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An analyst has determined that the probability that the S&P 500 index will increase on any given day is 0.60 and the probability that it will decrease is 0.40. The expected value and variance of the number of up days in a 5-day period are closest to: | A.3.0 and 1.2; B.3.0 and 1.1; C.2.0 and 0.5; D.2.0 and 2.1 | A | An analyst has determined that the probability that the S&P 500 index will increase on any given day is 0.60 and the probability that it will decrease is 0.40. The expected value and variance of the number of up days in a 5-day period are closest to: A.3.0 and 1.2; B.3.0 and 1.1; C.2.0 and 0.5; D.2.0 and 2.1 | A.3.0 and 1.2 | B.3.0 and 1.1 | C.2.0 and 0.5 | D.2.0 and 2.1 | A.3.0 and 1.2 |
The distribution of one-year returns for a portfolio of securities is normally distributed with an expected value of €45 million, and a standard deviation of €16 million. What is the probability that the value of the portfolio, one year hence, will be between €39 million and €43 million? | A.8.6%; B.9.6%; C.10.6%; D.11.6% | B | The distribution of one-year returns for a portfolio of securities is normally distributed with an expected value of €45 million, and a standard deviation of €16 million. What is the probability that the value of the portfolio, one year hence, will be between €39 million and €43 million? A.8.6%; B.9.6%; C.10.6%; D.11.6% | A.8.6% | B.9.6% | C.10.6% | D.11.6% | B.9.6% |
You are given that X and Y are random variables, and each of which follows a standard normal distribution with Covariance (X,Y) = 0.4. What is the variance of (5X + 2Y)? | A.11.0; B.29.0; C.29.4; D.37.0 | D | You are given that X and Y are random variables, and each of which follows a standard normal distribution with Covariance (X,Y) = 0.4. What is the variance of (5X + 2Y)? A.11.0; B.29.0; C.29.4; D.37.0 | A.11.0 | B.29.0 | C.29.4 | D.37.0 | D.37.0 |
A portfolio of bonds consists of five bonds whose default correlation is zero. The one-year probabilities of default of the bonds are: 1%, 2%, 5%, 10% and 15%. What is the one-year probability of no default within the portfolio? | A.71%; B.67%; C.85%; D.99% | A | A portfolio of bonds consists of five bonds whose default correlation is zero. The one-year probabilities of default of the bonds are: 1%, 2%, 5%, 10% and 15%. What is the one-year probability of no default within the portfolio? A.71%; B.67%; C.85%; D.99% | A.71% | B.67% | C.85% | D.99% | A.71% |
A certain low-severity administrative (operational) process tends to produce an average of eight errors per week (where each week is five workdays). If this loss frequency process can be characterized by a Poisson distribution, which is NEAREST to the probability that more than one error will be produced tomorrow? | A.20.19%; B.32.30%; C.47.51%; D.66.49% | C | A certain low-severity administrative (operational) process tends to produce an average of eight errors per week (where each week is five workdays). If this loss frequency process can be characterized by a Poisson distribution, which is NEAREST to the probability that more than one error will be produced tomorrow? A.20.19%; B.32.30%; C.47.51%; D.66.49% | A.20.19% | B.32.30% | C.47.51% | D.66.49% | C.47.51% |
Bonds rated B have a 25% chance of default in five years. Bonds rated CCC have a 40% chance of default in five years. A portfolio consists of 30% B and 70% CCC-rated bonds. If a randomly selected bond defaults in a five-year period, what is the probability that it was a B-rated bond? | A.0.625; B.0.211; C.0.429; D.0.250 | B | Bonds rated B have a 25% chance of default in five years. Bonds rated CCC have a 40% chance of default in five years. A portfolio consists of 30% B and 70% CCC-rated bonds. If a randomly selected bond defaults in a five-year period, what is the probability that it was a B-rated bond? A.0.625; B.0.211; C.0.429; D.0.250 | A.0.625 | B.0.211 | C.0.429 | D.0.250 | B.0.211 |
There are 2 phone calls per hour in a call center every day. The probability that they will receive 20 calls in an 8-hour day is closest to: | A.5.59%; B.6.56%; C.7.66%; D.8.40% | A | There are 2 phone calls per hour in a call center every day. The probability that they will receive 20 calls in an 8-hour day is closest to: A.5.59%; B.6.56%; C.7.66%; D.8.40% | A.5.59% | B.6.56% | C.7.66% | D.8.40% | A.5.59% |
Your firm uses a proprietary forecasting model and assumes that the random variables they used follow the Poisson distribution. You are trying to assess the probability of the number of defects in an assembly production process for a given company. Assume that there is a 0.005 probability of a defect for every production run. Which of the choices below is the probability of 7 defects in 1,000 production runs? | A.3.0%; B.4.4%; C.8.6%; D.10.4% | D | Your firm uses a proprietary forecasting model and assumes that the random variables they used follow the Poisson distribution. You are trying to assess the probability of the number of defects in an assembly production process for a given company. Assume that there is a 0.005 probability of a defect for every production run. Which of the choices below is the probability of 7 defects in 1,000 production runs? A.3.0%; B.4.4%; C.8.6%; D.10.4% | A.3.0% | B.4.4% | C.8.6% | D.10.4% | D.10.4% |
If the average rate of HFLS operational loss events instead is 20 per workweek (20 every five days), if we assume a Poisson distribution, what is the probability on a given single day that between four and six HFLS losses will occur, inclusive? | A.35.6%; B.45.6%; C.55.6%; D.65.6% | B | If the average rate of HFLS operational loss events instead is 20 per workweek (20 every five days), if we assume a Poisson distribution, what is the probability on a given single day that between four and six HFLS losses will occur, inclusive? A.35.6%; B.45.6%; C.55.6%; D.65.6% | A.35.6% | B.45.6% | C.55.6% | D.65.6% | B.45.6% |
An analyst is studying a stock that is currently trading at $35. The analyst estimates that there is 33% probability that the stock will trade at $50 after one year, a 20% probability that the stock will trade at $42, and a 47% probability that the stock will trade at $20. What is the volatility of this stock return? | A.13%; B.24%; C.31%; D.39% | D | An analyst is studying a stock that is currently trading at $35. The analyst estimates that there is 33% probability that the stock will trade at $50 after one year, a 20% probability that the stock will trade at $42, and a 47% probability that the stock will trade at $20. What is the volatility of this stock return? A.13%; B.24%; C.31%; D.39% | A.13% | B.24% | C.31% | D.39% | D.39% |
The return on a portfolio is normally distributed with an expected rate of return of 10%, and a standard deviation of 20%. What is the probability that the return will be between 0% and 5%? | A.7%; B.9%; C.11%; D.13% | B | The return on a portfolio is normally distributed with an expected rate of return of 10%, and a standard deviation of 20%. What is the probability that the return will be between 0% and 5%? A.7%; B.9%; C.11%; D.13% | A.7% | B.9% | C.11% | D.13% | B.9% |
Assume the annual returns of Fund A are normally distributed with a mean and standard deviation of 10%. The annual returns of Fund B are also normally distributed, but with a mean and standard deviation of 20%. The correlation between the returns of the funds is 0.40. At the end of the year, Fund B has returned 30%, and Fund A has returned 12%. Which is NEAREST to the probability that Fund B outperforms Fund A by this much or more? | A.7.00%; B.15.90%; C.33.22%; D.56.04% | C | Assume the annual returns of Fund A are normally distributed with a mean and standard deviation of 10%. The annual returns of Fund B are also normally distributed, but with a mean and standard deviation of 20%. The correlation between the returns of the funds is 0.40. At the end of the year, Fund B has returned 30%, and Fund A has returned 12%. Which is NEAREST to the probability that Fund B outperforms Fund A by this much or more? A.7.00%; B.15.90%; C.33.22%; D.56.04% | A.7.00% | B.15.90% | C.33.22% | D.56.04% | C.33.22% |
Your staff has determined that your 95% daily VaR model is perfectly accurate: on any given day, the probability that the loss exceeds VaR is 5%. What is the probability that next month, which has 20 trading days, VaR will be exceeded on two days or less? | A.86.47%; B.91.97%; C.92.45%; D.99.99% | C | Your staff has determined that your 95% daily VaR model is perfectly accurate: on any given day, the probability that the loss exceeds VaR is 5%. What is the probability that next month, which has 20 trading days, VaR will be exceeded on two days or less? A.86.47%; B.91.97%; C.92.45%; D.99.99% | A.86.47% | B.91.97% | C.92.45% | D.99.99% | C.92.45% |
The variance of the returns from stock A is 0.018 and that of the market is 0.025. If the covariance between the stock and the market index is -0.002, their correlation coefficient is CLOSEST to: | A.-0.23; B.-0.11; C.-0.09; D.-0.08 | C | The variance of the returns from stock A is 0.018 and that of the market is 0.025. If the covariance between the stock and the market index is -0.002, their correlation coefficient is CLOSEST to: A.-0.23; B.-0.11; C.-0.09; D.-0.08 | A.-0.23 | B.-0.11 | C.-0.09 | D.-0.08 | C.-0.09 |
A high growth stock has a daily return volatility of 1.60%. The returns are positivelyautocorrelated such that the correlation between consecutive daily returns is +0.30. What is the two-day volatility of the stock? | A.1.800%; B.2.263%; C.2.580%; D.3.200% | C | A high growth stock has a daily return volatility of 1.60%. The returns are positivelyautocorrelated such that the correlation between consecutive daily returns is +0.30. What is the two-day volatility of the stock? A.1.800%; B.2.263%; C.2.580%; D.3.200% | A.1.800% | B.2.263% | C.2.580% | D.3.200% | C.2.580% |
The covariance between the return from two securities is 4 and the correlation between them is 0.5. If the variance of the first return is 16, the variance of the second return will be CLOSEST to: | A.0.25; B.0.50; C.2.00; D.4.00 | D | The covariance between the return from two securities is 4 and the correlation between them is 0.5. If the variance of the first return is 16, the variance of the second return will be CLOSEST to: A.0.25; B.0.50; C.2.00; D.4.00 | A.0.25 | B.0.50 | C.2.00 | D.4.00 | D.4.00 |
The mean equity risk premium over a 40-year period is equal to 8.0%. The standard deviation of the sample is 12%. The standard error of the sample mean is closest to: | A.0.30%; B.1.90%; C.1.26%; D.8.00% | B | The mean equity risk premium over a 40-year period is equal to 8.0%. The standard deviation of the sample is 12%. The standard error of the sample mean is closest to: A.0.30%; B.1.90%; C.1.26%; D.8.00% | A.0.30% | B.1.90% | C.1.26% | D.8.00% | B.1.90% |
Your firm uses a proprietary forecasting model that requires parameter estimates of random variables that are believed to follow the Poisson distribution. You are attempting to assess the probability of the number of defects in an assembly production process for a given company. Assume that there is a 0.005 probability of a defect for every production run. What is the probability of 7 defects in 1,000 production runs? | A.3.0%; B.4.4%; C.8.6%; D.10.4% | D | Your firm uses a proprietary forecasting model that requires parameter estimates of random variables that are believed to follow the Poisson distribution. You are attempting to assess the probability of the number of defects in an assembly production process for a given company. Assume that there is a 0.005 probability of a defect for every production run. What is the probability of 7 defects in 1,000 production runs? A.3.0%; B.4.4%; C.8.6%; D.10.4% | A.3.0% | B.4.4% | C.8.6% | D.10.4% | D.10.4% |
The annual marginal probability of default of a bond is 15% in year 1 and 20% in year 2. What is the probability of the bond surviving (i.e. no default) to the end of two years? | A.68%; B.65%; C.80%; D.85% | A | The annual marginal probability of default of a bond is 15% in year 1 and 20% in year 2. What is the probability of the bond surviving (i.e. no default) to the end of two years? A.68%; B.65%; C.80%; D.85% | A.68% | B.65% | C.80% | D.85% | A.68% |
Assume today's stock price S(0) is $100, the daily log (continuously compounded) return has mean of 0.0 and standard deviation of 0.10 (10%), and tomorrow's stock price is lognormally distributed. What is the approximate probability that tomorrow's stock price will exceed $117.94? | A.about 1%; B.1.43%; C.4.46%; D.about 5% | D | Assume today's stock price S(0) is $100, the daily log (continuously compounded) return has mean of 0.0 and standard deviation of 0.10 (10%), and tomorrow's stock price is lognormally distributed. What is the approximate probability that tomorrow's stock price will exceed $117.94? A.about 1%; B.1.43%; C.4.46%; D.about 5% | A.about 1% | B.1.43% | C.4.46% | D.about 5% | D.about 5% |
Bond A and Bond B have the same rating and probability of default. The estimated probability that both bonds will default during the next year is 5%. If Bond A defaults next year, there is a 50% probability that Bond B will also default. What is the probability that neither Bond A nor Bond B will default over the next year? | A.75%.; B.80%.; C.85%; D.95%. | C | Bond A and Bond B have the same rating and probability of default. The estimated probability that both bonds will default during the next year is 5%. If Bond A defaults next year, there is a 50% probability that Bond B will also default. What is the probability that neither Bond A nor Bond B will default over the next year? A.75%.; B.80%.; C.85%; D.95%. | A.75%. | B.80%. | C.85% | D.95%. | C.85% |
An operational risk manager uses the Poisson distribution to estimate the frequency of losses in excess of USD 2 million during the next year. It is observed that the frequency of losses greater than USD 2 million is 3 per year on average over the last 10 years. If this observation is indicative of future occurrences and all the losses are independent of each other, what is the probability of at most one loss over USD 2 million occurring during the next two years? | A.1.01%; B.1.40%; C.1.61%; D.1.74% | D | An operational risk manager uses the Poisson distribution to estimate the frequency of losses in excess of USD 2 million during the next year. It is observed that the frequency of losses greater than USD 2 million is 3 per year on average over the last 10 years. If this observation is indicative of future occurrences and all the losses are independent of each other, what is the probability of at most one loss over USD 2 million occurring during the next two years? A.1.01%; B.1.40%; C.1.61%; D.1.74% | A.1.01% | B.1.40% | C.1.61% | D.1.74% | D.1.74% |
Jackson Lu, FRM, participates in a shareholders’ meeting of HITE Inc., a company he follows. In the meeting, the board announces that the company has a probability of 60% to pay dividend if the economy blooms in the next quarter, or a probability of 30% if the economy oscillates continuously. An economist predicts the economy has a probability of 20% to trend upward, and 80% to oscillate. Based on his understanding of the company, what is the probability that the economy actually blooms on the condition that HITE Inc. pays dividend? | A.33%.; B.72%.; C.66%.; D.45% | A | Jackson Lu, FRM, participates in a shareholders’ meeting of HITE Inc., a company he follows. In the meeting, the board announces that the company has a probability of 60% to pay dividend if the economy blooms in the next quarter, or a probability of 30% if the economy oscillates continuously. An economist predicts the economy has a probability of 20% to trend upward, and 80% to oscillate. Based on his understanding of the company, what is the probability that the economy actually blooms on the condition that HITE Inc. pays dividend? A.33%.; B.72%.; C.66%.; D.45% | A.33%. | B.72%. | C.66%. | D.45% | A.33%. |
A risk manager is backtesting a firm’s model for estimating 1-day 99% VaR and observes five exceedances over the prior 150 trading days. Assuming the model is correctly calibrated, and all the exceedances are independent of each other, what is the probability that there are exactly six exceedances over a period of 250 trading days? | A.0.84%; B.2.75%; C.36.97%; D.39.25% | B | A risk manager is backtesting a firm’s model for estimating 1-day 99% VaR and observes five exceedances over the prior 150 trading days. Assuming the model is correctly calibrated, and all the exceedances are independent of each other, what is the probability that there are exactly six exceedances over a period of 250 trading days? A.0.84%; B.2.75%; C.36.97%; D.39.25% | A.0.84% | B.2.75% | C.36.97% | D.39.25% | B.2.75% |
An analyst runs a regression of monthly stock returns on four independent variables over 48 months. From the regression, the total sum of squares (TSS) is 580, and the residual sum of squared (RSS) is 220. The regression coefficient of determination(R2) and the adjusted R2are closest to: | A.62% 58.5%; B.38% 41.5%; C.62% 41.5%; D.38% 58.5% | A | An analyst runs a regression of monthly stock returns on four independent variables over 48 months. From the regression, the total sum of squares (TSS) is 580, and the residual sum of squared (RSS) is 220. The regression coefficient of determination(R2) and the adjusted R2are closest to: A.62% 58.5%; B.38% 41.5%; C.62% 41.5%; D.38% 58.5% | A.62% 58.5% | B.38% 41.5% | C.62% 41.5% | D.38% 58.5% | A.62% 58.5% |
The term structure of swap rates is: 0.60% at 1 year; 0.90% at 2 years; 1.00% at 3 years; 2.20% at 4 years; 3.10% at 5 years. What is the two-year forward swap rate starting in three years, F(3,5), under respectively, semi-annual (s.a.) and annual compounding? | A.4.89% (s.a.) and 5.07% (annual); B.5.25% (s.a.) and 5.22% (annual); C.6.29% (s.a.) and 6.33% (annual); D.7.03% (s.a.) and 7.14% (annual) | C | The term structure of swap rates is: 0.60% at 1 year; 0.90% at 2 years; 1.00% at 3 years; 2.20% at 4 years; 3.10% at 5 years. What is the two-year forward swap rate starting in three years, F(3,5), under respectively, semi-annual (s.a.) and annual compounding? A.4.89% (s.a.) and 5.07% (annual); B.5.25% (s.a.) and 5.22% (annual); C.6.29% (s.a.) and 6.33% (annual); D.7.03% (s.a.) and 7.14% (annual) | A.4.89% (s.a.) and 5.07% (annual) | B.5.25% (s.a.) and 5.22% (annual) | C.6.29% (s.a.) and 6.33% (annual) | D.7.03% (s.a.) and 7.14% (annual) | C.6.29% (s.a.) and 6.33% (annual) |
A fixed rate bond, currently priced at 102.9, has one year remaining to maturity and is paying an 8% coupon. Assuming the coupon is paid semiannually, what is the yield of the bond? | A.8%; B.7.77%; C.6%; D.5% | D | A fixed rate bond, currently priced at 102.9, has one year remaining to maturity and is paying an 8% coupon. Assuming the coupon is paid semiannually, what is the yield of the bond? A.8%; B.7.77%; C.6%; D.5% | A.8% | B.7.77% | C.6% | D.5% | D.5% |
You have been asked to check for arbitrage opportunities in the Treasury bond market by comparing the cash flows of selected bonds with the cash flows of combinations of other bonds. If a 1-year zero-coupon bond is priced at USD 96.12 and a 1-year bond paying a 10% coupon semiannually is priced at USD 106.20, what should be the price of a 1-year Treasury bond that pays a coupon of 8% semiannually? | A.USD 98.10; B.USD 101.23; C.USD 103.35; D.USD 104.18 | D | You have been asked to check for arbitrage opportunities in the Treasury bond market by comparing the cash flows of selected bonds with the cash flows of combinations of other bonds. If a 1-year zero-coupon bond is priced at USD 96.12 and a 1-year bond paying a 10% coupon semiannually is priced at USD 106.20, what should be the price of a 1-year Treasury bond that pays a coupon of 8% semiannually? A.USD 98.10; B.USD 101.23; C.USD 103.35; D.USD 104.18 | A.USD 98.10 | B.USD 101.23 | C.USD 103.35 | D.USD 104.18 | D.USD 104.18 |
An investor buys $10,000 face amount of the U.S. Treasury 6 1/2 (coupon rate = 6.50%) of August 15, 2017, for settlement on July 1st, 2014. The last coupon paid on February 15, 2014 and the next coupon pays on August 15, 2014. The bond's yield to maturity happens to be 4.00%. What is nearest to the bond's quoted price at settlement? (this adds a level of difficulty by not giving you the invoice price) | A.$9,338.48; B.$9,904.15; C.$10,095.07; D.$10,726.83 | D | An investor buys $10,000 face amount of the U.S. Treasury 6 1/2 (coupon rate = 6.50%) of August 15, 2017, for settlement on July 1st, 2014. The last coupon paid on February 15, 2014 and the next coupon pays on August 15, 2014. The bond's yield to maturity happens to be 4.00%. What is nearest to the bond's quoted price at settlement? (this adds a level of difficulty by not giving you the invoice price) A.$9,338.48; B.$9,904.15; C.$10,095.07; D.$10,726.83 | A.$9,338.48 | B.$9,904.15 | C.$10,095.07 | D.$10,726.83 | D.$10,726.83 |
The six-month and one-year discount factors are, respectively, d(0.5) = 0.9920 and d(1.0) = 0.9760. What is the implied six-month forward rate, under semi-annual compounding? | A.2.34%; B.3.28%; C.3.95%; D.4.01% | B | The six-month and one-year discount factors are, respectively, d(0.5) = 0.9920 and d(1.0) = 0.9760. What is the implied six-month forward rate, under semi-annual compounding? A.2.34%; B.3.28%; C.3.95%; D.4.01% | A.2.34% | B.3.28% | C.3.95% | D.4.01% | B.3.28% |
The price of a six-month zero-coupon bond (bill) is $99.90 and the price of a one-year zerocoupon bond is $98.56. What is the implied six-month forward rate, under semi-annual compounding? | A.1.30%; B.2.95%; C.2.72%; D.3.08% | C | The price of a six-month zero-coupon bond (bill) is $99.90 and the price of a one-year zerocoupon bond is $98.56. What is the implied six-month forward rate, under semi-annual compounding? A.1.30%; B.2.95%; C.2.72%; D.3.08% | A.1.30% | B.2.95% | C.2.72% | D.3.08% | C.2.72% |
Exactly one year ago, Sally purchased a $100.00 face value bond that pays a semiannual coupon with a coupon rate of 9.0% per annum. When she purchased the bond, it had a maturity of 10.0 years and its yield to maturity (YTM; aka, yield) was 6.00%. If the bond's price today happens to be unchanged from one year ago (when she purchased the bond), which of the following is nearest to the bond's yield (yield to maturity) today? | A.5.57%; B.5.78%; C.6.00%; D.6.22% | B | Exactly one year ago, Sally purchased a $100.00 face value bond that pays a semiannual coupon with a coupon rate of 9.0% per annum. When she purchased the bond, it had a maturity of 10.0 years and its yield to maturity (YTM; aka, yield) was 6.00%. If the bond's price today happens to be unchanged from one year ago (when she purchased the bond), which of the following is nearest to the bond's yield (yield to maturity) today? A.5.57%; B.5.78%; C.6.00%; D.6.22% | A.5.57% | B.5.78% | C.6.00% | D.6.22% | B.5.78% |
Assuming the 92-day and 274-day interest rate is 8% (act/360, money market yield) compute the 182-day forward rate starting in 92 days (act/360, money market yield). | A.7.8%; B.8.0%; C.8.2%; D.8.4% | B | Assuming the 92-day and 274-day interest rate is 8% (act/360, money market yield) compute the 182-day forward rate starting in 92 days (act/360, money market yield). A.7.8%; B.8.0%; C.8.2%; D.8.4% | A.7.8% | B.8.0% | C.8.2% | D.8.4% | B.8.0% |
Consider the following, a 7-year zero-coupon bond carries an annual yield of 6.75% and a 6-; year zero coupon bond carries an annual yield of 5.87%. Calculate the 1 year forward rate 6 years from now. Assume annual compounding. | A.6.31%; B.12.03%; C.12.19%; D.12.62% | C | Consider the following, a 7-year zero-coupon bond carries an annual yield of 6.75% and a 6-; year zero coupon bond carries an annual yield of 5.87%. Calculate the 1 year forward rate 6 years from now. Assume annual compounding. A.6.31%; B.12.03%; C.12.19%; D.12.62% | A.6.31% | B.12.03% | C.12.19% | D.12.62% | C.12.19% |
Peter paid $93.40 to purchase a bond on June 1st, 2018; the bond pays a semi-annual coupon with a coupon rate of 3.0% per annum and matures in 10.0 years on June 1st, 2028. One year later, on June 1st, 2019, the bond's yield is unchanged; aka, unchanged yield assumption. Peter can reinvest his received coupons at a rate of 4.0% per annum. If Peter were to sell the bond on June 1st, 2019, which of the following is nearest to his gross realized return over the one year period since he purchased the bond? | A.-1.09%; B.2.50%; C.3.84%; D.4.11% | C | Peter paid $93.40 to purchase a bond on June 1st, 2018; the bond pays a semi-annual coupon with a coupon rate of 3.0% per annum and matures in 10.0 years on June 1st, 2028. One year later, on June 1st, 2019, the bond's yield is unchanged; aka, unchanged yield assumption. Peter can reinvest his received coupons at a rate of 4.0% per annum. If Peter were to sell the bond on June 1st, 2019, which of the following is nearest to his gross realized return over the one year period since he purchased the bond? A.-1.09%; B.2.50%; C.3.84%; D.4.11% | A.-1.09% | B.2.50% | C.3.84% | D.4.11% | C.3.84% |
The spot rate term structure is upward-sloping: 1.0% at 0.5 years, 2.0% at 1.0 years, 3.0% at 1.5 years, and 4.0% at 2.0 years. What is the price of two-year $100 face value bond that pays a semi-annual coupon with a 6.0% per annum coupon rate? | A.$99.74; B.$101.67; C.$102.27; D.$103.95 | D | The spot rate term structure is upward-sloping: 1.0% at 0.5 years, 2.0% at 1.0 years, 3.0% at 1.5 years, and 4.0% at 2.0 years. What is the price of two-year $100 face value bond that pays a semi-annual coupon with a 6.0% per annum coupon rate? A.$99.74; B.$101.67; C.$102.27; D.$103.95 | A.$99.74 | B.$101.67 | C.$102.27 | D.$103.95 | D.$103.95 |
Assume the following discount function, which is a set of discount factors: d(0.5) = 0.990, d(1.0) = 0.970, d(1.5) = 0.960, d(2.0) = 0.950. A U.S. Treasury bond pays a semi-annual coupon at a rate of 5.0% per annum and matures with a face value of $1,000 in eighteen months (T = 1.5 years). What is the price of the bond? | A.$985.00; B.$1,002.00; C.$1,015.00; D.$1,033.00 | D | Assume the following discount function, which is a set of discount factors: d(0.5) = 0.990, d(1.0) = 0.970, d(1.5) = 0.960, d(2.0) = 0.950. A U.S. Treasury bond pays a semi-annual coupon at a rate of 5.0% per annum and matures with a face value of $1,000 in eighteen months (T = 1.5 years). What is the price of the bond? A.$985.00; B.$1,002.00; C.$1,015.00; D.$1,033.00 | A.$985.00 | B.$1,002.00 | C.$1,015.00 | D.$1,033.00 | D.$1,033.00 |
A bank entered into a 5-year $150 million annual-pay LIBOR-based interest rate swap three years ago as the fixed rate payer at 5.5%. The relevant discount rates (continuously compounded) for 1-year and 2-year obligations are currently 5.75% and 6.25%, respectively. A payment was just made. The value of the swap is closest to: | A.-$2,555,860; B.$2,555,860; C.$6,450,000; D.-$6,450,000 | B | A bank entered into a 5-year $150 million annual-pay LIBOR-based interest rate swap three years ago as the fixed rate payer at 5.5%. The relevant discount rates (continuously compounded) for 1-year and 2-year obligations are currently 5.75% and 6.25%, respectively. A payment was just made. The value of the swap is closest to: A.-$2,555,860; B.$2,555,860; C.$6,450,000; D.-$6,450,000 | A.-$2,555,860 | B.$2,555,860 | C.$6,450,000 | D.-$6,450,000 | B.$2,555,860 |
On the OTC market there are two options available on Microsoft stock: a European put with premium of USD 2.25 and an American call option with premium of USD 0.46. Both options have strike price of USD 24 and an expiration date 3 months from now. Microsoft’s stock price is currently at USD 22 and no dividend is due during the next 6 months. Assuming that there is no arbitrage opportunity, which of the following choices is closest to the level of the continuous compounding risk-free rate: | A.0.25%; B.1.76%; C.3.52%; D.Insufficient information | C | On the OTC market there are two options available on Microsoft stock: a European put with premium of USD 2.25 and an American call option with premium of USD 0.46. Both options have strike price of USD 24 and an expiration date 3 months from now. Microsoft’s stock price is currently at USD 22 and no dividend is due during the next 6 months. Assuming that there is no arbitrage opportunity, which of the following choices is closest to the level of the continuous compounding risk-free rate: A.0.25%; B.1.76%; C.3.52%; D.Insufficient information | A.0.25% | B.1.76% | C.3.52% | D.Insufficient information | C.3.52% |
Consider a U.K. based company that exports goods to the EU. The U.K. company expects to receive payment on a shipment of goods in 60 days. Because the payment will be in euros, the U.K. company wants to hedge against a decline in the value of the euro against the pound over the next 60 days. The U.K. risk-free rate is 3% and the EU risk-free rate is 4%. No change is expected in these rates over the next 60 days. The current spot rate is EURGBP0.9230. To hedge the currency risk, the U.K. company should take a short position in a Euro contract at a forward price of (Assume annual compounding): | A.0.9205.; B.0.9215.; C.0.9244.; D.0.9141. | B | Consider a U.K. based company that exports goods to the EU. The U.K. company expects to receive payment on a shipment of goods in 60 days. Because the payment will be in euros, the U.K. company wants to hedge against a decline in the value of the euro against the pound over the next 60 days. The U.K. risk-free rate is 3% and the EU risk-free rate is 4%. No change is expected in these rates over the next 60 days. The current spot rate is EURGBP0.9230. To hedge the currency risk, the U.K. company should take a short position in a Euro contract at a forward price of (Assume annual compounding): A.0.9205.; B.0.9215.; C.0.9244.; D.0.9141. | A.0.9205. | B.0.9215. | C.0.9244. | D.0.9141. | B.0.9215. |
Stock A is expected to pay a $1 dividend after 2 month and a $2 dividend after 5 months. The stock price is now priced at $30, the continuous compounded risk-free rate for all maturities is 8%. An investor has just entered into a short position in a 6-month forward contract of the stock. Based on the information above, what is the reasonable price of this stock forward contract? | A.USD 28.19; B.USD 29.34; C.USD 29.98; D.USD 30.41 | A | Stock A is expected to pay a $1 dividend after 2 month and a $2 dividend after 5 months. The stock price is now priced at $30, the continuous compounded risk-free rate for all maturities is 8%. An investor has just entered into a short position in a 6-month forward contract of the stock. Based on the information above, what is the reasonable price of this stock forward contract? A.USD 28.19; B.USD 29.34; C.USD 29.98; D.USD 30.41 | A.USD 28.19 | B.USD 29.34 | C.USD 29.98 | D.USD 30.41 | A.USD 28.19 |
A Canadian-based tire company will receive $2,500,000 payment from its American-based distributor in two months. The Canadian firm hedges the exchange rate risk using a forward contract and the exchange rate of USDCAD is priced at 1.20. If the US dollar depreciates over the next two months and the expected future spot exchange rate of USDCAD would be 1.08, how much more or less will the Canadian-based tire firm receive in Canadian dollars by hedging, versus an unhedged position? | A.300,000 CAD more; B.300,000 CAD less; C.277,778 USD more; D.277,778 USD less | A | A Canadian-based tire company will receive $2,500,000 payment from its American-based distributor in two months. The Canadian firm hedges the exchange rate risk using a forward contract and the exchange rate of USDCAD is priced at 1.20. If the US dollar depreciates over the next two months and the expected future spot exchange rate of USDCAD would be 1.08, how much more or less will the Canadian-based tire firm receive in Canadian dollars by hedging, versus an unhedged position? A.300,000 CAD more; B.300,000 CAD less; C.277,778 USD more; D.277,778 USD less | A.300,000 CAD more | B.300,000 CAD less | C.277,778 USD more | D.277,778 USD less | A.300,000 CAD more |
Tom enterprise entered a swap with USD 5 million notional and received a floating rate based on 6-month Libor. It paid a fixed rate of 7% semiannually. The last cash flow of the swap exchanged 3 months ago. The swap has a remaining life of 15 months, with payment dates at 3, 9 and 15months. Today, continuously compounded spot Libor rates for 3-month, 9-month, 15-month are 5.8%, 6.5% and 6.8% respectively. The Libor at last payment was 6.1%. The value of the swap to Tom is closest to: | A.-$13,024; B.$13,024; C.-$14,127; D.$14,127 | C | Tom enterprise entered a swap with USD 5 million notional and received a floating rate based on 6-month Libor. It paid a fixed rate of 7% semiannually. The last cash flow of the swap exchanged 3 months ago. The swap has a remaining life of 15 months, with payment dates at 3, 9 and 15months. Today, continuously compounded spot Libor rates for 3-month, 9-month, 15-month are 5.8%, 6.5% and 6.8% respectively. The Libor at last payment was 6.1%. The value of the swap to Tom is closest to: A.-$13,024; B.$13,024; C.-$14,127; D.$14,127 | A.-$13,024 | B.$13,024 | C.-$14,127 | D.$14,127 | C.-$14,127 |
A stock is currently trading at USD 45, and its annual price volatility is 30%. The risktree rate is 1.5% per year. A risk manager is developing a 1-step binomial tree for a 2-year horizon. What is the risk-neutral probability that the stock will move down? | A.30%; B.43%; C.57%; D.70% | C | A stock is currently trading at USD 45, and its annual price volatility is 30%. The risktree rate is 1.5% per year. A risk manager is developing a 1-step binomial tree for a 2-year horizon. What is the risk-neutral probability that the stock will move down? A.30%; B.43%; C.57%; D.70% | A.30% | B.43% | C.57% | D.70% | C.57% |
An analyst is pricing a 2-year European put option on a non-dividend-paying stock using a binomial tree with two steps of one year each. The stock price is currently USD 38, and the strike price of the put is USD 40. What is the value of the put closest to, assuming that the annual risk-free rate will remain constant at 2% over the next two years and the annual stock volatility is 15%? | A.3.04 USD; B.3.48 USD; C.3.62 USD; D.3.81 USD | B | An analyst is pricing a 2-year European put option on a non-dividend-paying stock using a binomial tree with two steps of one year each. The stock price is currently USD 38, and the strike price of the put is USD 40. What is the value of the put closest to, assuming that the annual risk-free rate will remain constant at 2% over the next two years and the annual stock volatility is 15%? A.3.04 USD; B.3.48 USD; C.3.62 USD; D.3.81 USD | A.3.04 USD | B.3.48 USD | C.3.62 USD | D.3.81 USD | B.3.48 USD |
The spot rate term structure is upward-sloping: 1.0% at 0.5 years, 2.0% at 1.0 years, 3.0% at 1.5 years, and 4.0% at 2.0 years. What is the price of two-year $100 face value bond that pays a semi-annual coupon with a 6.0% per annum coupon rate? | A.$99.74; B.$101.67; C.$102.27; D.$103.95 | D | The spot rate term structure is upward-sloping: 1.0% at 0.5 years, 2.0% at 1.0 years, 3.0% at 1.5 years, and 4.0% at 2.0 years. What is the price of two-year $100 face value bond that pays a semi-annual coupon with a 6.0% per annum coupon rate? A.$99.74; B.$101.67; C.$102.27; D.$103.95 | A.$99.74 | B.$101.67 | C.$102.27 | D.$103.95 | D.$103.95 |
The price of a six-month zero-coupon bond is $99.90 and the price of a one-year zero-coupon bond is $98.56. What is the implied six-month forward rate, under semi-annual compounding? | A.1.30%; B.2.95%; C.2.72%; D.3.08% | C | The price of a six-month zero-coupon bond is $99.90 and the price of a one-year zero-coupon bond is $98.56. What is the implied six-month forward rate, under semi-annual compounding? A.1.30%; B.2.95%; C.2.72%; D.3.08% | A.1.30% | B.2.95% | C.2.72% | D.3.08% | C.2.72% |
The purchase price of a 3-year 9 percent semiannual coupon bond that is currently yielding 7 percent will be: | A.105.11; B.105.25; C.105.33; D.105.45 | C | The purchase price of a 3-year 9 percent semiannual coupon bond that is currently yielding 7 percent will be: A.105.11; B.105.25; C.105.33; D.105.45 | A.105.11 | B.105.25 | C.105.33 | D.105.45 | C.105.33 |
Consider a 7.75% semiannual coupon bond with a par value of $100 and four remaining coupons, which is trading at a yield of 8.375%. There are 74 days remaining in the current period that has a total of 182 days. The accrued coupon of this bond is closest to: | A.1.59; B.2.30; C.3.18; D.4.57 | B | Consider a 7.75% semiannual coupon bond with a par value of $100 and four remaining coupons, which is trading at a yield of 8.375%. There are 74 days remaining in the current period that has a total of 182 days. The accrued coupon of this bond is closest to: A.1.59; B.2.30; C.3.18; D.4.57 | A.1.59 | B.2.30 | C.3.18 | D.4.57 | B.2.30 |
The following discount function contains semi-annual discount factors out to two years: d(0.5) = 0.9970, d(1.0) = 0.9911, d(1.5) = 0.9809, d(2.0) = 0.9706. What is the implied eighteen-month (1.5 year) spot rate (aka, 1.5 year zero rate)? | A.0.600%; B.1.176%; C.1.290%; D.1.505% | C | The following discount function contains semi-annual discount factors out to two years: d(0.5) = 0.9970, d(1.0) = 0.9911, d(1.5) = 0.9809, d(2.0) = 0.9706. What is the implied eighteen-month (1.5 year) spot rate (aka, 1.5 year zero rate)? A.0.600%; B.1.176%; C.1.290%; D.1.505% | A.0.600% | B.1.176% | C.1.290% | D.1.505% | C.1.290% |
Given the following 30 ordered simulated percentage returns of an asset, calculate the VaR and expected shortfall (both expressed in terms of returns) at a 90% confidence level.-16, -14, -10, -7, -7, -5, -4, -4, -4, -3, -1, -1, 0, 0, 0, 1, 2, 2, 4, 6, 7, 8, 9, 11, 12, 12, 14, 18, 21, 23 | A.VaR(90%)=10,Expected shortfall=14; B.VaR(90%)=10,Expected shortfall=15; C.VaR(90%)=14,Expected shortfall=15; D.VaR(90%)=18,Expected shortfall=22 | B | Given the following 30 ordered simulated percentage returns of an asset, calculate the VaR and expected shortfall (both expressed in terms of returns) at a 90% confidence level.-16, -14, -10, -7, -7, -5, -4, -4, -4, -3, -1, -1, 0, 0, 0, 1, 2, 2, 4, 6, 7, 8, 9, 11, 12, 12, 14, 18, 21, 23 A.VaR(90%)=10,Expected shortfall=14; B.VaR(90%)=10,Expected shortfall=15; C.VaR(90%)=14,Expected shortfall=15; D.VaR(90%)=18,Expected shortfall=22 | A.VaR(90%)=10,Expected shortfall=14 | B.VaR(90%)=10,Expected shortfall=15 | C.VaR(90%)=14,Expected shortfall=15 | D.VaR(90%)=18,Expected shortfall=22 | B.VaR(90%)=10,Expected shortfall=15 |
A portfolio manager bought 1,000 call options on a non-dividend-paying stock, with a strike price of USD 100, for USD 6 each. The current stock price is USD 104 with a daily stock return volatility of 1.89%, and the delta of the option is 0.6. Using the delta-normal approach to calculate VaR, what is an approximation of the 1-day 95% VaR of this position? | A.USD 1,120; B.USD 1,946; C.USD 3,243; D.USD 5,406 | B | A portfolio manager bought 1,000 call options on a non-dividend-paying stock, with a strike price of USD 100, for USD 6 each. The current stock price is USD 104 with a daily stock return volatility of 1.89%, and the delta of the option is 0.6. Using the delta-normal approach to calculate VaR, what is an approximation of the 1-day 95% VaR of this position? A.USD 1,120; B.USD 1,946; C.USD 3,243; D.USD 5,406 | A.USD 1,120 | B.USD 1,946 | C.USD 3,243 | D.USD 5,406 | B.USD 1,946 |
Over the next year, an operational process model predicts a 95% probability of no loss occurrence and a 5% probability of a single loss occurrence. If the single loss occurs, the severity is characterized by three possible outcomes: $10.0 million loss with 20% probability, $18.0 million loss with 50% probability, and $25.0 million loss with 30% probability. What is the model's one-year 90% expected shortfall (ES)? | A.$9.25 million; B.$10.00 million; C.$13.88 million; D.$18.50 million | A | Over the next year, an operational process model predicts a 95% probability of no loss occurrence and a 5% probability of a single loss occurrence. If the single loss occurs, the severity is characterized by three possible outcomes: $10.0 million loss with 20% probability, $18.0 million loss with 50% probability, and $25.0 million loss with 30% probability. What is the model's one-year 90% expected shortfall (ES)? A.$9.25 million; B.$10.00 million; C.$13.88 million; D.$18.50 million | A.$9.25 million | B.$10.00 million | C.$13.88 million | D.$18.50 million | A.$9.25 million |
Mixed Fund has a portfolio worth USD 12,428,000 that consists of 42% of fixed income investments and 58% of equity investments. The 95% annual VaR for the entire portfolio is USD 1,367,000 and the 95% annual VaR for the equity portion of the portfolio is USD 1,153,000. Assume that there are 250 trading days in a year and that the correlation between stocks and bonds is zero. What is the 95% daily VaR for the fixed income portion of the portfolio? | A.USD 21,263; B.USD 46,445; C.USD 55,171; D.USD 72,635 | B | Mixed Fund has a portfolio worth USD 12,428,000 that consists of 42% of fixed income investments and 58% of equity investments. The 95% annual VaR for the entire portfolio is USD 1,367,000 and the 95% annual VaR for the equity portion of the portfolio is USD 1,153,000. Assume that there are 250 trading days in a year and that the correlation between stocks and bonds is zero. What is the 95% daily VaR for the fixed income portion of the portfolio? A.USD 21,263; B.USD 46,445; C.USD 55,171; D.USD 72,635 | A.USD 21,263 | B.USD 46,445 | C.USD 55,171 | D.USD 72,635 | B.USD 46,445 |
A small hedge fund is running a portfolio with a 5-day VaR of $3.1 million. Assuming normal conditions what is the best estimate for VaR over a 2-day horizon? | A.$1.2 million; B.$2.0 million; C.$2.5 million; D.$3.1 million | B | A small hedge fund is running a portfolio with a 5-day VaR of $3.1 million. Assuming normal conditions what is the best estimate for VaR over a 2-day horizon? A.$1.2 million; B.$2.0 million; C.$2.5 million; D.$3.1 million | A.$1.2 million | B.$2.0 million | C.$2.5 million | D.$3.1 million | B.$2.0 million |
A trader has an option position in crude oil with a delta of 100,000 barrels and gamma of 50,000 barrels per dollar move in price. Using the delta-gamma methodology, compute the VaR on this position, assuming the extreme move on crude oil is $2.00 per barrel. | A.$100,000; B.$200,000; C.$300,000; D.$400,000 | A | A trader has an option position in crude oil with a delta of 100,000 barrels and gamma of 50,000 barrels per dollar move in price. Using the delta-gamma methodology, compute the VaR on this position, assuming the extreme move on crude oil is $2.00 per barrel. A.$100,000; B.$200,000; C.$300,000; D.$400,000 | A.$100,000 | B.$200,000 | C.$300,000 | D.$400,000 | A.$100,000 |
A commodity-trading firm has an options portfolio with a two-day Value-at-Risk (VaR) of $2.5 million. What would be an appropriate translation of this VaR to a ten-day horizon under normal conditions? | A.$3.713 million; B.$4.792 million; C.$5.590 million; D.Cannot be determined | C | A commodity-trading firm has an options portfolio with a two-day Value-at-Risk (VaR) of $2.5 million. What would be an appropriate translation of this VaR to a ten-day horizon under normal conditions? A.$3.713 million; B.$4.792 million; C.$5.590 million; D.Cannot be determined | A.$3.713 million | B.$4.792 million | C.$5.590 million | D.Cannot be determined | C.$5.590 million |
A market risk manager uses historical information on 1,000 days of profit/loss information to calculate a daily VaR at the 99th percentile, of USD 8 million. Loss observations beyond the 99th percentile are then used to estimate the conditional VaR. If the losses beyond the VaR level, in millions, are USD 9, USD 10, USD 11, USD 13, USD 15, USD 18, USD 21, USD 24, and USD 32, then what is the conditional VaR? | A.USD 9 million; B.USD 32 million; C.USD 15 million; D.USD 17 million | D | A market risk manager uses historical information on 1,000 days of profit/loss information to calculate a daily VaR at the 99th percentile, of USD 8 million. Loss observations beyond the 99th percentile are then used to estimate the conditional VaR. If the losses beyond the VaR level, in millions, are USD 9, USD 10, USD 11, USD 13, USD 15, USD 18, USD 21, USD 24, and USD 32, then what is the conditional VaR? A.USD 9 million; B.USD 32 million; C.USD 15 million; D.USD 17 million | A.USD 9 million | B.USD 32 million | C.USD 15 million | D.USD 17 million | D.USD 17 million |
Consider the risk of a long call on an asset with a notional amount of $1 million. The VaR of the underlying asset is 7.8%. If the option is a short-term at-the-money option, the VaR of the option position is slightly: | A.Less than $39,000 when second-order terms are considered.; B.More than $39,000 when second-order terms are considered.; C.Less than $78,000 when second-order terms are considered.; D.More than $78,000 when second-order terms are considered. | A | Consider the risk of a long call on an asset with a notional amount of $1 million. The VaR of the underlying asset is 7.8%. If the option is a short-term at-the-money option, the VaR of the option position is slightly: A.Less than $39,000 when second-order terms are considered.; B.More than $39,000 when second-order terms are considered.; C.Less than $78,000 when second-order terms are considered.; D.More than $78,000 when second-order terms are considered. | A.Less than $39,000 when second-order terms are considered. | B.More than $39,000 when second-order terms are considered. | C.Less than $78,000 when second-order terms are considered. | D.More than $78,000 when second-order terms are considered. | A.Less than $39,000 when second-order terms are considered. |
If stock returns are independently, identically, normally distribution and the annual volatility is 30%, then the daily VaR at the 99% confidence level of a stock market portfolio is approximately: | A.2.41%; B.3.11%; C.4.40%; D.1.89% | C | If stock returns are independently, identically, normally distribution and the annual volatility is 30%, then the daily VaR at the 99% confidence level of a stock market portfolio is approximately: A.2.41%; B.3.11%; C.4.40%; D.1.89% | A.2.41% | B.3.11% | C.4.40% | D.1.89% | C.4.40% |
Consider the following single stock portfolio: Stock ABC has a market position of $200,000 and an annualized volatility of 30%. Calculate the linear VaR with 99% confidence level for a 10 business day holding period. Assume normal distribution and round to the nearest dollar. | A.$11,952; B.$27,849; C.$60,000; D.$88,066 | B | Consider the following single stock portfolio: Stock ABC has a market position of $200,000 and an annualized volatility of 30%. Calculate the linear VaR with 99% confidence level for a 10 business day holding period. Assume normal distribution and round to the nearest dollar. A.$11,952; B.$27,849; C.$60,000; D.$88,066 | A.$11,952 | B.$27,849 | C.$60,000 | D.$88,066 | B.$27,849 |
A company reports a one-week VaR of $1 million at the 95% confidence level. Which of the following statements is most likely to be true? | A.The daily return on the company portfolio follows a normal distribution so that a one-week VaR could be computed.; B.The one-week VaR at the 99% confidence level is $5 million.; C.With probability 5%, the company will lose $1 million or more in one week.; D.With probability 95%, the company will not experience a loss greater than $95 million in one week. | C | A company reports a one-week VaR of $1 million at the 95% confidence level. Which of the following statements is most likely to be true? A.The daily return on the company portfolio follows a normal distribution so that a one-week VaR could be computed.; B.The one-week VaR at the 99% confidence level is $5 million.; C.With probability 5%, the company will lose $1 million or more in one week.; D.With probability 95%, the company will not experience a loss greater than $95 million in one week. | A.The daily return on the company portfolio follows a normal distribution so that a one-week VaR could be computed. | B.The one-week VaR at the 99% confidence level is $5 million. | C.With probability 5%, the company will lose $1 million or more in one week. | D.With probability 95%, the company will not experience a loss greater than $95 million in one week. | C.With probability 5%, the company will lose $1 million or more in one week. |
A large bank currently has a security portfolio with a market value of $145 million. The daily returns on the bank's portfolio are normally distributed with 80% of the distribution lying within 1.28 standard deviations above and below the mean and 90% of the distribution lying within 1.65 standard deviations above and below the mean. Assuming the standard deviation of the bank's portfolio returns is 1.2%, calculate the VaR(5%) on a one-day basis. | A.$2.87 million; B.$2.23 million; C.$2.04 million; D.Cannot be determined from information given | A | A large bank currently has a security portfolio with a market value of $145 million. The daily returns on the bank's portfolio are normally distributed with 80% of the distribution lying within 1.28 standard deviations above and below the mean and 90% of the distribution lying within 1.65 standard deviations above and below the mean. Assuming the standard deviation of the bank's portfolio returns is 1.2%, calculate the VaR(5%) on a one-day basis. A.$2.87 million; B.$2.23 million; C.$2.04 million; D.Cannot be determined from information given | A.$2.87 million | B.$2.23 million | C.$2.04 million | D.Cannot be determined from information given | A.$2.87 million |
A single stock has a price of USD 10 and a current daily volatility of 2%. Using the deltanormal method, the VaR at the 95% confidence level of a long at-the-money call on this stock over a one-day holding period is approximately: | A.USD 1.645; B.USD 0.16; C.USD 0.33; D.USD 0.23 | B | A single stock has a price of USD 10 and a current daily volatility of 2%. Using the deltanormal method, the VaR at the 95% confidence level of a long at-the-money call on this stock over a one-day holding period is approximately: A.USD 1.645; B.USD 0.16; C.USD 0.33; D.USD 0.23 | A.USD 1.645 | B.USD 0.16 | C.USD 0.33 | D.USD 0.23 | B.USD 0.16 |
Howard Freeman manages a portfolio of investment securities for a regional bank. The portfolio has a current market value equal to USD 6,247,000 with a daily variance of 0.0002. Assuming there are 250 trading days in a year and that the portfolio returns follow a normal distribution, the estimate of the annual VaR at the 95% confidence level is closest to which of the following? | A.USD 32,595; B.USD 145,770; C.USD 2, 297,854; D.USD 2,737,868 | C | Howard Freeman manages a portfolio of investment securities for a regional bank. The portfolio has a current market value equal to USD 6,247,000 with a daily variance of 0.0002. Assuming there are 250 trading days in a year and that the portfolio returns follow a normal distribution, the estimate of the annual VaR at the 95% confidence level is closest to which of the following? A.USD 32,595; B.USD 145,770; C.USD 2, 297,854; D.USD 2,737,868 | A.USD 32,595 | B.USD 145,770 | C.USD 2, 297,854 | D.USD 2,737,868 | C.USD 2, 297,854 |
Rational Investment Inc. is estimating a daily VaR for its fixed income portfolio currently valued at USD 800 million. Using returns for the last 400 days. (ordered in decreasing order, from highest daily return to lowest daily return), the daily returns are the following: 1.99%, 1.89%, 1.88%, 1.87%, …, -1.76%, -1.82%, -1.84%, -1.87%, -1.91%. At the 99% confidence level, what is your estimate of the daily dollar VaR using the historical simulation method? | A.USD 14.08m; B.USD 14.56m; C.USD 14.72m; D.USD 15.04m | B | Rational Investment Inc. is estimating a daily VaR for its fixed income portfolio currently valued at USD 800 million. Using returns for the last 400 days. (ordered in decreasing order, from highest daily return to lowest daily return), the daily returns are the following: 1.99%, 1.89%, 1.88%, 1.87%, …, -1.76%, -1.82%, -1.84%, -1.87%, -1.91%. At the 99% confidence level, what is your estimate of the daily dollar VaR using the historical simulation method? A.USD 14.08m; B.USD 14.56m; C.USD 14.72m; D.USD 15.04m | A.USD 14.08m | B.USD 14.56m | C.USD 14.72m | D.USD 15.04m | B.USD 14.56m |
Consider the following single stock portfolio: Stock ABC has a market position of $200,000 and an annualized volatility of 30%. Calculate the linear VaR with 99% confidence level for a 10 business day holding period. Assume normal distribution and round to the nearest dollar. | A.$11,952; B.$27,849; C.$60,000; D.$88,066 | B | Consider the following single stock portfolio: Stock ABC has a market position of $200,000 and an annualized volatility of 30%. Calculate the linear VaR with 99% confidence level for a 10 business day holding period. Assume normal distribution and round to the nearest dollar. A.$11,952; B.$27,849; C.$60,000; D.$88,066 | A.$11,952 | B.$27,849 | C.$60,000 | D.$88,066 | B.$27,849 |
The VaR of a portfolio at 95% confidence level is 15.2. If the confidence level is raised to 99% (assuming a one-tailed normal distribution), the new value of VaR will be closest to: | A.10.8; B.5.2; C.18.1; D.21.5 | D | The VaR of a portfolio at 95% confidence level is 15.2. If the confidence level is raised to 99% (assuming a one-tailed normal distribution), the new value of VaR will be closest to: A.10.8; B.5.2; C.18.1; D.21.5 | A.10.8 | B.5.2 | C.18.1 | D.21.5 | D.21.5 |
We assume a lambda parameter of 0.850 under an exponential smoothing (i.e., EWMA) approach to the estimation of today's (t) daily volatility. Yesterday (t-1) is the most recent daily return in our series. What are the weights assigned, respectively, to yesterday's and the day before yesterday's returns; i.e., weight (t-1) and weight (t-2)? | A.15.00% (t-1) and 2.25% (t-2); B.15.00% and 12.75%; C.72.25% and 61.41%; D.85.00% and 72.25% | B | We assume a lambda parameter of 0.850 under an exponential smoothing (i.e., EWMA) approach to the estimation of today's (t) daily volatility. Yesterday (t-1) is the most recent daily return in our series. What are the weights assigned, respectively, to yesterday's and the day before yesterday's returns; i.e., weight (t-1) and weight (t-2)? A.15.00% (t-1) and 2.25% (t-2); B.15.00% and 12.75%; C.72.25% and 61.41%; D.85.00% and 72.25% | A.15.00% (t-1) and 2.25% (t-2) | B.15.00% and 12.75% | C.72.25% and 61.41% | D.85.00% and 72.25% | B.15.00% and 12.75% |
John Flag, the manager of a USD 150 million distressed bond portfolio, conducts stress tests on the portfolio. The portfolio’s annualized return is 12%, with an annualized return volatility of 25%. In the last two years, the portfolio encountered several days when the daily value change of the portfolio was more than 3 standard deviations. If the portfolio suffered a 4-sigma daily event, which of the following is the best estimate of the change in the value of this portfolio? Assume that there are 250 trading days in a year. | A.USD 9.48 million; B.USD 23.70 million; C.USD 37.50 million; D.USD 150 million | A | John Flag, the manager of a USD 150 million distressed bond portfolio, conducts stress tests on the portfolio. The portfolio’s annualized return is 12%, with an annualized return volatility of 25%. In the last two years, the portfolio encountered several days when the daily value change of the portfolio was more than 3 standard deviations. If the portfolio suffered a 4-sigma daily event, which of the following is the best estimate of the change in the value of this portfolio? Assume that there are 250 trading days in a year. A.USD 9.48 million; B.USD 23.70 million; C.USD 37.50 million; D.USD 150 million | A.USD 9.48 million | B.USD 23.70 million | C.USD 37.50 million | D.USD 150 million | A.USD 9.48 million |
An at-the money European call on the DJ EURO STOXX 50 index a strike of 2200 and maturing in 1 year is trading at EUR 350, where contract value is determined by EUR 10 per index point. The risk-free rate is 3% per year, and the daily volatility of the index is 2.05%. If we assume that the expected return on the DJ EURO STOXX 50 is 0%, the 99% 1-day VaR of a short position on a single call calculated using the delta-normal approach is closest to: | A.EUR 8; B.EUR 53; C.EUR 84; D.EUR 525 | D | An at-the money European call on the DJ EURO STOXX 50 index a strike of 2200 and maturing in 1 year is trading at EUR 350, where contract value is determined by EUR 10 per index point. The risk-free rate is 3% per year, and the daily volatility of the index is 2.05%. If we assume that the expected return on the DJ EURO STOXX 50 is 0%, the 99% 1-day VaR of a short position on a single call calculated using the delta-normal approach is closest to: A.EUR 8; B.EUR 53; C.EUR 84; D.EUR 525 | A.EUR 8 | B.EUR 53 | C.EUR 84 | D.EUR 525 | D.EUR 525 |
You have been asked to estimate the VaR of an investment in Big Pharma Inc. The company’s stock is trading at USD 23 and the stock has a daily volatility of 1.5%. Using the delta-normal method, the VaR at the 95% confidence level of a long position in an at-the-money put on this stock with a delta of -0.5 over a 1-day holding period is closest to which of the following choices? | A.USD 0.28; B.USD 0.40; C.USD 0.57; D.USD 2.84 | A | You have been asked to estimate the VaR of an investment in Big Pharma Inc. The company’s stock is trading at USD 23 and the stock has a daily volatility of 1.5%. Using the delta-normal method, the VaR at the 95% confidence level of a long position in an at-the-money put on this stock with a delta of -0.5 over a 1-day holding period is closest to which of the following choices? A.USD 0.28; B.USD 0.40; C.USD 0.57; D.USD 2.84 | A.USD 0.28 | B.USD 0.40 | C.USD 0.57 | D.USD 2.84 | A.USD 0.28 |
Bank Omega's foreign currency trading desk is composed of 2 dealers: dealer A, who holds a long position of 10 million CHF against the USD, and dealer B, who holds a long position of 10 million SGD against the USD. The current spot rates for USD/CHF and USD/SGD are 1.2350 and 1.5905 respectively. Using the variance/covariance approach, you worked out the 1 day, 95% VaR of dealer A to be USD77,632 and that of dealer B to be USD27,911. If the correlation coefficient between the SGD and CHF is +0.602 and assuming that these are the only trading exposures for dealer A and dealer B, what would you report as the 1 day, 95% VaR of Bank Omega’s foreign currency trading desk using the variance/covariance approach? | A.USD 97,027; B.USD 105,543; C.USD 113,932; D.Cannot be determined due to insufficient data | A | Bank Omega's foreign currency trading desk is composed of 2 dealers: dealer A, who holds a long position of 10 million CHF against the USD, and dealer B, who holds a long position of 10 million SGD against the USD. The current spot rates for USD/CHF and USD/SGD are 1.2350 and 1.5905 respectively. Using the variance/covariance approach, you worked out the 1 day, 95% VaR of dealer A to be USD77,632 and that of dealer B to be USD27,911. If the correlation coefficient between the SGD and CHF is +0.602 and assuming that these are the only trading exposures for dealer A and dealer B, what would you report as the 1 day, 95% VaR of Bank Omega’s foreign currency trading desk using the variance/covariance approach? A.USD 97,027; B.USD 105,543; C.USD 113,932; D.Cannot be determined due to insufficient data | A.USD 97,027 | B.USD 105,543 | C.USD 113,932 | D.Cannot be determined due to insufficient data | A.USD 97,027 |
Consider a stock portfolio consisting of two stocks with normally distributed returns. The joint distribution of daily returns is constant over time and there is no serial correlation. Stock Epsilon has a market value of $100,000 with an annualized volatility of 22%. Stock Omega has a market value of $175,000 with an annualized volatility of 27%. Calculate the 95% confidence interval 1-day VaR of the portfolio. Assume a correlation coefficient of 0.3. Round to the nearest dollar assuming 252 business days in a year. The daily expected return is assumed to be zero. | A.$3,641; B.$5,023; C.$6,007; D.$7,176 | C | Consider a stock portfolio consisting of two stocks with normally distributed returns. The joint distribution of daily returns is constant over time and there is no serial correlation. Stock Epsilon has a market value of $100,000 with an annualized volatility of 22%. Stock Omega has a market value of $175,000 with an annualized volatility of 27%. Calculate the 95% confidence interval 1-day VaR of the portfolio. Assume a correlation coefficient of 0.3. Round to the nearest dollar assuming 252 business days in a year. The daily expected return is assumed to be zero. A.$3,641; B.$5,023; C.$6,007; D.$7,176 | A.$3,641 | B.$5,023 | C.$6,007 | D.$7,176 | C.$6,007 |
We regressed daily returns of a stock against a market index. The regression produced a beta for the stock, with respect to the market index, of 1.050. The stock's volatility was 30.0% and the market's volatility was 20.0%. If the regression's total sum of squares (TSS) is 0.300, what is the regression's explained sum of squares (ESS)? | A.0.0960; B.0.1470; C.0.4900; D.1.2500 | B | We regressed daily returns of a stock against a market index. The regression produced a beta for the stock, with respect to the market index, of 1.050. The stock's volatility was 30.0% and the market's volatility was 20.0%. If the regression's total sum of squares (TSS) is 0.300, what is the regression's explained sum of squares (ESS)? A.0.0960; B.0.1470; C.0.4900; D.1.2500 | A.0.0960 | B.0.1470 | C.0.4900 | D.1.2500 | B.0.1470 |
A return series with 250 observations has a sample mean of 10% and a standard deviation of 15%. The standard error of the sample mean is closest to: | A.0.06%; B.15.80%; C.0.95%; D.3.87% | C | A return series with 250 observations has a sample mean of 10% and a standard deviation of 15%. The standard error of the sample mean is closest to: A.0.06%; B.15.80%; C.0.95%; D.3.87% | A.0.06% | B.15.80% | C.0.95% | D.3.87% | C.0.95% |
For the last three years, we regressed monthly dollar change in gasoline prices against the monthly change in oil prices (regressor; independent). The number of observations (n) is therefore 36. If the coefficient of determination is 0.18 and the total sum of squares (TSS) is 3.23, what is the standard error of the regression (SER)? | A.0.28; B.0.42; C.2.65; D.3.23 | A | For the last three years, we regressed monthly dollar change in gasoline prices against the monthly change in oil prices (regressor; independent). The number of observations (n) is therefore 36. If the coefficient of determination is 0.18 and the total sum of squares (TSS) is 3.23, what is the standard error of the regression (SER)? A.0.28; B.0.42; C.2.65; D.3.23 | A.0.28 | B.0.42 | C.2.65 | D.3.23 | A.0.28 |
A portfolio has a mean value of $75 million and a daily standard deviation of $4.27 million. Assuming that the portfolio values are normally distributed, the probability of the portfolio value falling below $40 million within the next seven days is closest to: | A.0.10%; B.1.00%; C.5.00%; D.15.87% | A | A portfolio has a mean value of $75 million and a daily standard deviation of $4.27 million. Assuming that the portfolio values are normally distributed, the probability of the portfolio value falling below $40 million within the next seven days is closest to: A.0.10%; B.1.00%; C.5.00%; D.15.87% | A.0.10% | B.1.00% | C.5.00% | D.15.87% | A.0.10% |
If the correlation coefficient of a linear regression is 0.6, the percentage of variation of the dependent variable that is not explained by the independent variable is closest to: | A.36%; B.40%; C.60%; D.64% | D | If the correlation coefficient of a linear regression is 0.6, the percentage of variation of the dependent variable that is not explained by the independent variable is closest to: A.36%; B.40%; C.60%; D.64% | A.36% | B.40% | C.60% | D.64% | D.64% |
An analyst is seeking to generate a simple linear regression equation that will allow him to estimate the returns of a beverage company's stock against the returns of the S&P 500. The analyst has compiled the following information: σ(S&P500 )=16.4% σ(beverage company)=22.0% ρ=0.82 mean annual return S&P 500=8.2% risk-free interest rate=4% What is the slope coefficient of the regression equation? | A.1.85; B.1.10; C.2.34; D.0.80 | B | An analyst is seeking to generate a simple linear regression equation that will allow him to estimate the returns of a beverage company's stock against the returns of the S&P 500. The analyst has compiled the following information: σ(S&P500 )=16.4% σ(beverage company)=22.0% ρ=0.82 mean annual return S&P 500=8.2% risk-free interest rate=4% What is the slope coefficient of the regression equation? A.1.85; B.1.10; C.2.34; D.0.80 | A.1.85 | B.1.10 | C.2.34 | D.0.80 | B.1.10 |
A linear time trend model is estimated on annual real euro-area GDP. measured in billions of 2010 euros, using data from 1995 until 2018. The estimated model is RGDPt=- 234178.8+121.3×t+εt. The estimate of the residual standard deviation is σ=262.8. (assuming Gaussian white noise errors). Note that t is the year, so that in the first observation, t = 1995, and in the last, t = 2018. What is the expected mean in 2019? | A.10,725.9; B.10,847.2; C.10,968.5; D.10,765.2 | A | A linear time trend model is estimated on annual real euro-area GDP. measured in billions of 2010 euros, using data from 1995 until 2018. The estimated model is RGDPt=- 234178.8+121.3×t+εt. The estimate of the residual standard deviation is σ=262.8. (assuming Gaussian white noise errors). Note that t is the year, so that in the first observation, t = 1995, and in the last, t = 2018. What is the expected mean in 2019? A.10,725.9; B.10,847.2; C.10,968.5; D.10,765.2 | A.10,725.9 | B.10,847.2 | C.10,968.5 | D.10,765.2 | A.10,725.9 |
An analyst regresses the returns of 60 stocks in a stock market and finds that the best fitting line is: Return=8% +9%×BetaIf the standard error of the estimate is 6% and the standard error of the coefficient of Beta is 4%, the test statistic for the coefficient is closest to: | A.1.33; B.1.43; C.1.50; D.2.25 | D | An analyst regresses the returns of 60 stocks in a stock market and finds that the best fitting line is: Return=8% +9%×BetaIf the standard error of the estimate is 6% and the standard error of the coefficient of Beta is 4%, the test statistic for the coefficient is closest to: A.1.33; B.1.43; C.1.50; D.2.25 | A.1.33 | B.1.43 | C.1.50 | D.2.25 | D.2.25 |
Assume the shock (aka, innovation), ε(t), in a time series is approximated by Gaussian white noise. The lagged (yesterday's) realization was 0.0160 and the lagged shock was - 0.280;i.e., y(t-1) = 0.0160 and ε(t-1) = -0.280. Today's shock, ε(t), is 0.190. If the weight parameter theta, θ, is equal to 0.60, which is nearest to the today's realization, y(t), under a first-order moving average, MA(1), process? | A.-0.0027; B.0.0018; C.0.0220; D.0.1140 | C | Assume the shock (aka, innovation), ε(t), in a time series is approximated by Gaussian white noise. The lagged (yesterday's) realization was 0.0160 and the lagged shock was - 0.280;i.e., y(t-1) = 0.0160 and ε(t-1) = -0.280. Today's shock, ε(t), is 0.190. If the weight parameter theta, θ, is equal to 0.60, which is nearest to the today's realization, y(t), under a first-order moving average, MA(1), process? A.-0.0027; B.0.0018; C.0.0220; D.0.1140 | A.-0.0027 | B.0.0018 | C.0.0220 | D.0.1140 | C.0.0220 |
If the correlation coefficient of a linear regression is 0.7, the percentage of variation of the dependent variable that is not explained by the independent variable is closest to: | A.36%; B.49%; C.51%; D.64% | C | If the correlation coefficient of a linear regression is 0.7, the percentage of variation of the dependent variable that is not explained by the independent variable is closest to: A.36%; B.49%; C.51%; D.64% | A.36% | B.49% | C.51% | D.64% | C.51% |
The result of the linear regression is: Y=0.10-0.50X, with a correlation coefficient ρ=-0.90. The fraction of the variance of Y attributable to X is equal to: | A.-0.90; B.+0.90; C.+0.81; D.-0.50 | C | The result of the linear regression is: Y=0.10-0.50X, with a correlation coefficient ρ=-0.90. The fraction of the variance of Y attributable to X is equal to: A.-0.90; B.+0.90; C.+0.81; D.-0.50 | A.-0.90 | B.+0.90 | C.+0.81 | D.-0.50 | C.+0.81 |
A risk manager gathers five years of historical returns to calculate the Spearman rank correlation coefficient for stocks X and Y. The stock returns for X and Y from 2010 to 2014 are as follows: What is the Spearman rank correlation coefficient for the stock returns of X and Y? | A.-0.7; B.-0.3; C.0.3; D.0.7 | A | A risk manager gathers five years of historical returns to calculate the Spearman rank correlation coefficient for stocks X and Y. The stock returns for X and Y from 2010 to 2014 are as follows: What is the Spearman rank correlation coefficient for the stock returns of X and Y? A.-0.7; B.-0.3; C.0.3; D.0.7 | A.-0.7 | B.-0.3 | C.0.3 | D.0.7 | A.-0.7 |
For a standard normal distribution, which of the following choices is the approximate area under the probability density function from values -1.96 to 1.96? | A.50%; B.66%; C.75%; D.95% | D | For a standard normal distribution, which of the following choices is the approximate area under the probability density function from values -1.96 to 1.96? A.50%; B.66%; C.75%; D.95% | A.50% | B.66% | C.75% | D.95% | D.95% |
You sample 25 observations from a sample of unknown variance. You calculate a sample mean of 70 and sample standard deviation of 60. You wish to conduct a two-tailed test of the null hypothesis that the mean is equal to 50. The most appropriate test statistic is a: | A.z-statistic of 1.67; B.z-statistic of 0.33; C.t-statistic of 0.33 with 24 degrees of freedom; D.t-statistic of 1.67 with 24 degrees of freedom | D | You sample 25 observations from a sample of unknown variance. You calculate a sample mean of 70 and sample standard deviation of 60. You wish to conduct a two-tailed test of the null hypothesis that the mean is equal to 50. The most appropriate test statistic is a: A.z-statistic of 1.67; B.z-statistic of 0.33; C.t-statistic of 0.33 with 24 degrees of freedom; D.t-statistic of 1.67 with 24 degrees of freedom | A.z-statistic of 1.67 | B.z-statistic of 0.33 | C.t-statistic of 0.33 with 24 degrees of freedom | D.t-statistic of 1.67 with 24 degrees of freedom | D.t-statistic of 1.67 with 24 degrees of freedom |
An analyst has constructed the following t-test for a portfolio of financial securities whose returns are normally distributed: Number of securities=40 H0: Mean return<=18% Significance level=0.1 What is the rejection point for this test? | A.1.304; B.1.684; C.2.021; D.2.023 | A | An analyst has constructed the following t-test for a portfolio of financial securities whose returns are normally distributed: Number of securities=40 H0: Mean return<=18% Significance level=0.1 What is the rejection point for this test? A.1.304; B.1.684; C.2.021; D.2.023 | A.1.304 | B.1.684 | C.2.021 | D.2.023 | A.1.304 |
Let random variable W be distributed normally as N(0,10). What are, respectively, the following: 1)The fourth moment of ; and 2)The kurtosis of W? | A.30.0 (4th moment) and zero (kurtosis); B.100.0 and 3.0; C.300.0 and zero; D.300.0 and 3.0 | D | Let random variable W be distributed normally as N(0,10). What are, respectively, the following: 1)The fourth moment of ; and 2)The kurtosis of W? A.30.0 (4th moment) and zero (kurtosis); B.100.0 and 3.0; C.300.0 and zero; D.300.0 and 3.0 | A.30.0 (4th moment) and zero (kurtosis) | B.100.0 and 3.0 | C.300.0 and zero | D.300.0 and 3.0 | D.300.0 and 3.0 |
A portfolio has a mean value of $75 million and a daily standard deviation of $4.27 million. Assuming that the portfolio values are normally distributed, the probability of the portfolio value falling below $40 million within the next seven days is closest to: | A.0.10%; B.1.00%; C.5.00%; D.15.87% | A | A portfolio has a mean value of $75 million and a daily standard deviation of $4.27 million. Assuming that the portfolio values are normally distributed, the probability of the portfolio value falling below $40 million within the next seven days is closest to: A.0.10%; B.1.00%; C.5.00%; D.15.87% | A.0.10% | B.1.00% | C.5.00% | D.15.87% | A.0.10% |
X, Y, and Z have entered into many derivative transactions. When transactions between X and Y are netted, the net value to X is 60. When transactions between Y and Z are netted, the net value to Y is 70. When transactions between Z and X are netted, the net value to Z is 80. Suppose that all transactions are cleared through a CCP rather than bilaterally. What is the net position of X? | A.20; B.-20; C.10; D.-10 | B | X, Y, and Z have entered into many derivative transactions. When transactions between X and Y are netted, the net value to X is 60. When transactions between Y and Z are netted, the net value to Y is 70. When transactions between Z and X are netted, the net value to Z is 80. Suppose that all transactions are cleared through a CCP rather than bilaterally. What is the net position of X? A.20; B.-20; C.10; D.-10 | A.20 | B.-20 | C.10 | D.-10 | B.-20 |
A hedge fund has USD 100 million of investors’ funds and its fees are 2 plus 20%. The fund manager chooses a highly risky strategy that has a 50% chance of producing a profit of USD 30 million and a 50% chance of a loss of USD 12 million. The hurdle rate is 4% and the management fees are based on the beginning of the asset. What is the net expected return to the investor? | A.$9.0 million; B.$4.4 million; C.$4.6 million; D.$4.2 million | C | A hedge fund has USD 100 million of investors’ funds and its fees are 2 plus 20%. The fund manager chooses a highly risky strategy that has a 50% chance of producing a profit of USD 30 million and a 50% chance of a loss of USD 12 million. The hurdle rate is 4% and the management fees are based on the beginning of the asset. What is the net expected return to the investor? A.$9.0 million; B.$4.4 million; C.$4.6 million; D.$4.2 million | A.$9.0 million | B.$4.4 million | C.$4.6 million | D.$4.2 million | C.$4.6 million |
Considering ALIBABA corporation which the stock price of no-dividend paying is currently trading at USD 30, and its annual price volatility is 30%. The continuously compounding risktree interest rate is 5%per year. A financial risk manager is considering a two-step binomial tree for a 2-year horizon. What is the price of the American put option with the strike price of USD 33? | A.5.7042; B.$4.9537; C.$2.5706; D.$4.6698 | A | Considering ALIBABA corporation which the stock price of no-dividend paying is currently trading at USD 30, and its annual price volatility is 30%. The continuously compounding risktree interest rate is 5%per year. A financial risk manager is considering a two-step binomial tree for a 2-year horizon. What is the price of the American put option with the strike price of USD 33? A.5.7042; B.$4.9537; C.$2.5706; D.$4.6698 | A.5.7042 | B.$4.9537 | C.$2.5706 | D.$4.6698 | A.5.7042 |
Based on the covered interest rate parity, if the risk-free rate for currency XXX is higher than that for currency YYY, XXX is weaker in the forward market than in the spot market. A currency trader noticesthat the interest rates in currencies USD and EUR are 3% and 5% per annum (respectively) and the spot exchangerate is EURUSD 1.2500. Based on the covered interest rate parity, how many percent will the euro appreciate or depreciate in one year? | A.appreciate 2%; B.appreciate 5%; C.depreciate 5%; D.depreciate 2% | D | Based on the covered interest rate parity, if the risk-free rate for currency XXX is higher than that for currency YYY, XXX is weaker in the forward market than in the spot market. A currency trader noticesthat the interest rates in currencies USD and EUR are 3% and 5% per annum (respectively) and the spot exchangerate is EURUSD 1.2500. Based on the covered interest rate parity, how many percent will the euro appreciate or depreciate in one year? A.appreciate 2%; B.appreciate 5%; C.depreciate 5%; D.depreciate 2% | A.appreciate 2% | B.appreciate 5% | C.depreciate 5% | D.depreciate 2% | D.depreciate 2% |
Six months ago a company entered in a one-year forward contract to buy the stock. At the time, the one-year forward price was USD 88. The stock price is now USD 95 and the stock will pay a dividend of USD 3 at the end of forward contract. The continuously compounded risk free rate is 4% per year for all maturities, and there are no storage costs. Which of the following is closest to the value of the forward contract? | A.-$5.80; B.$5.80; C.-$8.74; D.$8.74 | B | Six months ago a company entered in a one-year forward contract to buy the stock. At the time, the one-year forward price was USD 88. The stock price is now USD 95 and the stock will pay a dividend of USD 3 at the end of forward contract. The continuously compounded risk free rate is 4% per year for all maturities, and there are no storage costs. Which of the following is closest to the value of the forward contract? A.-$5.80; B.$5.80; C.-$8.74; D.$8.74 | A.-$5.80 | B.$5.80 | C.-$8.74 | D.$8.74 | B.$5.80 |
A portfolio is worth USD 200 million that has a beta relative to the S&P 500 index of 0.75. The S&P 500 index is currently trading at 5,000. The 3-month S&P 500 futures with a contract size of 250USD × futures price is trading at 4,500. Using the 3-month S&P 500 futures contract, which of the following transactions would increase the portfolio's beta to 0.9? | A.Long 27 futures contracts.; B.Short 27 futures contracts.; C.Long 24 futures contracts.; D.Short 24 futures contracts. | A | A portfolio is worth USD 200 million that has a beta relative to the S&P 500 index of 0.75. The S&P 500 index is currently trading at 5,000. The 3-month S&P 500 futures with a contract size of 250USD × futures price is trading at 4,500. Using the 3-month S&P 500 futures contract, which of the following transactions would increase the portfolio's beta to 0.9? A.Long 27 futures contracts.; B.Short 27 futures contracts.; C.Long 24 futures contracts.; D.Short 24 futures contracts. | A.Long 27 futures contracts. | B.Short 27 futures contracts. | C.Long 24 futures contracts. | D.Short 24 futures contracts. | A.Long 27 futures contracts. |
Serena is a risk analyst in Golden Investment Group. She is monitoring the return volatility of Security Alpha based on a 12-month lookback window of monthly returns. She calculated the standard deviation of the monthly returns of 3%. Which of the following is most likely correct? | A.The implied volatility of semi-annual returns is 18%.; B.The implied volatility of semi-annual returns is 7.35%.; C.The estimated volatility of semi-annual returns is 18%.; D.The estimated volatility of semi-annual returns is 7.35%. | D | Serena is a risk analyst in Golden Investment Group. She is monitoring the return volatility of Security Alpha based on a 12-month lookback window of monthly returns. She calculated the standard deviation of the monthly returns of 3%. Which of the following is most likely correct? A.The implied volatility of semi-annual returns is 18%.; B.The implied volatility of semi-annual returns is 7.35%.; C.The estimated volatility of semi-annual returns is 18%.; D.The estimated volatility of semi-annual returns is 7.35%. | A.The implied volatility of semi-annual returns is 18%. | B.The implied volatility of semi-annual returns is 7.35%. | C.The estimated volatility of semi-annual returns is 18%. | D.The estimated volatility of semi-annual returns is 7.35%. | D.The estimated volatility of semi-annual returns is 7.35%. |
An analyst runs a regression of monthly stock returns on four independent variables over 48 months. From the regression, the total sum of squares (TSS) is 580, and the residual sum of squared (RSS) is 220. The regression coefficient of determination(R2) and the adjusted R2are closest to: | A.62%58.5%; B.38% 41.5%; C.62% 41.5%; D.38%58.5% | A | An analyst runs a regression of monthly stock returns on four independent variables over 48 months. From the regression, the total sum of squares (TSS) is 580, and the residual sum of squared (RSS) is 220. The regression coefficient of determination(R2) and the adjusted R2are closest to: A.62%58.5%; B.38% 41.5%; C.62% 41.5%; D.38%58.5% | A.62%58.5% | B.38% 41.5% | C.62% 41.5% | D.38%58.5% | A.62%58.5% |
Suppose that a hedger plans to sell 100,000 bushels of corn in June and uses the July futures contract for hedging. Each contract is on 5,000 bushels of corn and therefore a total of twenty contracts are shorted. Suppose that the futures price at the time the hedge is initiated is 200 cents per bushel and that the futures price is 220 cents per bushel when the hedge is closed out in June. The spot price for the corn being sold in June is 225 cents per bushel. What is the USD price received for the corn when the loss from hedging is considered? | A.225,000 USD; B.245,000 USD; C.200,000 USD; D.205,000 USD | D | Suppose that a hedger plans to sell 100,000 bushels of corn in June and uses the July futures contract for hedging. Each contract is on 5,000 bushels of corn and therefore a total of twenty contracts are shorted. Suppose that the futures price at the time the hedge is initiated is 200 cents per bushel and that the futures price is 220 cents per bushel when the hedge is closed out in June. The spot price for the corn being sold in June is 225 cents per bushel. What is the USD price received for the corn when the loss from hedging is considered? A.225,000 USD; B.245,000 USD; C.200,000 USD; D.205,000 USD | A.225,000 USD | B.245,000 USD | C.200,000 USD | D.205,000 USD | D.205,000 USD |
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