrect regarding the margining of exchange-traded futures contracts?a. Day trades and spread transactions require lower margin levels.b. If an investor fails to deposit variation margin in a timely manner, the positions may be liquidated by the carrying
An investor enters into a short position in a gold futures contract at USD 294.20. Each futures contract controls 100 troy ounces. The initial margin is USD 3,200, and the maintenance margin is USD 2,900. At the end of the first day, the futures price drops to USD 286.6. Which of the following is
A three-month futures contract on an equity index is currently priced at USD 1,000. The underlying index stocks are valued at USD 990 and pay dividends at a continuously compounded rate of 2%. The current continuously compounded risk-free rate is 4%. The potential arbitrage profit per contract,
Consider a forward contract on a stock market index. Identify the false statement. Everything else being constant,a. The forward price depends directly on the level of the stock market index.b. The forward price will fall if underlying stocks increase the level of dividend payments over the life of
Suppose that U.S. interest rates rise from 3% to 4% this year. The spot exchange rate quotes at 112.5 JPY/USD and the forward rate for a one-year contract is at 110.5. What is the Japanese interest rate?a. 1.81%b. 2.15%c. 3.84%d. 5.88%
The one-year U.S. dollar interest rate is 2.75% and one-year Canadian dollar interest rate is 4.25%. The current USD/CAD spot exchange rate is 1.0221–1.0225. Calculate the one-year USD/CAD forward rate. Assume annual compounding.a. 1.0076b. 1.0074c. 1.0075d. 1.03722
Which of the following is not an advantage of establishing CCPs?a. CCPs allow netting of contracts.b. CCPs can be applied to some types of OTC trades.c. CCPs can create more transparency in trading.d. CCPs eliminate all counterparty risk in the financial system.
Novation is the process of:a. Creating a new trade between two counterpartiesb. Terminating an existing trade between two counterpartiesc. Discharging a contract between the original counterparties and creating two new contracts, each with a central counterpartyd. Assigning a trade to another party
Which of the following statements is correct regarding the effects of interest rate shift on fixed-income portfolios with similar durations?a. A barbell portfolio has greater convexity than a bullet portfolio because convexity increases linearly with maturity.b. A barbell portfolio has greater
Consider the following portfolio of bonds (par amounts are in millions of USD).Bond Price Par Amount Held Modified Duration A 101.43 3 2.36 B 84.89 5 4.13 C 121.87 8 6.27 What is the value of the portfolio’s DV01 (dollar value of 1 basis point)?a. $8,019b. $8,294c. $8,584d. $8,813
A bond portfolio has the following composition:1. Portfolio A: price $90,000, modified duration 2.5, long position in 8 bonds 2. Portfolio B: price $110,000, modified duration 3, short position in 6 bonds 3. Portfolio C: price $120,000, modified duration 3.3, long position in 12 bonds All interest
Which of the following statements is/are true?I. The convexity of a 10-year zero-coupon bond is higher than the convexity of a 10-year 6% bond.II. The convexity of a 10-year zero-coupon bond is higher than the convexity of a 6% bond with a duration of 10 years.III. Convexity grows proportionately
Consider the following bonds:Bond Maturity Coupon Yield Number (Years) Rate Frequency (Annual)1 10 6% 1 6%2 10 6% 2 6%3 10 0% 1 6%4 10 6% 1 5%5 9 6% 1 6%How would you rank the bonds from the shortest to longest duration?a. 5-2-1-4-3b. 6-2-3-4-5c. 5-4-3-1-2d. 2-4-5-1-3
When the maturity of a plain coupon bond increases, its duration increasesa. Indefinitely and regularlyb. Up to a certain levelc. Indefinitely and progressivelyd. In a way dependent on the bond being priced above or below par
A manager wants to swap a bond for a bond with the same price but higher duration. Which of the following bond characteristics would be associated with a higher duration?I. A higher coupon rate II. More frequent coupon payments III. A longer term to maturity IV. A lower yielda. I, II, and IIIb. II,
A and B are two perpetual bonds; that is, their maturities are infinite. A has a coupon of 4% and B has a coupon of 8%. Assuming that both are trading at the same yield, what can be said about the duration of these bonds?a. The duration of A is greater than the duration of B.b. The duration of A is
A Treasury bond has a coupon rate of 6% per annum (the coupons are paid semiannually) and a semiannually compounded yield of 4% per annum. The bond matures in 18 months and the next coupon will be paid 6 months from now. Which number of years is closest to the bond’s Macaulay duration?a. 1.023
Suppose the face value of a three-year option-free bond is USD 1,000 and the annual coupon is 10%. The current yield to maturity is 5%. What is the modified duration of this bond?a. 2.62b. 2.85c. 3.00d. 2.75
A portfolio manager uses her valuation model to estimate the value of a bond portfolio at USD 125.482 million. The term structure is flat. Using the same model, she estimates that the value of the portfolio would increase to USD 127.723 million if all interest rates fell by 30bp and would decrease
A portfolio manager has a bond position worth USD 100 million. The position has a modified duration of eight years and a convexity of 150 years.Assume that the term structure is flat. By how much does the value of the position change if interest rates increase by 25 basis points?a. USD
A zero-coupon bond with a maturity of 10 years has an annual effective yield of 10%. What is the closest value for its modified duration?a. 9 yearsb. 10 yearsc. 99 yearsd. 100 years
A five-year corporate bond paying an annual coupon of 8% is sold at a price reflecting a yield to maturity of 6%. One year passes and the interest rates remain unchanged. Assuming a flat term structure and holding all other factors constant, the bond’s price during this period will havea.
Consider a savings account that pays an annual interest rate of 8%. Calculate the amount of time it would take to double your money. Round to the nearest year.a. 7 yearsb. 8 yearsc. 9 yearsd. 10 years
Lisa Smith, the treasurer of Bank AAA, has $100 million to invest for one year. She has identified three alternative one-year certificates of deposit (CDs), with different compounding periods and annual rates. CD1: monthly, 7.82%;CD2: quarterly, 8.00%; CD3: semiannually, 8.05%; and CD4: continuous,
An investor buys a Treasury bill maturing in one month for $987. On the maturity date the investor collects $1,000. Calculate effective annual rate(EAR).a. 17.0%b. 15.8%c. 13.0%d. 11.6%
Assume that an asset’s daily return is normally distributed with zero mean.Suppose you have historical return data, u1, u2,..., um and that you want to use the maximum likelihood method to estimate the parameters of a EWMA volatility model. To do this, you define vi = 2 i as the variance
Which of the following four statements on models for estimating volatility is incorrect?a. In the EWMA model, some positive weight is assigned to the long-run average variance rate.b. In the EWMA model, the weights assigned to observations decrease exponentially as the observations become older.c.
Until January 1999 the historical volatility for the Brazilian real versus the U.S. dollar had been very small for several years. On January 13, Brazil abandoned the defense of the currency peg. Using the data from the close of business on January 13, which of the following methods for calculating
Using a daily RiskMetrics EWMA model with a decay factor = 0.95 to develop a forecast of the conditional variance, which weight will be applied to the return that is four days old?a. 0.000b. 0.043c. 0.048d. 0.950
A bank uses the exponentially weighted moving average (EWMA) technique with of 0.9 to model the daily volatility of a security. The current estimate of the daily volatility is 1.5%. The closing price of the security is USD 20 yesterday and USD 18 today. Using continuously compounded returns, what
A risk manager estimates daily variance ht using a GARCH model on daily returns rt: ht = 0 + 1r2 t−1 + ht−1, with 0 = 0.005, 1 = 0.04, = 0.94.The long-run annualized volatility is approximatelya. 13.54%b. 7.94%c. 72.72%d. 25.00%
Assume you are using a GARCH model to forecast volatility that you use to calculate the one-day VAR. If volatility is mean reverting, what can you say about the T-day VAR?a. It is less than the √T× one-day VAR.b. It is equal to √T× one-day VAR.c. It is greater than the √T× one-day VAR.d.
Consider a portfolio with 40% invested in asset X and 60% invested in asset Y. The mean and variance of return on X are 0 and 25 respectively.The mean and variance of return on Y are 1 and 121 respectively. The correlation coefficient between X and Y is 0.3. What is the nearest value for portfolio
Assume we calculate a one-week VAR for a natural gas position by rescaling the daily VAR using the square root of time rule. Let us now assume that we determine the true gas price process to be mean reverting and recalculate the VAR. Which of the following statements is true?a. The recalculated VAR
Consider a stock with daily returns that follow a random walk. The annualized volatility is 34%. Estimate the weekly volatility of this stock assuming that the year has 52 weeks.a. 6.80%b. 5.83%c. 4.85%d. 4.71%
Continuing with the previous question, you have implemented the simulation process discussed earlier using a time interval t = 0.001, and you are analyzing the following stock price path generated by your implementation.t St−1 S 0 30.00 0.0930 0.03 1 30.03 0.8493 0.21 2 30.23 0.9617 0.23 3
Consider a stock that pays no dividends, has a volatility of 25% pa, and has an expected return of 13% pa. The current stock price is S0 = $30. This implies the model St+1 = St(1 + 0.13t + 0.25√t ), where is a standard normal random variable. To implement this simulation, you generate a path of
Let N be a 1 × n vector of independent draws from a standard normal distribution, and let V be a covariance matrix of market time-series data.Then, if L is a diagonal matrix of the eigenvalues of V, E is a matrix of the eigenvectors of V, and CC is the Cholesky factorization of V, which of the
The measurement error in VAR, due to sampling variation, should be greater witha. More observations and a high confidence level (e.g., 99%)b. Fewer observations and a high confidence levelc. More observations and a low confidence level (e.g., 95%)d. Fewer observations and a low confidence level
A risk manager has been requested to provide some indication of the accuracy of a Monte Carlo simulation. Using 1,000 replications of a normally distributed variable S, the relative error in the one-day 99% VAR is 5%.Under these conditions,a. Using 1,000 replications of a long option position on S
Which one of the following statements about Monte Carlo simulation is false?a. Monte Carlo simulation can be used with a lognormal distribution.b. Monte Carlo simulation can generate distributions for portfolios that contain only linear positions.c. One drawback of Monte Carlo simulation is that it
A plausible stochastic process for the short-term rate is often considered to be one where the rate is pulled back to some long-run average level. Which one of the following term-structure models does not include this characteristic?a. The Vasicek modelb. The Ho-Lee modelc. The Hull-White modeld.
Which group of term-structure models do the Ho-Lee, Hull-White, and Heath-Jarrow-Morton models belong to?a. No-arbitrage modelsb. Two-factor modelsc. Lognormal modelsd. Deterministic models
The term a(b − r) in the previous question represents which term?a. Gammab. Stochasticc. Reversiond. Vega
The Vasicek model defines a risk-neutral process for r that is dr = a(b −r)dt + dz, wherea, b, and are constant, and r represents the rate of interest. From this equation we can conclude that the model is aa. Monte Carlo type modelb. Single-factor term-structure modelc. Two-factor
Consider that a stock price S that follows a geometric Brownian motion dS = aSdt + bSdz, with b strictly positive. Which of the following statements is false?a. If the drift a is positive, the price one year from now will be above today’s price.b. The instantaneous rate of return on the stock
In the geometric Brown motion process for a variable S, I. S is normally distributed.II. dln(S) is normally distributed.III. dS/S is normally distributed.IV. S is lognormally distributed.a. I onlyb. II, III, and IVc. IV onlyd. III and IV
Suppose you simulate the price path of stock HHF using a geometric Brownian motion model with drift = 0, volatility = 0.14, and time stept = 0.01. Let St be the price of the stock at time t. If S0 = 100, and the first two simulated (randomly selected) standard normal variables are 1 = 0.263 and
Under what circumstances could the explanatory power of regression analysis be overstated?a. The explanatory variables are not correlated with one another.b. The variance of the error term decreases as the value of the dependent variable increases.c. The error term is normally distributed.d. An
Which of the following statements regarding linear regression is false?a. Heteroskedasticity occurs when the variance of residuals is not the same across all observations in the sample.b. Unconditional heteroskedasticity leads to inefficient estimates, whereas conditional heteroskedasticity can
You built a linear regression model to analyze annual salaries for a developed country. You incorporated two independent variables, age and experience, into your model. Upon reading the regression results, you notice that the coefficient of experience is negative, which appears to be
Which of the following statements about the linear regression of the return of a portfolio over the return of its benchmark presented below are correct?Portfolio Parameter Value Beta 1.25 Alpha 0.26 Coefficient of determination 0.66 Standard deviation of error 2.42 I. The correlation is 0.71.II.
A portfolio manager is interested in the systematic risk of a stock portfolio, so he estimates the linear regression: RPt − RF = P + P [RMt − RF ] + Pt where RPt is the return of the portfolio at time t, RMt is the return of the market portfolio at time t, and RF is the risk-free rate, which
Consider two stocks, A and B. Assume their annual returns are jointly normally distributed, the marginal distribution of each stock has mean 2% and standard deviation 10%, and the correlation is 0.9. What is the expected annual return of stock A if the annual return of stock B is 3%?a. 2%b. 2.9%c.
Consider the following linear regression model: Y = a + b X +e. Suppose a = 0.05, b = 1.2, SD(Y) = 0.26, and SD(e) = 0.1. What is the correlation between X and Y?a. 0.923b. 0.852c. 0.701d. 0.462
A population has a known mean of 1,000. Suppose 1,600 samples are randomly drawn (with replacement) from this population. The mean of the observed samples is 998.7, and the standard deviation of the observed samples is 100. What is the standard error of the sample mean?a. 0.025b. 0.25c. 2.5d. 25
What does a hypothesis test at the 5% significance level mean?a. P(not reject H0 | H0 is true) = 0.05b. P(not reject H0 | H0 is false) = 0.05c. P(reject H0 | H0 is true) = 0.05d. P(reject H0 | H0 is false) = 0.05
When can you use the normal distribution to approximate the Poisson distribution, assuming you have n independent trials, each with a probability of success of p?a. When the mean of the Poisson distribution is very smallb. When the variance of the Poisson distribution is very smallc. When the
On a multiple-choice exam with four choices for each of six questions, what is the probability that a student gets fewer than two questions correct simply by guessing?a. 0.46%b. 23.73%c. 35.60%d. 53.39%
Which of the following statements is the most accurate about the relationship between a normal distribution and a Student’s t distribution that have the same mean and standard deviation?a. They have the same skewness and the same kurtosis.b. The Student’s t distribution has larger skewness and
For a lognormal variable X, we know that ln(X) has a normal distribution with a mean of zero and a standard deviation of 0.5. What are the expected value and the variance of X?a. 1.025 and 0.187b. 1.126 and 0.217c. 1.133 and 0.365d. 1.203 and 0.399
Consider a stock with an initial price of $100. Its price one year from now is given by S = 100 × exp(r), where the rate of return r is normally distributed with a mean of 0.1 and a standard deviation of 0.2. With 95% confidence, after rounding, S will be betweena. $67.57 and $147.99b. $70.80 and
The skew of a lognormal distribution is alwaysa. Positiveb. Negativec. 0d. 3
Which of the following statements best characterizes the relationship between the normal and lognormal distributions?a. The lognormal distribution is the logarithm of the normal distribution.b. If the natural log of the random variable X is lognormally distributed, then X is normally distributed.c.
Which type of distribution produces the lowest probability for a variable to exceed a specified extreme value that is greater than the mean, assuming the distributions all have the same mean and variance?a. A leptokurtic distribution with a kurtosis of 4b. A leptokurtic distribution with a kurtosis
Which of the following statements about the normal distribution is not accurate?a. Kurtosis equals 3.b. Skewness equals 1.c. The entire distribution can be characterized by two moments, mean and variance.d. The normal density function has the following expression:f(x) = 1√2 2 exp[− 1 22 (x −

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