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

In this case, we need a portfolio that is "dollar duration" neutral, ie the net effect of any change in interest rates creates offsetting gains and losses in the asset and liability portfolios. The $125m asset portfolio with a duration of 15 years has a dollar-duration of $125*15/100=$18.75m, implying that a 1% change in interest rates will create a $18.75m change in the value of the asset portfolio. Similarly, the liabilities of $100m with a duration of 20 years mean that a 1% change in interest rates will lead to a $20m change in their value. Since $18.75m<$20m, the pension fund is short duration, and needs a strategy that will give it more duration. It can do so by buying more bonds, or swapping out some of its shorter duration bonds with longer duration bonds, or doing other things that will increase the duration of the portfolio so it becomes duration neutral.

Entering into an interest rate swap to receive fixed and pay floating is like a long position in a bond, which will increase duration. Thus Choice 'b' is the correct answer.

A swap to pay fixed and receive floating will have the opposite effect, and so will selling bond futures. Choice 'c' and Choice 'a' are therefore incorrect. As we have seen, Choice 'd' is incorrect as the fund does have interest rate exposure.

The yield to maturity for a bond trading at par will be identical to its coupon. Therefore the yield to maturity for this bond will be 5%

The swap can be valued by using the new swap rate of 5%. The investor is paying fixed and receiving LIBOR, and can effectively get out of his position by entering into a swap to receive 5% and pay LIBOR. This will leave him/her with a net cash flow of 1% for two years, ie $1m for 2 years that can be discounted to the present using the rates provided, ie =(1/1.05 + 1/(1.05^2)) = $1,859,410.

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 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.

The put-call parity makes sure that all else remaining equal, an increase in the value of a call option will be accompanies by an increase in the value of the corresponding put option.

Simply stated, the put-call parity can be expressed as:

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

The two terms on the right hand side of this equation are fixed. Therefore, for the equality to be maintained, any increase in the value of the call option on the left hand side has to be accompanied by the value of the put.

Choice 'c' is therefore 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 'hard call protection' means the bond cannot be called until a certain date, regardless of what the share price is. Therefore statement I is false. Also note that a 'soft call protection' means that a bond can be called only if the share price reaches a certain threshold.

It is advantageous for the issuer to call its convertible securities when the share price exceeds the conversion price - because these shares can instead be sold in the market at the higher share price than the lower conversion price. Statement II is true.

When the issuer's share price is very high, the convertible bond trades at a discount to the share price because it is almost certain to be called by the issuer and be redeemed at par. Therefore statement III is right. Statement IV is incorrect because convertible bonds need to pay less coupon than equivalent non-convertible bonds because of the value of the option embedded in them.

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.

A hedge based on portfolio duration alone makes the assumption that the price/yield relationship is linear, and ignores the convexity or non-linearity of the price/yield relationship. As prices change beyond small changes, the non-linear effect kicks in, which can be offset by making a convexity adjustment to the hedge. Therefore statements I and II are correct.

Statement III is incorrect - negative convexity has an adverse effect on bond prices regardless of whether prices rise or fall.

Statement IV is correct, a bond hedge based on duration alone may be mismatched along the yield curve (eg, hedging a 10 year maturity bond with a 3 year futures contract, even though of identical total durations), which is based upon the implicit assumption that all rates will move together (ie parallel shifts).

A higher coupon brings forward the cash flows of a bond, thereby lowering duration. Therefore statement I is true. The lower the duration the lower the convexity. Therefore a higher coupon leads to lower duration and therefore lower convexity. Thus statement II is true.

Bonds do not have negative modified duration, therefore statement III is false.

If the bond is callable, it leads to negative convexity as a fall in interest rates is likely to induce the issuer to call the bond and re-issue at the new lower interest rates (much like refinancing mortgages when interest rates fall), therefore the upside from a fall in rates is limited. This creates 'negative convexity'. Thus statement IV is correct.

The London Interbank Offered Rate (LIBOR) is published by the British Bankers' Association (BBA). The BBA polls the rates offered by at least eight banks drops the top and bottom quartile, and averages the middle two quartiles of the rates to arrive at the LIBOR.