8006 Exam Dumps - Exam I: Finance Theory Financial Instruments Financial Markets - 2015 Edition

An increase in coupon brings the 'average' cash flows closer, thereby decreasing duration. The higher the coupon, the lower the duration.

An increase in yield discounts the cash flows that are further away more than it does the closer cash flows, so an increase in yield decreases duration.

An increase in coupon frequency brings the bond's cash flows closer, thereby decreasing duration. Decreasing the coupon frequency has the opposite effect.

An increase in maturity pushes the payments further out, thereby increasing duration.

The objective of decisions relations to capital structure is to maximize the value to shareholders. The management of the company is entrusted with the job of maximizing shareholder value, and this objective is generally achieved by attempting to maximize enterprise value. Enterprise value includes the value of both debt and equity, and since debt has a fixed claim on the assets of the business, maximizing enterprise value also maximizes the value of equity.

A protective put is a put option purchased to protect against the fall in value of a long position. If the price of the underlying in respect of the long position goes down, the put options helps limit losses. If the price of the underlying goes up, the premium paid on the puts is lost but the investor gets to keep the entire upside from the rise in the price.

Therefore statements I, III and IV are correct. Statement II is not correct as any decline in the value of the underlying is offset by the gain from the put, which is the entire idea behind a protective put.

All the choices list inputs into the determination of futures prices. Therefore volatility in any of them affects the volatility of futures prices. Of course, the largest contributor to the volatility is the volatility of the spot price of the underlying. Choice 'd' is the correct answer.

When assets are uncorrelated, variances are additive. But volatility (which is standard deviation) is not. In the given situation, the total variance of the portfolio will be equal to the the square root of the sum of the variances of the assets in the portfolio weighted by the square of their weights. Its volatility will be the square root of this variance. Thus Choice 'c' is the correct answer.

(This is because V(cA + dB) = c^2 V(A) + d^2 V(B) - refer tutorial on combining variances.)

Choice 'a' is incorrect as it describes the calculation of variance, not volatility. Also, the presence of a large number of uncorrelated assets does not create a portfolio with volatility equal to zero or that of the market. The other choices are therefore incorrect.

Explanation:

The correct answer is the index value times the contract size, in this case 1500 x 50.

One way to think about index futures is this: Consider equity index trading as trading in the shares of a company whose share price is equal to a number of dollars which is the same as the index. If the 'contract multiplier' for a index futures contract is 50, that means the futures contract is for 50 shares of such a fictitious company. Therefore the notional value of the contract will be 15000 x 50, and Choice 'a' is the correct answer.

Fixed income instruments go through the 'pull-to-par' phenomenon as they get closer to maturity. In this case, since interest rates stay constant, the bond will rise in price over the year to get closer to its redemption value. Of course, you can apply the standard discounting logic as well to say that while one year's coupon payment drops off, the remaining years' cash flows get discounted for a year less and the value would go up. However it is just easier to remember that at maturity the bond will be close to its notional or face value, and therefore if it is selling at a discount now, it will rise in value over its remaining life to get to the face value.

Exactly the reverse logic would apply to bonds sold at a premium, they would decline in value over time as to get to the par value at maturity.

The square root of time rule can be used to convert, say a 1-day volatility to a 10-day volatility, by multiplying the known volatility number by the square root of time to get the volatility over a different time horizon. However, there are key assumptions that underlie the application of this rule, and statements I to III correctly state those assumptions. If serial correlations (whether negative or positive) exist, then asset returns are not independent as they are affected by the prior day or prior period's returns, and we cannot use the square root of time rule. Therefore Choice 'd' is the correct answer.

In order to use the 'square root of time' rule, asset returns should be iid, volatility should stay constant (ie there should be no volatility clustering), and no serial correlations (ie the returns of one day should not be affected by the returns of the prior periods). Choice 'd' is the correct answer.

Statement I correctly describes an IRS.

Statement II is correct - in an IRS the parties do not exchange the principal or the notional amounts as they are in the same currency and can be netted off, but in a currency swap the amounts are in different currencies that cannot be netted (not at least without doing a spot transaction simultaneously), and principals are exchanged.

Statement III is incorrect as the floating rate leg actually is subject to no risk as it resets itself to the current interest rate. The true risk is in the fixed leg which is sensitive to changes in interest rates.

Swaps carry counterparty risks just like any other OTC contract, therefore statement IV is false.

When hedging one fixed income security with another, the question as to how much of the hedge to buy (or sell) (ie the hedge ratio) for a given primary position is determined by their respective basis point values, which in turn are determined by their duration. Therefore, when hedging a long maturity bond with a PV01 of $3 with a short maturity bond that has a PV of $1, we will need to buy 3 times the notional value of the short maturity bond to achieve the same sensitivity to interest rates as the longer maturity bond.

Additionally, we may also expect the interest rates on the hedge to move differently from the interest rates on the primary instrument being hedged, and this needs to be accounted for as well as part of the hedge ratio calculation. This is called the yield beta and is calculated as change in yield for primary position/change in yield for the hedge security.

The hedge ratio is determined both by the yield beta and the BPVs of the two securities. Choice 'd' is the correct answer.

The change in the price of the bond will be equal to $100* (-11*0.1% + 0.5* 80 *(0.1%)^2) = -1.096. Therefore the new price will be $100 - 1.096 = $98.904. Thus Choice 'd' is the correct answer, the rest are incorrect.

Note that the change in the price of a bond if you are given modified duration is convexity is given by the formula P * (-Duration*δi + 0.5*Convexity*(δi)^2); where δi is the change in interest rates. 10 basis points equal 0.1%, or 0.001.

Treasury bond futures do not specify which bond can be used to effect delivery, but allow the seller to pick from a number of available bonds. As a result, one of these eligible bonds emerges as being the 'cheapest' to deliver, and this CTD bond is determined by the basis between the cash price of the bond and the futures spot price as adjusted by the conversion factor for this specific bond. (ie, basis = Cash Price of the Bond - Futures Price x Conversion Factor)

The bond with the lowest basis is generally the CTD - therefore Choice 'c' is the correct answer.

From the put-call parity, we know that Call - Put = Stock - Bank deposit. Since the bank deposit has a zero delta, and the delta of the Stock itself is 1, we get the relationship Delta of Call - Delta of Put = 1. Therefore, if the delta of a call option is 0.3, the delta of the corresponding put option is 0.3 - 1 = -0.7

A CDS contract provides exposure to default risk and the credit spread for a particular credit. It does not provide an exposure to the risk of interest rates going up or down. It is an instrument that allows institutions to take a view on the price of credit risk alone. Therefore statement I is false and statement II is true.

A total return swap (TRS) exchanges the return from an asset for a fixed or floating exchange rate. It is in essence a financing arrangement where one party pays the other interest to earn a return on an asset that it does not wish to hold itself, perhaps for liquidity reasons. The financed asset is held by the party paying the asset's returns, effectively creating a 'collateral'. Therefore statement III is correct.

A credit linked note is a funded instrument where the sellers of the protection have put up the money upfront in the form of a subscription to a note in case the credit losses are realized. Therefore statement IV is not correct.

A utility function is graphed with utility on the y-axis and the variable driving utility (generally wealth) along the x-axis.

A concave utility function, ie a function with a downward sloping curve, indicates risk aversion. A convex utility function indicates a risk seeking attitude and a straight line (ie no curvature) indicates a risk neutral attitude.

Choice 'a' is the correct answer as the issue of the floating rate note will provide the utility with the funds it needs, and the interest rate swap would offset the floating rate payment and leave it with a net fixed payment.

Choice 'd' is incorrect as the swap is in the wrong direction.

Choice 'c' is incorrect as buying and selling a floating rate bond would mean the utility will not have any funds that it wants to issue the note for, and combining it with interest rate futures would be just absurd.

Choice 'b' is incorrect as buying a floating rate note would use funds while the utility is trying to raise funds.

The key point in this question is that the bond is zero coupon, and can only be called at face value. Since the bond is zero coupon, its value will always be less than its par value at any time during its existence (as any interest rate will be a positive number). Therefore the issuer will never exercise the call. Thus the bond will have a duration equal to what an equivalent non-callable bond would have.

Since zero coupon bonds have a duration equal to their maturity, the bond's duration is 10 years.

All the statements are correct, therefore Choice 'd' is the correct answer. Let us look at each of these statements one by one.

I. A deep in-the-money call option has a value very close to that of a forward contract with a forward price equal to the exercise price. This is true because a deep in the money call option is most likely to be exercised, and is therefore effectively like a forward contract to buy the stock at the exercise price.

We can also look at this using the BSM formula for a call option. If c be the value of a call option, and all other variables have their usual meaning (S0 is the spot price, K is exercise price, and t is time to expiry), then according to the Black Scholes model the value of a call is given by the following expression:

202.22.e1

As S0 becomes large, d1 and d2 become large, and therefore N(d1) and N(d2) approach 1, leaving the value of the call to be equal to 202.22.e2, which is the formula for a forward contract.

II. If the volatility of a stock goes down to zero, the value of a call option on the stock will tend to be close to that of a forward contract so long as the option is in the money.

Again, this is true because if volatility is low or zero, the stock price will grow at its expected rate, and end up to be what the forward price is (S0 ert). If the option is out of the money, the value of the option will tend to 0.

III. All other things remaining the same, the issue of stock warrants exercisable at a future date will cause a decline in the current stock price.

This is true because the stock warrants are likely to be exercised only when they are in the money, ie when their exercise price is less than the going stock price, and at that time it will dilute the value of the existing shares. However, the reduction in the price is priced into the share price at the time of the issue of the warrants, and it is not that the share price falls the day they are exercised.

IV. Implied volatilities are calculated from market prices of options and are forward looking. This statement is true: historical volatilities calculated from past prices are backward looking, while 'implied volatility' is the volatility implied from market prices, and is forward looking as it encapsulates the market's view of how volatile the future is likely to be.

The transformation line represents the various possible combinations of the 'risky bundle' and the risk free asset. Investors can choose different combinations of the risky and risk-free asset depending upon their risk appetite. The transformation line meets the y-axis (portfolio returns) at the point equal to the risk free rate. Choice 'a' is the correct answer and the rest are incorrect.

The highest possible transformation line, ie the transformation line with the maximum slope, is the transformation line joining the risk free rate on the y-axis and the portfolio with the maximum Sharpe ratio on the efficient frontier. This line is called the 'capital markets line'. Investors can pick any point on this line according to their risk appetite, and doing so would maximize the return they can obtain for their desired level of risk. The capital markets line is tangential to the efficient frontier. The Sharpe ratio stays constant throughout the CML.

Remember that the transformation line and the capital markets lines are different from each other - there is only one CML for an efficient frontier, whereas there can be multiple transformation lines.

The effect of higher convexity is that when yields rise, the price decrease is lower than the increase in yields, and when yields fall, the increase in price is greater than the fall in yield. In either case, it benefits the holder of the fixed income instrument that carries such positive convexity. The converse is true for someone short a bond - such an investor would prefer lower convexity to higher convexity. Therefore statement I is not true for an investor who is short a bond.

An increase in yields makes bond prices decrease, something that would benefit the short. Therefore statement II is true for an investor short a bond.

Negative convexity has exactly the opposite effect as the one described for positive convexity for statement I above. An investor short a bond would prefer negative convexity (which by the way is exhibited by very few fixed income instruments such as mortgages) to positive convexity, therefore statement III is true for such an investor.

Choice 'b' is the correct answer.

The price of an interest rate cap is affected by all of the listed choices except the risk free rate. The risk free rate does not come into play in the pricing of caps, and therefore Choice 'b' is the correct answer.

A CLN is a form of a funded credit derivative. The investors in the note are the protection sellers, and receive the CDS premiums in addition to any risk free rate on their investment. If a default occurs, the money put up by the investors in the CLN is used to make good the party that has brought the protection.

Therefore if a default occurs, the investors in a CLN do not receive their entire investment back, but only what remains after fullfilling their obligations on the credit protection, plus any premiums that might have been earned. In return for this risk, the CLN yields the risk free rate plus the CDS premiums. Only Choice 'd' is correct, all other options are incorrect.

A covered call is an attempt to earn premium income by selling calls while protecting against the downside by holding long the underlying. In case prices rise, the holder of the covered call can give away the held underlying. In case prices fall or stay below the strike price of the sold call, the holder of the covered call gets to keep the premium.

The holder of the covered call will suffer a loss if the price of the underlying declines due to the long position held in the underlying. However, these losses will be partly offset by the premiums earned on the calls sold.

Choice 'd' does not represent a correct statement as in the event of a rise in the price of the underlying the holder of the covered call will lose any upside, but will not have unlimited losses. In the event of a decline in stock prices, his losses will be equal to the loss on the underlying, minus the premium earned.

The swap can be valued by valuing the two individual components of the swap.

The fixed rate bond equivalent in the swap is valued at =4/1.05 + 104/(1.06^2) = $96,369,154.

The FRN component will be valued at par as we are at a point where the rate has just been reset, ie $100m.

The investor is paying the fixed rate, and is therefore short the bond. He/she is receiving LIBOR, and is therefore long the FRN. The value of the swap to the investor therefore is +$100,000,000-$96,369,154 = $3,630,846

Detailed explanation:

An Interest Rate Swap exchanges fixed interest flows for floating rate flows. The floating rate leg is tied to some reference rate, such as LIBOR. The parties exchange net cash flows periodically. Conceptually, an interest rate swap is the combination of a fixed coupon bond and a floating rate note. The party receiving the fixed rate is long the fixed coupon bond and short the FRN, and the party receiving the floating rate is long the FRN and short the fixed coupon bond.

An interest rate swap can be valued as the difference between the two hypothetical bonds. FRNs sell for par at issue time as they pay whatever the current rate is, subject to periodic resets. Therefore immediately after a payment is made on a swap, the value of the FRN component is equal to its par value. The bond can be valued by discounting its cash flows. The difference between the two represents the value of the swap. When the swap is entered into, the fixed rate leg is set in such a way that the value of the hypothetical bond is equal to that of the FRN, and therefore the swap is valued at zero. The rate at which the fixed rate leg is set is called the swap rate. Over its life, market rates change and the value of the fixed coupon bond equivalent in our swap diverges from par (whereas the FRN stays at par - at least right after payments are exchanged and the new floating rate is set for the next period). Thus the swap acquires a non-zero value.

There are two ways to value a swap. If interest rates for the future are known, the bond and the FRN can be valued and their difference will be equal to the value of the swap. Sometimes, the current swap rates are known. In such a case, the swap can be valued by imagining entering into an opposite swap at the new swap rate, which will leave a residual fixed cash flow for the remaining life of the swap. This residual cash flow can be valued and that represents the value of the swap. For example, if a 4 year swap was entered into exchanging an annual fixed 5% payment on a notional of $100m for a floating payment equal to LIBOR, and at the end of year 1 the swap rate is 6%, then the party paying fixed can choose to enter into a new swap to receive 6% and pay LIBOR. All cash flows between the old and the new swap will offset each other except a net receipt of 1% for the next 3 years. This cash flow can be valued using the current yield curve and represents the value of the swap.

A utility function provides a description of an individual or a firm's risk attitude. It expresses how risk seeking or risk averse a firm or an individual is. The utility function would explain differences between risk seeking and risk averse behavior, for example, as an individual becomes richer, he may seek (or shun) risk more than before. A utility function incorporates all of this, and therefore Choice 'd' is the correct answer.

Choice 'b' is the correct answer. The other relationships are not correct.

The price of a treasury bill can be calculated as [Future value / (1 + yield x days-to-maturity/365)] = 100/(1+5%*90/365) = $98.78.

Systematic risk refers to market risk that cannot be diversified away. Specific risk relates to the unique risk from the securities selected in the portfolio, and these can be diversified away by adding other securities to the portfolio. Diversifiable risk is risk that can be diversified away, ie the same as specific risk. Portfolio risk is the total risk of the portfolio that includes both specific and systematic risk.

The loss to the fund manager is $20*100 = $2,000. The initial margin placed was $5,000. After the loss is charged to his account, the margin balance is only $3,000 ($5,000 - $2,000). The margin to be maintained is $5,000. Therefore the margin call is $2,000.

Note that there would have been no margin call till the balance in the margin account had reduced to the 'maintenance' level of $4,000. So if the price had fallen by $5, and the loss had been $500, there would have been no margin call. But when the margin call would be made, it would require the balance to be brought up to the initial margin of $5,000 (and not the maintenance margin of $4,000).

The Sharpe ratio is the ratio of excess returns to risk. Excess returns are measured as the returns over the risk-free rate, and risk is measured in terms of volatility, ie standard deviation. Two portfolios with identical Sharpe ratios will certainly have the same ratio of risk and return, though the absolute levels of the return and the risk may vary. Therefore Choice 'c' is the correct answer.

The basis point value is equal to $102 x 5 /10000 = $0.051. Therefore Choice 'd' is the correct answer.

The basis point value, also called the PV01, is the dollar value change in the price of a bond as a result of a 1 basis point (=1/10000) change in interest rates. Since the modified duration is 5, it means a 1% change in interest rates produces a 5% change in the price of the bond, and a 1 bps change will therefore produce a 0.05% change in the value of the bond. Since the bond is currently valued at $102, the change works out to $102 x 0.05% = $0.051.

A utility function is graphed with utility on the y-axis and the variable driving utility (generally wealth) along the x-axis.

A concave utility function, ie a function with a downward sloping curve, indicates risk aversion. A convex utility function indicates a risk seeking attitude and a straight line (ie no curvature) indicates a risk neutral attitude.

The tax advantage of debt is an important input into a decision on the financial structure of a firm. Increasing debt increases the fixed expenses of a business that must be paid out of current cash flows, thereby increasing the cost of financial distress. CFOs consider the volatility of their earnings, outlook for the future and the possibility of financial distress at varying levels of debt, so that certainly is an input into the debt-equity tradeoff. Holding higher levels of equity increases financial flexibility for financing new investments or acquisitions, and depending upon their plans for such activities, they may decide to hold a certain level of equity versus debt.

The agency costs of equity refer to the cost to shareholders arising from the management acting in its own interest rather than that of shareholders - and this is irrelevant to a decision on capital structure. Therefore Choice 'd' is the correct answer.

The vast majority of exchange traded futures contracts are closed out prior to expiry by the parties acquiring offsetting positions. Very few contracts are settled by delivery. Since P&L on futures contracts is settled daily, 'cash settlement' really does not mean much as only the previous day's P&L is due or receivable on any given day.

Credit derivatives can indeed be used for reducing credit exposures, earning credit risk premiums and getting market exposure without taking cash market positions. They cannot be used for reducing interest rate risks, as they pay out only when agreed 'credit events' take place. Changes in interest rates are not a credit event. Therefore Choice 'b' is the correct answer.

The existence of derivative markets actually drives liquidity out of cash markets into derivative markets. Derivative markets are far more liquid than cash markets. Therefore statement I is not correct.

In times of crises, instruments or financial products bearing greater credit risk lose liquidity rapidly. Therefore statement II is correct.

A higher bid-ask spread indicates lower liquidity, not greater liquidity. Therefore statement III is false.

Normal market size (NMS) refers the 'normal' transaction size for which a dealer's quote is valid. A higher NMS is associated with greater liquidity, therefore statement IV is correct.

The investor would benefit from the risk reversal and the bull spread as both these strategies have a payoff profile that benefit from rising prices of the underlying. The collar is the opposite of risk reversal, and benefits during a bear market, and the butterfly spread benefits when prices remain range bound. Therefore Choice 'c' is the correct answer.

A fixed for floating interest rate swap would be the most appropriate to the company's needs. It will allow it to receive a fixed rate (which will offset the fixed payment it has to make on the loan) and pay a floating rate which it expects will be lower than the fixed rates. Choice 'a' is the correct answer.

Answer:

A repo, or a repurchase agreement, is the lending of securities in return for cash, with an agreement to buy the securities back at a later date at the borrowed amount plus interest. It is a form of collateralized borrowing. A 'reverse repo' is exactly the opposite of a repo transaction, ie where cash is lent and securities borrowed. Therefore Choice 'b' is the correct answer. In any repo transaction, the counterparty will therefore always have a 'reverse repo' position.

A reverse repo is a useful transaction - not merely for the purpose of lending short term funds, but more importantly to enable short positions. For example, if an investor wishes to short a bond, he can borrow the bond on a 'reverse repo' and sell it. Of course, he will have to return the bond when the reverse repo matures, but hopefully by that time prices of the bond would have fallen to allow him to do so profitably. Short positions in physical bonds are nearly always facilitated by reverse repos.