Question: Suppose daily losses (gains) from trading are

> You are given 1.00 gram of each of five substances. In which of the substances will there be the greatest number of potassium ions when dissolved in water? a. potassium chloride b. potassium chlorate c. potassium phosphate d. potassium nitrate e. po

> For each of the following solutions, the mass of the solute is given, followed by the total volume of solution prepared. Calculate the molarity. a. 5.0 g of BaCl2; 2.5 L b. 3.5 g of KBr; 75 mL c. 21.5 g of Na2CO3; 175 mL d. 55 g of CaCl2; 1.2 L

> Approximately 0.14 g of nickel(II) hydroxide, Ni(OH)2(s), dissolves per liter of water at 20 °C. Calculate Ksp for Ni(OH)2(s) at this temperature.

> Chromium(III) hydroxide dissolves in water only to the extent of 8.21 * 10-5 M at 25 °C. Calculate Ksp for Cr(OH)3 at this temperature.

> Approximately 1.5 * 10-3 g of iron(II) hydroxide, Fe(OH)2(s), dissolves per liter of water at 18 °C. Calculate Ksp for Fe(OH)2(s) at this temperature.

> What does it mean to say that a state of chemical or physical equilibrium is dynamic?

> The three common silver halides (AgCl, AgBr, and AgI) are all sparingly soluble salts. Given the values for Ksp for these salts below, calculate the concentration of silver ion, in mol/L, in a saturated solution of each salt. Silver Halide……….Ksp AgCl……

> Consider 0.25 M solutions of the following salts: NaCl, RbOCl, KI, Ba(ClO4)2, and NH4NO3. For each salt, indicate whether the solution is acidic, basic, or neutral.

> Write the formulas for three combinations of weak acid and salt that would act as buffered solutions. For each of your combinations, write chemical equations showing how the components of the buffered solution would consume added acid and base.

> Calculate the hydrogen ion concentration, in moles per liter, for solutions with each of the following pH or pOH values. a. pH = 5.41 b. pOH = 12.04 c. pH = 11.91 d. pOH = 3.89

> A 15.0% (by mass) NaCl solution is available. Determine what mass of the solution should be taken to obtain the following quantities of NaCl. a. 10.0 g b. 25.0 g c. 100.0 g d. 1.00 lb

> Calculate the hydrogen ion concentration and the pH of each of the following solutions of strong acids. a. 1.4 * 10-3 M HClO4 b. 3.0 * 10-5 M HCl c. 5.0 * 10-2 M HNO3 d. 0.0010 M HCl

> Calculate the hydrogen ion concentration, in moles per liter, for solutions with each of the following pH or pOH values. a. pOH = 0.90 b. pH = 0.90 c. pOH = 10.3 d. pH = 5.33

> You mix 225.0 mL of a 2.5 M HCl solution with 150.0 mL of a 0.75 M HCl solution. What is the molarity of the final solution?

> Calculate [OH-] in each of the following solutions, and indicate whether the solution is acidic, basic, or neutral. a. [H+] = 4.21 * 10-7 M b. [H+] = 0.00035 M c. [H+] = 0.00000010 M d. [H+] = 9.9 * 10-6 M

> For each hydrogen or hydroxide ion concentration listed, calculate the concentration of the complementary ion and the pH and pOH of the solution. a. [H+] = 5.72 * 10-4 M b. [OH-] = 8.91 * 10-5 M c. [H+] = 2.87 * 10-12 M d. [OH-] = 7.22 * 10-8 M

> How do chemists recognize a system that has reached a state of chemical equilibrium? When writing chemical equations, how do we indicate reactions that come to a state of chemical equilibrium?

> What are some physical properties that historically led chemists to classify various substances as acids and bases?

> A financial institution has the following portfolio of over-the-counter options on sterling: A traded option is available with a delta of 0.6, a gamma of 1.5, and a vega of 0.8. (a) What position in the traded option and in sterling would make the port

> A portfolio manager has maintained an actively managed portfolio with a beta of 0.2. During the last year, the risk-free rate was 5% and major equity indices performed very badly, providing returns of about −30%. The portfolio manager produced a return o

> A bank estimates that its profit next year is normally distributed with a mean of 0.8% of assets and the standard deviation of 2% of assets. How much equity (as a percentage of assets) does the company need to be (a) 99% sure that it will have a positiv

> Explain the moral hazard problems with deposit insurance. How can they be overcome?

> Consider a one-year European call option on a stock when the stock price is $30, the strike price is $30, the risk-free rate is 5%, and the volatility is 25% per annum. Use the RMFI software to calculate the price, delta, gamma, vega, theta, and rho of t

> Suppose that one investment has a mean return of 8% and a standard deviation of return of 14%. Another investment has a mean return of 12% and a standard deviation of return of 20%. The correlation between the returns is 0.3. Produce a chart similar to F

> Suppose that a one-day 97.5% VaR is estimated as $13 million from 2,000 observations. The one-day changes are approximately normal with mean zero and standard deviation $6 million. Estimate a 99% confidence interval for the VaR estimate.

> Suppose that each of two investments has a 4% chance of a loss of $10 million, a 2% chance of a loss of $1 million, and a 94% chance of a profit of $1 million. They are independent of each other. (a) What is the VaR for one of the investments when the co

> With the benefit of hindsight, we can say that Kodak was in the “imaging and moment-sharing business.” What business are banks in?

> Look at the data in Table 28.1. Is Lending Club good at assessing risk? Is there a reasonable trade-off between risk and return for lenders? What risks are lenders taking?

> What is meant by a bubble? Consider whether the increase in the price of bitcoin in 2017 is a bubble.

> Explain carefully the distinction between real-world and risk-neutral default probabilities. Which is higher? A bank enters into a credit derivative where it agrees to pay $100 at the end of one year if a certain company’s credit rating falls from A to B

> What position is equivalent to a long forward contract to buy an asset at K on a certain date and a long position in a European put option to sell it for K on that date?

> Suppose that a bank has a total of $10 million of small exposures of a certain type. The one-year probability of default is 1% and the recovery rate averages 40%. Estimate the 99.5% one-year credit VaR using Vasicek’s model if the copula correlation para

> Suppose that the spread between the yield on a three-year riskless zero-coupon bond and a three-year zero-coupon bond issued by a bank is 210 basis points. The Black–Scholes–Merton price of an option is $4.10. How much should you be prepared to pay for i

> A hedge fund charges 2 plus 20%. A pension fund invests in the hedge fund. Plot the return to the pension fund as a function of the return to the hedge fund.

> “Some aspects of the new regulations can be expected to increase the amount of collateral posted for derivatives and some can be expected to reduce it.” Explain this statement.

> Suppose that we back-test a VaR model using 1,000 days of data. The VaR confidence level is 99% and we observe 15 exceptions. Should we reject the model at the 5% confidence level? Use Kupiec’s two-tailed test.

> Suppose that daily changes for a portfolio have first-order autocorrelation with autocorrelation parameter 0.12. The 10-day VaR, calculated by multiplying the one-day VaR by, is $2 million. What is a better estimate of the VaR that takes account of autoc

> Prove (a) that the definitions of duration in equations (9.1) and (9.3) are the same when y is continuously compounded and (b) that when y is compounded m times per year they are the same if the right-hand side of equation (9.3) is divided by 1 + y/m.

> The gamma and vega of a delta-neutral portfolio are 50 per $ per $ and 25 per %, respectively. Estimate what happens to the value of the portfolio when there is a shock to the market causing the underlying asset price to decrease by $3 and its volatility

> Investigate what happens as the width of the mezzanine tranche of the ABS in Figure 6.4 is decreased, with the reduction in the mezzanine tranche principal being divided equally between the equity and senior tranches. In particular, what is the effect on

> Good years are followed by equally bad years for a mutual fund. It earns +8%, –8%, +12%, and –12% in successive years. What is the investor’s overall return for the four years?

> The expected return on the market is 12% and the risk-free rate is 7%. The standard deviation of the return on the market is 15%. One investor creates a portfolio on the efficient frontier with an expected return of 10%. Another creates a portfolio on th

> Regulators calculate that DLC bank (see Section 2.2) will report a profit that is normally distributed with a mean of $0.6 million and a standard deviation of $2.0 million. How much equity capital in addition to that in Table 2.2 should regulators requir

> Suppose that the principals assigned to the senior, mezzanine, and equity tranches for the ABSs and ABS CDO in Figure 6.4 are 70%, 20%, and 10% instead of 75%, 20%, and 5%. How are the results in Table 6.1 affected?

> A fund of funds divides its money between five hedge funds that earn –5%, 1%, 10%, 15%, and 20% before fees in a particular year. The fund of funds charges 1 plus 10% and the hedge funds charge 2 plus 20%. The hedge funds’ incentive fees are calculated o

> A fund's risk appetite is such that it wants to be 97.5% certain it will not lose more than 25% in any one year. Using the performance of the S&P 500 between 1997 and 2016 (see Table 27.2), determine the beta the fund should have. Assume a risk-free rate

> A binary option pays off $500 if a stock price is greater than $60 in three months. The current stock price is $61 and its volatility is 20%. The risk-free rate is 2% and the expected return on the stock is 8%. What is the value of the option? What is th

> An investor owns 10,000 shares of a particular stock. The current market price is $80. What is the “worst case” value of the portfolio in six months? For the purposes of this question, define the worst case value of the portfolio as the value which is su

> A stock price has an expected return of 9% and a volatility of 25%. It is currently $40. What is the probability that it will be less than $30 in 18 months?

> Suppose that a bank’s sole business is to lend in two regions of the world. The lending in each region has the same characteristics as in Example 26.5 of Section 26.8. Lending to Region A is three times as great as lending to Region B. The correlation be

> Suppose that the economic capital estimates for two business units are Business Units The correlation between market risk and credit risk in the same business unit is 0.3. The correlation between credit risk in one business unit and credit risk in anot

> Suppose that daily gains (losses) are normally distributed with standard deviation of $5 million. (a) Estimate the minimum regulatory capital the bank is required to hold. (Assume a multiplicative factor of 4.0.) (b) Estimate the economic capital using a

> Suppose that a financial institution uses an imprecise model for pricing and hedging a particular type of structured product. Discuss how, if at all, it is likely to realize its mistake.

> Using Table 25.1, calculate the volatility a trader would use for an 11-month option with a strike price of 0.98.

> An investor buys 100 shares in a mutual fund on January 1, 2018, for $50 each. The fund earns dividends of $2 and $3 per share during 2018 and 2019. These are reinvested in the fund. The fund’s realized capital gains in 2018 and 2019 are $5 per share and

> Suppose that all options traders decide to switch from Black–Scholes to another model that makes different assumptions about the behavior of asset prices. What effect do you think this would have on (a) the pricing of standard options and (b) the hedgi

> Suppose that a trader has bought some illiquid shares. In particular, the trader has 100 shares of A, which is bid $50 and offer $60, and 200 shares of B, which is bid $25 and offer $35. What are the proportional bid–offer spreads? What is the impact of

> Discuss whether hedge funds are good or bad for the liquidity of markets.

> A bank has a business indicator (BI) of 5.5 billion euros. It has had eight operational risk losses in the last 10 years. The amounts of the losses in millions of euros are: 3, 7, 15, 65, 85, 150, 250, and 300. What is the bank's operational risk regulat

> Consider the following two events: (a) a bank loses $1 billion from an unexpected lawsuit relating to its transactions with a counterparty, and (b) an insurance company loses $1 billion because of an unexpected hurricane in Texas. Suppose that you have

> Suppose that there is a 1% probability that operational risk losses of a certain type exceed $10 million. Use the power law to estimate the 99.97% worst-case operational risk loss when the α parameter equals (a) 0.25, (b) 0.5, (c) 0.9, and (d) 1.0.

> What difference does it make to the VaR calculated in Example 22.2 if the exponentially weighted moving average model is used to assign weights to scenarios as described in Section 13.3?

> Consider a European call option on a non-dividend-paying stock where the stock price is $52, the strike price $50, the risk-free rate is 5%, the volatility is 30%, and the time to maturity is one year. Answer the following questions assuming no recovery

> A company has one- and two-year bonds outstanding, each providing a coupon of 8% per year payable annually. The yields on the bonds (expressed with continuous compounding) are 6.0% and 6.6%, respectively. Risk-free rates are 4.5% for all maturities. The

> Consider a delta-neutral position in a single asset with a gamma (measured with respect to percentage changes in the asset) of (. Suppose that the 10-day return on the asset is normally distributed with a mean of zero and a standard deviation .

> During a certain year, interest rates fall by 200 basis points (2%) and equity prices are flat. Discuss the effect of this on a defined benefit pension plan that is 60% invested in equities and 40% invested in bonds.

> In Figure 17.4 where the CCP is used, suppose that an extra transaction between A and C that is worth 140 to A is cleared bilaterally. What effect does this have on the tables in Figure 17.4?

> A bank has the following balance sheet: (a) What is the net stable funding ratio? (b) The bank decides to satisfy Basel III by raising more retail deposits and keeping the proceeds in Treasury bonds. What extra retail deposits need to be raised? Re

> Explain one way that the Dodd–Frank Act is in conflict with (a) the Basel international regulations and (b) the regulations introduced by other national governments.

> Suppose that the assets of a bank consist of $500 million of loans to BBB-rated corporations. The PD for the corporations is estimated as 0.3%. The average maturity is three years and the LGD is 60%. What is the total risk-weighted assets for credit risk

> A bank has the following transaction with a AA-rated corporation: (a) A two-year interest rate swap with a principal of $100 million that is worth $3 million. (b) A nine-month foreign exchange forward contract with a principal of $150 million that is wor

> Estimate the capital required under Basel I for a bank that has the following transactions with another bank. Assume no netting. (a) A two-year forward contract on a foreign currency, currently worth $2 million, to buy foreign currency worth $50 million.

> Why is there an add-on amount in Basel I for derivatives transactions? “Basel I could be improved if the add-on amount for a derivatives transaction depended on the value of the transaction.” How would you argue this viewpoint?

> A company has a position in bonds worth $6 million. The modified duration of the portfolio is 5.2 years. Assume that only parallel shifts in the yield curve can take place and that the standard deviation of the daily yield change (when yield is measured

> A company has a long position in a two-year bond and a three-year bond as well as a short position in a five-year bond. Each bond has a principal of $100 and pays a 5% coupon annually. Calculate the company’s exposure to the one-year, two-year, three-yea

> Suppose that you know the gamma of the portfolio in Problem 14.18 (again measured with respect to actual changes) is –2.6. Derive a quadratic relationship between the change in the portfolio value and the percentage change in the underlying asset price i

> An insurance company’s losses of a particular type per year are to a reasonable approximation normally distributed with a mean of $150 million and a standard deviation of $50 million. (Assume that the risks taken on by the insurance company are entirely

> Consider a portfolio of options on a single asset. Suppose that the delta of the portfolio (calculated with respect to actual changes) is 12, the value of the asset is $10, and the daily volatility of the asset is 2%. What is the delta with respect to pr

> Consider a position consisting of a $300,000 investment in gold and a $500,000 investment in silver. Suppose that the daily volatilities of these two assets are 1.8% and 1.2%, respectively, and that the coefficient of correlation between their returns is

> The probability that the loss from a portfolio will be greater than $10 million in one month is estimated to be 5%. (a) What is the one-month 99% VaR assuming the change in value of the portfolio is normally distributed with zero mean? (b) What is the on

> The change in the value of a portfolio in three months is normally distributed, with a mean of $500,000 and a standard deviation of $3 million. Calculate the VaR and ES for a confidence level of 99.5% and a time horizon of three months.

> Suppose that the price of Asset X at close of trading yesterday was $300 and its volatility was estimated as 1.3% per day. The price of X at the close of trading today is $298. Suppose further that the price of Asset Y at the close of trading yesterday w

> The probability that the loss from a portfolio will be greater than $10 million in one month is estimated to be 5%. (a) What is the one-month 99% value at risk (VaR) assuming the change in value of the portfolio is normally distributed with zero mean? (b

> Suppose that the parameters in a GARCH (1, 1) model are = 0.03, = 0.95, and  = 0.000002. (a) What is the long-run average volatility? (b) If the current volatility is 1.5% per day, what is your estimate of the volatility in 20, 40, and 60 days? (c)

> Suppose that the price of an asset at close of trading yesterday was $300 and its volatility was estimated as 1.3% per day. The price at the close of trading today is $298. Update the volatility estimate using (a) The EWMA model with  = 0.94, (b) The GA

> Suppose that the change in a portfolio value for a one-basis-point shift in the 1-year, 2-year, 3-year, 4-year, 5-year, 7-year, 10-year, and 30-year rates are (in $ millions) +5, –3, –1, +2, +5, +7, +8, and +1, respectively. Estimate the delta of the por

> Estimate the interest rate paid by P&G on the 5/30 swap in Business Snapshot 5.4 if (a) the CP rate is 6.5% and the Treasury yield curve is flat at 6% and (b) the CP rate is 7.5% and the Treasury yield curve is flat at 7% with semiannual compounding.

> An investment bank has been asked to underwrite an issue of 10 million shares by a company. It is trying to decide between a firm commitment where it buys the shares for $10 per share and a best efforts arrangement where it charges a fee of 20 cents for

> What are the convexities of the portfolios in Problem 9.17? Problem 9.17: Portfolio A consists of a one-year zero-coupon bond with a face value of $2,000 and a 10-year zero-coupon bond with a face value of $6,000. Portfolio B consists of a 5.95-year z

> A company’s investments earn LIBOR minus 0.5%. Explain how it can use the quotes in Table 5.5 to convert them to (a) three-, (b) five-, and (c) 10-year fixed-rate investments.

> The price of gold is currently $1,500 per ounce. The forward price for delivery in one year is $1,700. An arbitrageur can borrow money at 5% per annum. What should the arbitrageur do? Assume that the cost of storing gold is zero and that gold provides no

> A bond issued by Standard Oil worked as follows. The holder received no interest. At the bond’s maturity the company promised to pay $1,000 plus an additional amount based on the price of oil at that time. The additional amount was equal to the product o

> The current price of a stock is $94, and three-month European call options with a strike price of $95 currently sell for $4.70. An investor who feels that the price of the stock will increase is trying to decide between buying 100 shares and buying 2,000

> A trader buys 200 shares of a stock on margin. The price of the stock is $20. The initial margin is 60% and the maintenance margin is 30%. How much money does the trader have to provide initially? For what share price is there a margin call?

> A company enters into a short futures contract to sell 5,000 bushels of wheat for 250 cents per bushel. The initial margin is $3,000 and the maintenance margin is $2,000. What price change would lead to a margin call? Under what circumstances could $1,50

> Portfolio A consists of a one-year zero-coupon bond with a face value of $2,000 and a 10-year zero-coupon bond with a face value of $6,000. Portfolio B consists of a 5.95-year zero-coupon bond with a face value of $5,000. The current yield on all bonds i

> Suppose that a bank has $10 billion of one-year loans and $30 billion of five-year loans. These are financed by $35 billion of one-year deposits and $5 billion of five-year deposits. The bank has equity totaling $2 billion and its return on equity is cur

> Consider again the situation in Problem 8.17. Suppose that a second traded option with a delta of 0.1, a gamma of 0.5, and a vega of 0.6 is available. How could the portfolio be made delta, gamma, and vega neutral? Problem 8.17: A financial institution

> The bidders in a Dutch auction are as follows: The number of shares being auctioned is 210,000. What is the price paid by investors? How many shares does each investor receive? Number of shares 60,000 20,000 30,000 40,000 40,000 40,000 50,000 50,00

> The comparative balance sheets for Mogilny Tours show the following changes in noncash current asset accounts: Accounts receivable decrease $75,000; prepaid expenses increase $16,000; and inventories increase $30,000. Compute net cash provided by operati