A fixed for floating interest rate swap is identical to a series of forward rate agreements coinciding with the settlement periods. For example, a 2 year fixed for floating interest rate swap where the investor pays fixed at 6 monthly rests is equivalent to a long position in 3 FRAs ( a 6 x12, a 12 x 18 and an 18 x 24 FRA). Thus I represents a correct replication of the swap.

An obligation to pay fixed is identical to a short position in a fixed rate bond, and receiving the floating rate is akin to a long position in a floating rate note. Thus II also correctly replicates the swap.

A long position in an FRN correctly replicates the floating cash flow from the swap, but a short position in the FRA obliges the investor to receive fixed and pay floating - which is not equivalent to the flows from the interest rate swap. Thus III is not a correct replication of the interest.

A long position in a cap means the investor will receive the difference between the floating and the cap rate if the floating rate is greater than the cap rate. Effectively, the investor will receive floating. A short postion in a floor at the same strike rate would mean the investor would end up paying the floor rate, effectively equivalent to the obligation to pay a fixed rate. Therefore this replication also correctly replicates the swap, and IV can also be used to replicate the investor ' s position.

Therefore Choice ' a ' is the correct answer and the rest are incorrect.

(For statement IV, let me explain with an example. Recall that the buyer of a cap receives the difference between the current interest rate and the agreed exercise rate if the current interest rate goes above the exercise rate. A cap can be used by a floating rate borrower to limit their exposure to a rise in interest rates. In the same way, the seller of a floor pays the buyer the difference between the current interest rate and the exercise rate if the current interest rate falls below the exercise rate. A floor can be used by a lender to protect against a fall in interest rates.

Now assume the exercise rate is r. Also assume that the current floating interest rate is r ' . the holder of the interest rate swap in the example in the question receives r and pays r ' . Therefore the net payout is r ' - r (pays fixed, ie -r, and receives floating, ie +r).

Now consider the long position in the cap and the short position in the floor.

Case 1: If r > r ' , the following will happen:

a. The long position in the cap will pay nothing, ie 0.

b. The short position in the floor will require a payment of r - r ' to the buyer of the floor, and because it is a payment, the cash flow will be -(r - r ' ) = r ' - r

Case 2: If r < r ' , the following will happen:

a. The long position in the cap will mean the investor receives r ' - r.

b. The short position in the floor will pay nothing as the interest rate is higher than the exercise rate.

In both cases, the net cash flow for the investor is r ' - r, which is the same as for the swap where the investor pays fixed and receives floating.)

Security A ' dominates ' security B, ie it offers the most return per unit of volatility. However, because it is less volatile, its returns are likely to be more concentrated around its mean compared to Security B which will have ' fatter tails ' compared to Security A. Therefore Security B will offer a much better chance of making the desired 25% return. Of course, this also means that Security B is much more likely to lose a lot more money than Security A. However, if the portfolio manager is only interested in maximizing his chances of making a 25% or greater return, he should select Security B. The answer can be verified using Excel ' s Normdist formula, and probability of exceeding 25% will be given by [=1-NORMDIST(0.25,0.1,0.1,TRUE)] for Security A and =1-NORMDIST(0.25,0.1,0.2,TRUE)] for Security B. A combined portfolio of the two will have a return of 10% and variance less than that of Security B (or at the most equal to the weighted average of the two variances, even if their correlation is 1), which means a combined portfolio will also have a lower probability of exceeding a 25% return.

This question reflects how portfolio managers may be tempted to make sub-optimum decisions for their investors by swinging for the fences by taking large bets, for example, when they have had a big drawdown and have to make it up to the high water mark levels before they earn performance fees.

Given volatility, weights and correlation, we do not need any additional information on covariances - and therefore statement I is incorrect.

To evaluate the other statements, consider the formula for portfolio variance (recalling that standard deviation is just the square root of the variance)

portfolio_var_diff_corr

Statement II is incorrect because this statement describes what the standard deviation of the portfolio would be if the assets were to be perfectly positively correlated (here they are negatively correlated).

Statement III is incorrect. When the two assets are uncorrelated (ie correlation = 0), the combined standard deviation is the square root of the weighted sum of variances, where the squares of the asset weights are used as weights (see formula above).

Statement IV is correct. When the assets are perfectly positively correlated, they are effectively the same asset and the combined standard deviation of a portfolio of such assets is nothing but the sum of their weighted standard deviations.

Also refer to the tutorial (and the Excel model - you will find it under Exam 2) for portfolio variances to see how portfolio volatility behaves when correlations are -1, 0 or +1.

Backwardation is said to occur when futures prices are lower than the current spot prices. This would happen only when carrying costs are negative. Carrying costs are equal to interest, plus storage costs and less any ' convenience yield ' . The existence of large convenience yields may explain backwardation in commodity futures prices. Therefore Choice ' d ' is the correct answer.

Contango is the ' normal ' market situation where forward prices are higher than spot prices. Storage costs explain contango, not backwardation. Risk free rates, or the cost of funding for the futures position, are always positive and do not explain backwardation.

When 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 as shorts try to buy in the spot market to cover their short positions. Similarly, expectations of oversupply in the future, for example due to a bumper harvest may create situations where the forward prices fall below spot prices. Convenience yield is the benefit from having access to the commodity - and if the convenience yield is very high, for example in a market where manufacturers must never run out of a particular raw material, then these can switch the costs of carry (which include interest and storage costs, less convenience yields) to being negative.

Since all these factors can contribute to backwardation in the market, Choice ' d ' is the correct answer.

The equivalent continuously compounded rate in this case can be calculated as ln(1+5.2%) = 5.07%. The other answers are incorrect.

Refer to the tutorial on interest rates for more details on how continuously compounded rates work.

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.