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

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').

In terms of beta, his exposure is $10m*0.7 = $7m. This exposure is long.  In order order to neutralize his long exposure, he needs to have an equal an identical short position with the same beta as this long position (of course, in the short direction).  We need to figure out how many contracts will have a beta equal to his held position.  (The beta of a futures contract is slightly different from 1 when compared to spot, but in the absence of other information in the question it is always okay to assume that the beta of the futures contract is 1.  Such precision does not matter because of other errors such as rounding etc that cannot be anyway done away with.)

He needs to short futures contracts on the index with $7m in notional value. The value of each contract is currently 1000*250 =$250,000. He therefore needs to short $7m/$250,000 = 28 contracts to become market or beta neutral.

Overcollateralization is when the notes issued by the special purpose vehicle are less in value compared to the underlying pool of assets, thereby providing a buffer to absorb losses. Excess spread implies that the notes issued carry a lower interest rate than the interest rate received on the underlying assets. Cash reserves are reserves intended to take first hits when losses happen. All of these are valid credit enhancements for structured products. Additionally, 'insurance wraps' are also used as a credit enhancement. Choice 'c' is the correct answer.

'Margin requirements' do not mean anything in this context and are not a valid credit enhancement used for credit derivatives.

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.

For a deep in the money option, the option value changes in line with the value of the underlying because at this point the option is effectively behaving like the underlying. Therefore its delta is the same as the delta of the underlying, ie 1. In the same way, its gamma will be the same as the gamma of the underlying, which is 0. Therefore Choice 'b' is the correct answer.

The delta of an at-the-money call option is close to 0.5. It is close to 1 when it is deep in the money. It is close to 0 when it is deep out of the money. It is never negative. Therefore Choice 'b' is the correct answer.

A total return swap allows an investor or a financial institution to gain exposure to an asset or a portfolio without actually having to go long in those positions. The counterparty provides the return from the exposure and receives LIBOR plus a spread in exchange. Effectively, the counterparty has funded the investor's position for a fixed interest rate, therefore a TRS is essentially a funding arrangement. However, the structure of a TRS may also have other consequences that are relevant for tax and accounting - the assets under a TRS are not held on the balance sheet of the investor receiving the total return. Statement I is correct as the TRS helps gain an exposure without having to fund the position with cash.

Repos are useful for shorting corporate bonds. The investor desirous of shorting a corporate bond would sell the bond in the market, and immediately borrow the bond from someone else using a repo to deliver to the party he has sold the bond to. Repos are used extensively to cover short bond positions, and therefore statement II is correct.

Statement III is not correct as counterparty risk continues to exist with a TRS. The counterparty may fail to provide the agreed returns, and the risk exists.

Statement IV is correct as the bank that borrows funds using a repo continues to hold the underlying assets on its balance sheet. Therefore Choice 'd' is the correct answer.

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.

A utility function is graphed with utility on the y-axis and the variable driving utility (generally wealth) along the x-axis.

A concave utility function, ie a function with a downward sloping curve, indicates risk aversion. A convex utility function indicates a risk seeking attitude and a straight line (ie no curvature) indicates a risk neutral attitude.

The LIBOR square is a (rare) derivative contract which pays, as mentioned in the question, the square of the interest rate move between two dates. If LIBOR at inception is y, and upon settlement is x, the contract pays (x - y)^2 for x > y; and -(x - y)^2 for x < y.

For any question that involves calculating delta or gamma, and the payoff is described in terms of variables as is the case here, remember that delta is always the first derivative and gamma is the second derivative. For this question, let us calculate the second derivative and see what the gamma is:

If x > y, then the payoff is (x - y)^2

The first derivative wrt x is 2(x - y)

The second derivative wrt x is 2.

ie, the gamma is 2

If x < y, then the payoff is -(x - y)^2

The first derivative wrt x is -2(x - y)

The second derivative wrt x is -2.

ie, the gamma is -2

If x = y, then the payoff is 0. Both the first and the second derivatives are zero. ie the gamma is 0.

Based on the above, we see that the contract can have a gamma of either 0, +2 or -2. 1 is not a possible value for gamma, and therefore Choice 'b' is the correct answer.