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

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.

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.

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.

We know from the put-call parity that:

Call - Put = Stock - Deposit

In the given situation,

Stock price = 100

call = 35

Put = ?

Exercise price = 100

However, we cannot use the stock price as-is, we need to adjust it for dividends that will be received during the period for which the option is valid. Dividends are $1, which need to be discounted to the present. In financial theory, dividends are often assumed to be continuously paid, though in reality they are single discrete payments at points in time. In this situation, for simplicity we assume that the dividend is paid at the end of the year, and needs to be discounted to the present and deducted from the spot price.

Therefore:

Stock price adjusted for dividends = $100 - ($1/1.05) = $100 - $0.95 = $99.05

Similarly, the bank deposit amount, which is the PV of the exercise price, can be calculated as $100/1.05 = $95.24

We can now calculate the price of the put by plugging the numbers above in the put-call parity:

35 - Put = $99.05 - $95.24

Therefore the value of the put = 31.19, which is closest to 31.20 which therefore is the correct answer.

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.

In a Dutch auction, the buyers put in their bids and the price at which the entire auction clears is the price at which each bidder receives the security. For example, if Bank A bids 5.5% for a bond, Bank B bids 5.6% and Bank C bids 5.7% and the total amounts bid by these three banks are enough to clear the auction, each of the banks will receive the bond at the price paid by the lowest successful bidder, ie Bank C. This is even though Banks A and B had bid higher (remember that bidding a higher yield means offering a lower price).

In a standard auction, every bidder pays the price they bid.

In a Dutch auction, there is an incentive to bid aggressively if a participant believes the final winning bid will be lower.

The investor's needs to sell futures contracts, as his current position is long. He needs to sell ($1,000,000 x (2.5-1)) / ($240,000 x 1.2) = 5.2 contracts, or rounded to 5 contracts.

It is important to note here that the investor wishes to retain a beta of 1, and does not want to get rid of all market exposure.

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.

A portfolio loses its delta neutrality if the delta of the portfolio changes but the underlying hedge is unchanged. The portfolio that will require the most rebalancing will be one whose delta changes by larger amounts in response to a given change in the price of the underlying. The sensitivity of the changes in delta in response to changes in the price of the underlying is measured by gamma. The higher the gamma, the more the portfolio will go out of delta neutrality given a change in the price of the underlying. Therefore Choice 'b' is the correct answer.

A portfolio with a low gamma will maintain its delta over a larger price range for the underlying, and is therefore likely to require less frequent rebalancing. The absolute level of the delta itself does not matter, what matters is the gamma. Vega is irrelevant to the delta hedging decision. Therefore the other choices are incorrect.

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.