PRMIA 8006 Exam I: Finance Theory Financial Instruments Financial Markets - 2015 Edition Exam Practice Test

The principle of maximum expected utility requires maximizing the expected utilities of the different possible outcomes of a gamble weighted according to the probabilities of their occurrence. This is very difficult to apply in practice in the financial markets where utility functions and various other inputs for maximizing expected utility are not known. Markowitz suggested the mean-variance criterion as a simplification of the principle of maximum expected utility, and it can be shown that the mean-variance gives a good approximation when the range of outcomes under consideration does not exceed plus or minus one coefficient of risk tolerance. (Recall that the coefficient of risk tolerance is the value of x where the gambler is indifferent between equal probabilities of winning x or losing x/2.)

The mean can be calculated quite easily as a weighted average, and in this case it is 0.6*5% + 0.4*3% = 4.2%.

The variance can be calculated with the formula for portfolio variance as = (0.6^2)*(20%^2) + (0.4^2)*(5%^2) + 2*(-0.6)*0.6*0.4*20%*5%=0.01192. Therefore the volatility of this portfolio is SQRT(0.01192)=10.92%

Choice 'a' correctly describes a 'holder extendible option'. Choice 'b' describes a 'writer extendible option'. Choice 'c' describes a 'shout option'. Choice 'd' describes a 'knock in' option.

It is important to note the distinction between the clearing house and the exchange itself. The clearing house does not get involved with physical delivery, nor does it provide any dispute settlement services. It only makes sure that cash is settled as and when due between the members. Therefore Choice 'c' is the correct answer

The relationship between the value of an option, and its delta, gamma and theta is given by rV = θ + rSΔ + 0.5Γ(σS)2, where V is the value of the option, r the risk-free rate, S the spot price of the underlying, and θ, Δ & Γ are the respective Greeks.

For a delta neutral portfolio, Δ = 0 and this equation reduces to rV = θ + 0.5Γ(σS)2. Now rV is generally a small number, which means that if θ is large and positive, Γ must be large and negative to offset that. Therefore Choice 'b' is the correct answer.

A short position in a fixed rate bond and a long position in an FRN has the effect of paying fixed and receiving floating. The floating received offsets the floating payment on the borrowing, leaving the borrower with just a fixed rate outflow. Therefore the combination identified in statement I can be used to achieve the objective of paying fixed.

A collar is equivalent to a long position in an interest rate cap combined with a short position in an interest rate floor. This has the effect of setting a range within which the investor's borrowing rate will vary. In the case where the cap and floor rates are the same, the combination of a collar and a long FRN effectively produces an outcome where the holder of such positions pays a fixed rate. Therefore, an interest rate collar can be used to convert the fixed payment to a floating rate payment. [Example: Assume current interest rate is 3%, and therefore the borrower has a liability of 3% on the FRN. Assume that the borrower now buys a collar at the strike rate of 4%. Now the borrower receives 0% (=Max(3 % - 4%, 0)) on the cap part of the collar, and pays 1% on the floor part of the collar (=Max(4% - 3%, 0)). The net borrowing cost therefore is 3% paid on the FRN plus 1% paid on the collar, equal to 4%. Now if interest rates rise to say 6%, the borrower pays 6% on the FRN, and receives 2% from the collar (=Max(6% - 4%, 0) - Max(4% - 6%, 0)), creating a net cost of 6% - 2% = 4%.

A collar is often issued with an FRN to convert floating flows to fixed. Therefore combination II is an acceptable choice.

A short position in a fixed rate bond and a short position in an FRN produces a cash flow that does not produce a net fixed cash outflow when combined with the borrowing. Therefore statement III is not a valid combination.

An interest rate swap where the investor pays fixed and receives floating, when combined with a floating payment on an FRN leaves a net fixed payment, Therefore statement IV is a valid way to achieve the borrower's objective.

The dividend payment has a present value of $2.20*e^( -6%*6/12) = $2.14. Therefore the forward price for delivery 9 months hence should be ($102 - $2.14)*e^(7%*9/12) = $105.25

The Sharpe ratio does not require investors to be risk neutral, only that for a given level of returns they prefer less risk to more risk. (Risk neutral means that investors are indifferent to the level of risk, and are only driven by a desire to maximizing expected value, regardless of risk levels.)

The ability to borrow and lend any amounts of money at the risk free rate is a fundamental assumption for the rule that optimal portfolios will maximize the Sharpe ratio.

This rule also assumes that risk preferences are completely described by return and standard deviation of returns.

Therefore Choice 'd' is the correct answer as statements I and II are correct.

To solve this question, we need to revisit how delta is calculated in a single step binomial model:

Consider a portfolio with just two positions: 1 Long Call option, and Δ Short Stock. We do not know what Δ (Delta) is.

Now if the current price of the stock is P, which can take the value P2 (higher value) and P1 (lower value) in the future at time T, then Δ needs to be such that the value of the portfolio is equal in both the cases. If the price goes up, the value of the option will be $1 (given) and the value of the short stock will be -Δ P2. If the price goes down, the value of the option will be $0, and the value of the stock will be -Δ P1.

Therefore, $1 - Δ P2 = $0 - Δ P1.

Solving for Δ, we get Δ = $1 /(P2 - P1) = $1 / ($102-$98) = 1/4.

The TED spread is a bet on the spread between treasury bill futures and Eurodollar futures. T-bill rates are lower than Eurodollar rates, as the former carries no risk. Eurodollars deposits, which are interbank deposits between the highest rated banks, carry very little risk as well. Therefore both these instruments generally trade at very narrow spreads. The spread widens, ie the Eurodollar rates rise in comparison to treasury bill rates when the market has credit risk fears.

A trader is said to be 'long' the spread when he benefits from the spread increasing, and 'short' the TED spread when he gains from the spread decreasing. A trader can buy the spread by being long t-bill futures and short Eurodollar futures. Similarly he can be short the spread by being short t-bill futures and long Eurodollar futures.

All the statements given are true, except that standard deviations cannot be averaged to get the portfolio standard deviation unless the assets are perfectly positively correlated. Therefore Choice 'd' is the false statement, and the correct answer.

For a portfolio of uncorrelated assets, ie correlations being equal to zero, variances can be added together to get portfolio variance. Also, regardless of correlations, portfolio returns are always the weighted average of asset returns, and just averages will do in this case as the portfolio is said to be equally weighted across the assets. A correlation of zero produces a risk level less than that possible with positive correlations.

Open interest refers to the number of outstanding contracts, which is the same as the number of long positions or short positions held by market participants. Note that since for every long futures contract position held there is a seller who holds the short side, the open interest that is long is identical to the open interest that is short. (This is unlike the spot market where one could have long positions without anyone else needing to be symmetrically short).

The total number of contracts traded refers to traded volumes, and not open interest. Other choices are irrelevant in the context.

As a bond approaches maturity, its value will be driven less by the time value of money or its coupons, and more by its redemption value, ie the par. Therefore as maturity approaches, its value converges to its par value and this phenomenon is called pull to par.

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.

An option on a futures contract is like any other option contract, and only the option premium is due upfront. If the option is exercised, then the futures contract comes into existence and futures margins become due in the normal way. Therefore Choice 'b' is the correct answer.

Forward rates can be calculated from spot rates and interest rates using the formula Spot x (1+domestic interest rate)/(1+foreign interest rate), where the 'Spot' is expressed as a direct rate (ie as the number of domestic currency units one unit of the foreign currency can buy). In this case the forward rate will be 1.1239 * (1 + 0.75%*90/360) / (1 + 0.4%*90/360) = 1.1249.

It can be confusing to determine which interest rate should be considered 'domestic', and which 'foreign' for this formula. For that, look at the spot rate. Think of the spot rate as being x units of one currency equal to 1 unit of the other currency. In this case, think of the spot rate 1.1239 as "CAD 1.1239 = USD 1". The currency that has the "1" in it is the 'foreign' and the other one is 'domestic'.

It is also important to remember how exchange rates are generally quoted. Most exchange rates are quoted in terms of how many foreign currencies does USD 1 buy. Therefore, a rate of 99 for the JPY means that USD 1 is equal to JPY 99. These are called 'direct rates'. However, there are four major world currencies where the rate quote convention is the other way round - these are EUR, GBP, AUD and NZD. For these currencies, the FX quote implies how many US dollars can one unit of these currencies buy. So a quote of "1.1023" for the Euro means EUR 1 is equal to USD 1.1023 and not the other way round.

The 'running yield' refers to the coupon rate divided by the current price. In this case, it is 6/96 = 6.25%. Remember that the running yield is also called the current yield.

The Sharpe ratio is the ratio of the excess returns of a portfolio to its volatility. It provides an intuitive measure of a portfolio's excess return over the risk free rate. The Sharpe ratio is calculated as [(Portfolio return - Risk free return)/Portfolio standard deviation].

The Treynor ratio is similar to the Sharpe ratio, but instead of using volatility in the denominator, it uses the portfolio's beta. Therefore the Treynor Ratio is calculated as [(Portfolio return - Risk free return)/Portfolio's beta]. Therefore Choice 'a' is the correct answer.

Jensen's alpha is another risk adjusted performance measure. It considers only the 'alpha', or the return attributable to a portfolio manager's skill. It is the difference between the return of the portfolio, and what the portfolio should theoretically have earned. Any portfolio can be expected to earn the risk free rate (rf), plus the market risk premium (which is given by [Beta x (Market portfolio's return - Risk free rate)]. Jensen's alpha is therefore the actual return earned less the risk free rate and the beta return.

Refer to the tutorial on risk adjusted performance measures for more details

The stock has a beta of 1.2, therefore intuitively it can be expected to earn more than the broad market index. It will earn the risk free rate, ie 3%, and 1.2 times the equity risk premium of 5% (8% - 3%). The expected returns from the stock therefore are 3% + (8% - 3%)*1.2 = 9%

Statement I is not correct because the 4% bond with the same modified duration as the zero coupon bond will have a maturity much later in the future than the zero coupon, and the final repayment coming much later will cause its convexity to be greater than the equivalent duration zero coupon bond.

Statement II is not correct as the convexity of a bond increases not in a linear fashion but in proportion to the square root of time as the maturity of the bond is increased.

Statement III is not correct as mortgage based bonds bring negative convexity even in the case of long positions,

Statement IV is not correct as the duration of a zero coupon bond maturing in 10 years has a modified duration greater than that of a coupon bearing bond of the same maturity, which means its convexity is higher and not lower (note this is different from statement I where the modified durations were identical. Here, the maturity is identical which has different implications.)

Therefore none of the statements is correct and Choice 'd' is the correct answer.

https://riskprep.com/images/stories/questions/102.07.a.png  is the coefficient of risk aversion at x. Its inverse, ie https://riskprep.com/images/stories/questions/102.07.b.png , is called the coefficient of risk tolerance.

Risk aversion or risk tolerance is indicated in a utility function by its curvature. A concave utility function indicates risk aversion and a convex function indicates risk tolerance. The curvature is measured as a ratio of the second derivative to the first derivative of a function. A negative second derivative implies concavity. The expression - is the coefficient of risk aversion, and its inverse, which is in the same units as wealth, is called the coefficient of risk tolerance.

Given covered interest parity, the currency with a lower interest rate will trade at a forward premium. Choice 'b' is the correct answer.

For an intuitive reasoning, consider a currency forward contract that matures in 3 months. The seller has agreed to sell, say JPY 1,000,000 in exchange for USD 10,000 in the future. In order to cover himself, he borrows the USD right now and converts it to JPY at spot which he puts in a JPY deposit. Assuming JPY interest rates are less than USD interest rates, he pays more on his USD borrowing than he receives on his JPY deposit. Therefore he has to price the forward contract at a premium to spot to cover the interest rate differential.

All the choices listed are valid assumptions underlying the BSM option valuation formula except that the BSM formula is based upon the option being exercisable only at expiry. The assumption is that early exercise is not permitted. In other words, BSM applies to European options and not American options. Therefore Choice 'd' represents the correct answer as it is not an assumption underlying Black Scholes.

'In store' delivery is for delivery in a standardized location, and the buyer is handed a 'warrant' that allows him to pick the goods up. This is the cheapest means of physical delivery. The other prices will be higher as they involve more costs for the seller who has to get the goods on board a ship, or to the docks, or insurance and freight as well. Choice 'c' is the correct answer.

The delivery price of a futures contract is given by Se^(rt), just as in the case of a forward contract. However, a key difference is that a forward is settled at maturity whereas a futures contract pays out the P&L daily. So if the spot price increases from S to δS, the holder of a futures contract immediately receives the change in the delivery price without any discounting to the present. That is, the holder of the futures contract receives (S + δS)e^(rt) - Se^(rt) = δSe^(rt) right away. Therefore the delta of a futures contract is e^rt, which given positive non-zero values of r and t can only be greater than zero.

Therefore Choice 'b' is the correct answer. Note the difference from a forward contract where this difference is not received till the delivery date, therefore making the delta of the forward contract to be equal to 1.

Repos are collateralized borrowing arrangements. They are used for providing short term funding. They are not used for managing credit risk exposures. They are also used by central banks as part of their money market operations. They are also useful for facilitating short positions, for example, in corporate bonds where the party desirous of shorting the bond may 'borrow' the bond on repo in order to be able to sell it short.

Delta hedges need to be rebalanced periodically because with changes in prices, delta changes, and the amount of hedge required changes as well, requiring a readjustment. The more frequent the rebalancing, the better the performance of the hedge. However, the greater the rebalancing frequency, the greater are the number of trades required, increasing the costs from trading. The trader has to balance transaction costs against the adverse effects from poorer hedge performance. Therefore rebalancing frequency is a consideration for a trader and statement I is true.

Statement II is not true. When options are granted, their future impact on the price gets priced in into the current price, and no change occurs when these are actually exercised.

Statement III is true. Consider the Black Scholes PDE

202.23.e1

and substitute delta = 0 (as this is a delta neutral portfolio), and we get the result 202.23.e. Since r is generally small, a large negative theta means a large positive gamma and vice-versa. Therefore theta can be used as a proxy for gamma and this statement is correct.

Statement IV is correct. Vega is highest closest to the strike price - look at the graph for vega to see how vega behaves with changes to spot. (Do it yourself or there is a graph in the tutorial too.)

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.

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:

Since $100 is convertible into two shares, the price upon conversion per share is $50, which is the same as the current share price. Therefore there is no premium, and Choice 'c' is the correct answer.

This question is based upon a weather derivative contract traded on the CME in the US. For each day, 'Heating-Degree-Days' (HDD) is calculated as equal to 65 degrees Fahrenheit minus the daily average temperature. The daily average temperature is based upon the temperature reported by the Earth Satellite Corporation using a specified automated weather station. Based upon daily values of HDD, an aggregated number called the 'CME degree days index' is calculated for each contract month. In other words, the index for a particular month is just the aggregation of the 'HDD' value for each of the days of that month. Each contract settles at the end of the month at a value equal to $20 x Degree Days Index. (In a similar way, 'Cooling Degree Days' are also calculated and a futures contract offered, except that CDD is equal to the average daily temperature minus 65 degrees). (Source: CME's website at CMEGroup.com)

In the given question, we are interested in hedging against the possibility of the temperature being too low. This means we should buy the HDD futures contract (the lower the temperature, the higher the difference of the average temperature from 65 degrees, and the higher the settlement). Therefore Choice 'b' is the correct answer. The lower the actual temperature turns out to be, the higher the payout to the grower. It would not be wise to wait till January to buy the contract as by then the prices of the contract would have already risen if the grower's fears of a colder January appear to be coming true. He can hedge his exposure by immediately locking in the January prices.

The forward price for a commodity is nothing but the spot price plus carrying costs till the maturity date of the forward contract. Any increase in carrying costs therefore has the effect of increasing the forward price. Note that carrying costs include interest cost in respect of funding the position, costs of storage, less any convenience yield.

Increase in the carrying costs will not affect the spot prices.

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.

Statement I is correct - since forward prices are determined as (Spot - PV of dividends)*e^(rt), an increase in dividends will reduce forward prices.

Statement II is incorrect as forward prices will be determined by near term interest rates, specifically by the borrowing rate for the period of the contract, and will stay unchanged if near term interest rates do not change.

Statement III is incorrect. Futures exchanges require both buyers and sellers to deposit initial margins as prices can move adversely for either of them.

Statement IV is incorrect, as the margin deposited when a contract is entered into is called initial margin. Margin calls thereafter resulting from movements in prices are called variation margin.

Statement V is incorrect. Most futures exchanges distinguish between hedgers and speculators and require different margins from each.

Statement VI is incorrect. Interest rate futures behave almost identically to their bond counterparts, and carry both duration and convexity.

The LIBOR square is a (rare) derivative contract which pays, as mentioned in the question, the square of the interest rate move between two dates. If LIBOR at inception is y, and upon settlement is x, the contract pays (x - y)^2 for x > y; and -(x - y)^2 for x < y.

For any question that involves calculating delta or gamma, and the payoff is described in terms of variables as is the case here, remember that delta is always the first derivative and gamma is the second derivative. For this question, let us calculate the second derivative and see what the gamma is:

If x > y, then the payoff is (x - y)^2

The first derivative wrt x is 2(x - y)

The second derivative wrt x is 2.

ie, the gamma is 2

If x < y, then the payoff is -(x - y)^2

The first derivative wrt x is -2(x - y)

The second derivative wrt x is -2.

ie, the gamma is -2

If x = y, then the payoff is 0. Both the first and the second derivatives are zero. ie the gamma is 0.

Based on the above, we see that the contract can have a gamma of either 0, +2 or -2. 1 is not a possible value for gamma, and 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.

This question relates to the Black Scholes PDE (partial differential equation). The Black Scholes PDE is derived by combining the results of a stock price following a Weiner process with a mathematical result known as Ito's lemma and holds true for all derivatives whose prices depend upon S, the price of the underlying and upon t, which indicates time.

The derivation of the Black Scholes PDE is beyond the scope of the PRM syllabus (and also of the author of this question), but we need to know what it is. The PDE can be written as:

202.21.q1

Substituting , this can also be written as

202.21.e

202.21.q2

Therefore the first and the second equations are correct, and the other two are wrong. Choice 'c' is the correct answer.

You should know the PDE in case there is a numerical question about it. The two ways of writing it (as I and II above in the question) express the same relationship. The BSM formula itself for valuing a vanilla European option is based upon the PDE. Most other options are also valued using the fundamental relationship expressed in the PDE.

The OTC market for foreign exchange is indeed much larger than the exchange traded futures market for FX. Therefore statement I is correct.

Delivery-versus-payment (DVP) arrangements make sure that title to a security passes only when payment has been made, and these arrangements, usually implemented through national clearing agencies such as the DTC in the US, help avoid the risk of counterparty defaults.

Electronic Clearing Networks (ECNs) offer cheaper trading costs than exchanges, in fact that is their primary attraction. Exchanges offer other advantages, but lower trading costs is not one of them.

ISDA master agreements provide templates that a large number of OTC market participants use to standardize their OTC trading activities. Therefore statement IV is correct.

Explanation:

The return on an asset is a function of the covariance of the asset's return to the returns of the market portfolio. They do not depend upon the standard deviation of the asset itself. Therefore Choice 'b' is correct and Choice 'c' is incorrect.

The expected returns on an asset are equal to the risk free rate plus the beta times the market risk premium, therefore Choice 'a' is correct.

Portfolios on the efficient frontier will all have a different Sharpe ratio, which is the ratio of excess returns to portfolio volatility.

Choice 'c' is the correct answer (note that the question is asking for an identification of the INCORRECT statement).

A normal yield curve is generally upward sloping. Downward sloping, humped or flat yield curves are less common and indicate exceptional market conditions.

The implied volatility for a call and a put is identical if the two have the same strike and expiry. Therefore Choice 'b' is the correct answer and the remaining choices are incorrect.

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 riskiest tranche of a structured product is called the equity tranche. All other choices are incorrect.