8006 PRMIA Exam I: Finance Theory Financial Instruments Financial Markets - 2015 Edition Free Practice Exam Questions (2025 Updated)

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 traditional collateralized debt obligation (CDO) involves the complete transfer of securities to an SPV, which then issues notes or securities to investors. Therefore Choice 'd' is the correct answer.

A synthetic CDO achieves the same result as a traditional CDO, but uses credit derivatives to synthetically create the same economic effect as a traditional CDO.

A credit default swap is a derivative instrument that pays in the event of the occurrence of agreed credit events. The arrangement described in the question is not a credit default swap purchase. n-th to default swap arrangements are similar to CDSs, but on a portfolio with the first 'n' losses being covered by the swap.

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.

This question requires us to use the CAPM.

Recall that according to CAPM the expected return on an asset = The risk free rate + β x Market risk premium.

Using the beta and expected return of security A, we can determine the market risk premium to be (8% - 3%)/1.2 = 4.1667%. The excess return is the return over the risk free rate, and for security B, this is nothing but the beta multiplied by the market risk premium. Therefore the correct answer is 4.1667% x 1.5 = 6.25%. Note that this is the 'excess return', and not the total return. (Total return will include the risk free rate).

The LIBOR rate to use is the one at the beginning of the period, is 4.5%. The fixed rate payer owes 5%, and the floating rate payer owes 4.5% + 100bps. Thus the fixed rate payer will receive a payment equal to 0.5% for six months on $1m. This works out to $2500.(Recall that a fixed for floating interest rate swap exchanges fixed for floating rate payments, with only the net payment being made by either party.)

The LIBOR rate to use is the one at the beginning of the period, is 4.5%. The fixed rate payer owes 5%, and the floating rate payer owes 4.5% + 100bps. Thus the fixed rate payer will receive a payment equal to 0.5% for six months on $1m. This works out to $2500.

(Recall that a fixed for floating interest rate swap exchanges fixed for floating rate payments, with only the net payment being made by either party.)

Choice 'd' represents the mean-variance function to be maximized for selecting between mutually exclusive gambles. The other choices are incorrect.

(The mean-variance criterion is a fairly complex subject, and this question is only intended to make sure that you know, and can identify the function that is being maximized. A complete explanation/derivation of the mean-variance criterion, that links together expected returns, volatility and the risk tolerance of the investor to arrive at the efficient frontier is beyond the scope of the PRM syllabus.)

Generally, it is not a good idea to exercise an option early as any more upside in the remaining period to expiry is being sacrificed. However, if an extraordinarily large dividend is coming due, and this dividend is larger than the interest foregone from holding the option, it may be a good idea to exercise the option early. In such cases, the exercise needs to happen before the ex-dividend date and not afterwards. Choice 'b' is therefore the correct answer.

Even if the option is deep in the money and delta is approaching 1, and exercise upon maturity is almost a certainty, it would still always be better to sell the option than exercise it . Therefore Choice 'a' is incorrect. Choice 'c' is correct in all cases except when a large dividend is coming in. Choice 'd' is not correct because an early exercise needs to happen prior to the ex-dividend date and not afterwards.

Eurodollar deposits refer to US dollar denominated deposits outside the US, for example in a banking center such as London, and held by a non-US bank or a foreign branch of a US bank. Choice 'b' is the correct answer.

This question addresses the key differences between futures and forward contracts. Forward contracts are over the counter (OTC) instruments, while futures are exchange traded. Therefore Choice 'b' is not a true statement.

Futures contracts require an initial margin to be paid to the exchange, and gains and losses to be settled daily, while forward contracts generally settle only at the maturity of the contract. Therefore Choice 'a' is a true statement.

The exchange is the counterparty in a futures contract, and through its system of initial and variation margins guarantees the performance of the contract. Futures therefore have very little credit risk when compared to forwards. Therefore Choice 'c' is a true statement.

Because futures gains and losses give rise to daily cash flows, while the P&L on forward contracts is settled only at the end of the contract, the timing differences create small pricing differences between the two. Therefore Choice 'd' is a true statement.

The bond equivalent yield for a treasury bill can be calculated as [(Future value - Present value)/Present value x 365/days to maturity]. In this case this works out to ($100-$98)/$98 * 365/90 = 8.28%

[Why do we use 365 days and not 360? And is there a different way to calculate treasury bill yields?

The answer to this question is that there are alternate ways to calculate these yields. For the exam, I would suggest that you calculate according to one method, see if you get an answer that matches, and pick that. I found the below on the NY Fed's website - a very clear example: (http://newyorkfed.org/aboutthefed/fedpoint/fed28.html)

The Discount Yield Method

The following formula is used to determine the discount yield for T-bills that have three- or six-month maturities:

Discount yield = [(FV - PP)/FV] * [360/M]

FV = face value

PP = purchase price

M = maturity of bill. For a three-month T-bill (13 weeks) use 91, and for a six-month T-bill (26 weeks) use 182

360 = the number of days used by banks to determine short-term interest rates (the investment yield method is based on a calendar year: 365 days, or 366 in leap years).

Example

What is the discount yield for a 182-day T-bill, auctioned at an average price of $9,659.30 per $10,000 face value?

Discount yield = [(FV - PP)/FV] * [360/M]

FV = $10,000 PP = $9,659.30 M = 182

Discount yield = [(10,000) - (9,659.30)] / (10,000) * [360/182]

Discount yield = [340.7 / 10,000] * [1.978022]

Discount yield = .0673912 = 6.74%

For the 13-week bill, the same formula would be used, dividing 360 by a maturity of 91 days rather than 182 days.

The Investment Yield Method

When comparing the return on investment in T-bills to other short-term investment options, the investment yield method can be used. This yield is alternatively called the bond equivalent yield, the coupon equivalent rate, the effective yield and the interest yield.

The following formula is used to calculate the investment yield for T-bills that have three- or six-month maturities:

Investment yield = [(FV - PP)/PP] * [365 or 366/M]

Example

What is the investment yield of a 182-day T-bill, auctioned at an average price of $9,659.30 per $10,000 face value?

Investment yield = [(FV - PP)/PP] * [365/M]

FV = $10,000 PP = $9,659.30 M = 182

Investment yield = [(10,000 - 9,659.30) / (9,659.30)] * [365/182]

Investment yield = [340.70] / 9,659.30] * [2.0054945]

Investment yield = .0707372 = 7.07%

For the 13-week bill, the same formula can be used, dividing 365 (or 366) by a maturity of 91 days.

This is a straightforward case of basic portfolio math - the only thing being that we are not explicitly given the correlation between the two assets, nor are we given the volatility of the risk free asset. But since the other asset in the portfolio is the risk free asset, it has no risk, ie its volatility is zero, and its correlation with the fund run by the hedge fund manager is also zero. Portfolio returns will be the average returns of the two assets, and portfolio variance will be given by the formula portfolio_vol. Its square root will provide the portfolio volatility.

Therefore the expected returns are = 60%*12% + 40%*4% = 8.8%

The combined volatility of this portfolio will be given by (in Excel formula format) as =SQRT((60%*12%)^2 + (40%*0%)^2 + 2*0*60%*40%*12%*0%) = 7.2%

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).

We can use the put-call parity to estimate the value of the call option in this case.

The put-call parity can be expressed as:

Value of call - Value of put = Spot price - Exercise price discounted to the present

Substituting the values we know:

Value of call - $5 = $100 - $110/(1 + 10%); which implies the value of a call is also $5.

Choice 'a' is therefore the correct answer.

Note about interest rates: How do we know if the interest rate provided in the question is continuous or discrete? For short periods of time, the difference between discrete and continuous exchange rates tends to be not material. For ease of computation, use discrete rates (as above), and it should allow you to answer the question.

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.

The crack spread is the difference between the price of refined products and crude oil. An option on the crack spread can protect a refiner from both a fall in the price of its output and a rise in the price of its inputs. Calendar spreads are options with different maturities. Crude oil futures and swaps only protect against an adverse change in the price of crude, and not that of refined products. Choice 'b' is the correct answer.

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.

When the forward prices are greater than the spot prices, the market is said to be in contango. When forward prices are lower than spot prices, the market is said to be backwarded. A short squeeze may contribute to backwardation. Choice 'a' 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.

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.