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

The forward rate from year 2 to year 3 in this case can be derived as =(1.05^3/1.04^2) - 1, or 7.03%. All other answers are incorrect.

There are two ways to think about this question: First, because the asset manager thinks that interest rates are going to decline, his profit will be maximized if he buys the bond with the greatest duration. The zero coupon bond has the greatest duration among the alternatives listed. Therefore Choice 'c' is the correct answer.

The second way to look at this question is to consider what is called 'reinvestment risk'. Yields to maturity calculations have an implicit assumption that any cash flows received prior to maturity are investible at the ytm rate. Thus, an yield to maturity calculation for a coupon bearing bond assumes that coupon payments get invested at the same rate as the calculated ytm from the time they are received till the time the bond matures. In an environment where interest rates fall, this assumption will not hold true. Reinvestment risk is the risk that coupons will not be able to earn the ytm that the bond was brought at - and the investor will be at a loss to the extent the money does not earn the ytm rate till the end of the investment. One way to reduce reinvestment risk is to minimize coupon receipts so the money stays invested as part of the bond, and the zero coupon bond helps to do exactly that.

The underlying asset in a Treasury note futures contract is any long term Treasury note with a maturity of no less than 6.5 years and no more than 10 years. The underlying asset in a treasury bond futures contract is any long term US Treasury bond with a maturity of more than 15 years and not callable within 15 years.

Note the difference betwen what the underlying asset is for treasury bond futures and treasury note futures. In either case, adjustments will be made for the coupon and maturity of the actual bond delivered (the concept of the adjustment of 'cheapest-to-deliver').

The operating free cash flows can be considered a perpetual annuity with a given growth rate.

The value of a perpetuity of a periodic cash flow of 'c', with a discount rate 'r' and growth rate 'g' is given by c/(r - g). In the given case, the company can be considered as providing a perpetual annuity which provides an annual cash flow of $100 which are growing at 2.5% (equal to the GDP's growth rate, as given), and whose cost of capital, or the discount rate to use, is 7.5%

Therefore the value of the firm in this case is given by $100/(7.5% - 2.5%) = $2,000. Recall that the value of the firm is equal to the Operating Free Cash Flow/Weighted Average Cost of Capital (OFCF/WACC). Therefore Choice 'd' is the correct answer.

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

The prices must satisfy the put-call parity, and if they do not, it means there is an arbitrage opportunity, The put-call parity is as follows. We plug in the values to check if the parity is maintainted.

Buying a call + Bank Deposit (PV of exercise price) = Buying the stock + Buying a put

Thus the LHS = $10 + $100/(1 + 5%) = $105.24

and RHS = $100 + $10 = $110, ie the equality does not hold.

Since the trader can make a profit by buying low and selling high, and the set of positions on the left should be brought, and those on the RHS should be sold. Thus the trader should buy the call, sell the put and sell the stock to make a risk free profit. (There is no need to explicitly place a bank deposit at the risk-free rate).

The greater the rebalancing frequency, the more effective the hedge. But the higher the rebalancing frequency (ie the how often the hedge is true-ed up as a response to changes in the market), higher are the transaction costs. Higher transaction costs reduce hedge performance. Therefore transaction costs limit the ability of traders to continuously trade and keep delta at or close to zero. Transaction costs include a number of elements, including market impact costs, dollar costs per trade, and the bid-offer spread on the security.

Traders have to strike a balance between transaction costs and the rebalancing frequency when making decisions on hedging. Bid-offer spreads, cost per trade and the rebalancing frequency are therefore relevant considerations. The volatility of the underlying is not something the trader would consider when taking decisions to delta hedge (unless as part of an active bet on future volatility) and therefore Choice 'c' is irrelevant to the trader's decision, and 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 using a futures contract to hedge a position, the correct way to determine the number of futures contracts to use is to use the following formula. This adjusts for the 'tailing the hedge' adjustment required as a result of the daily settlement feature of futures contracts.

Minimum Variance Hedge Ratio x Dollar Value of Position / Dollar Value of Single Futures Contract

When using forward contracts to hedge a position, no adjustment to tail the hedge is required (as settlement happens only at the end), and the number of units of the exposure when compared to the number of units per contract should be used. The formula in the case of forward contracts is:

Minimum Variance Hedge Ratio x Units in Position Held / Units in Single Futures Contract

In practice however, the difference between the above two formulae is de-minimis; and for the exam you should be okay to use either of the above two to determine the number of contracts - unless the question is directed to testing your knowledge of the 'tailing the hedge' adjustment.

Basis risk between spot and futures prices is the risk that the prices of the futures contract will not move in lockstep with the spot prices. Basis risk creates a problem when investors are trying to get exposure to a stock price through a futures contract, or are trying to hedge a position using a futures contract, and over time the prices of these two diverge.

To understand why basis risk arises, we need to think about how futures prices are determined. Futures prices are nothing but the spot prices plus the carrying cost, ie what it would cost for the seller of the contract to buy the spot security and hold it till the time of delivery in the future. During this holing period, the seller of the contract has to pay interest to fund his purchase in the spot market, and also receives and distributions such as dividends. In the case of commodity futures, he may also have to pay storage charges. When determining the futures prices, it is not known with complete certainty as to what the carrying costs will ultimately turn out to be - interest rates may change, dividends may turn out to be more or less, leading to changes in the futures prices without changes in the spot prices. This gives rise to basis risk.

Therefore changes to the risk free rate, which is a proxy for the true funding cost of the futures position and changes in expected dividends creates basis risk. Volatility of the underlying is irrelevant for futures.

Therefore Choice 'b' is the correct answer.

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.

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.

Since the stock is selling for $100 spot, its 3 month forward price for you would be $100*(1 + 6%*3/12) = $101.50. Since the forward is priced at $104, it is 'rich' compared to the spot and should be sold. A profitable trade would be to buy the spot and sell the forward.

Imagine you borrow $100 and buy the stock, and simultaneously sell the forward. At the end of 3 months, you will receive $104 in return from the forward, and be obliged to return the initial $100 borrowed together with interest of $1.50 for the three months. You would make a riskless profit of $2.50 per share in three months. Thus Choice 'c' is the correct answer.

Note that the treasury yield is irrelevant, what matters is the rate at which you can finance the trade which is 6% per annum.

On-the-run bonds yield less, and therefore are priced higher than similar off-the-run bonds. The difference in their pricing reflects the fact that on-the-run bonds are more liquid than off-the-run bonds. Therefore statements I and II are correct. Bonds are on-the-run when they are issued, and change hands frequently, and over time as they become 'seasoned', newer bonds take their place as on-the-run bonds making them off-the-run.

Strips are zero coupon instruments, and do not carry any coupon. Therefore statement III is not correct.

A lower bid-ask or bid-offer spread indicates lower transaction costs and is a result of greater liquidity. A higher bid-ask spread results for less liquid securities. Therefore statement IV is not correct.

The futures price of the contract will be the future value of the spot price, calculated at a net rate equal to the cost of funding the futures position, less any dividends or other distributions. Also note that when rates are continuously compounded, Future Value = Present Value x (exp(rate x time)).

Therefore in this case the futures price for the S&P = 1000 * exp((5%-2%)*3/12) = 1007.53

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

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.

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.

Profits and losses on futures contracts are settled daily. (P&L on forward contracts is often settled upon the expiry of the contract, and may even be collateralized.) Therefore Choice 'd' is the correct answer.