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).

According to the CAPM, the expected return from a risky asset is a function of the contribution of the risky asset to the total risk of the market portfolio. Nothing else matters. All assets are priced according to the risk they bring to the market portfolio, regardless of their individual level of risk. An asset that is very volatile on its own, but has a negative correlation to the market may be priced high, ie have low expected return, because of its impact on the risk of the market portfolio. Therefore Choice ' a ' is the correct answer, and the other options are incorrect.

Recall that according to the CAPM β = covariancex, y / variancex, where x is the market portfolio and y is the risky asset.

The beta itself is a function of the covariance of the asset ' s returns with market returns, and therefore only the driver of expected return for an asset is its beta, which is determined by the asset ' s contribution to portfolio risk. (β = covariance(x, y) / variance(x), where x is the market portfolio and y is the risky asset. )

The modified duration of a perpetual bond is given by 1/i, where i is the yield. Since I is a positive number greater than zero, it means the modified duration of a perpetual bond is not infinity. Also note that this formula makes no reference to the coupon rate at all - in other words, the modified duration of a perpetual bond is independent of the coupon. The Macaulay duration of a perpetual bond is given by (1+i)/i, again a formula devoid of any references to the coupon. The price of a perpetual bond can be calculated as Coupon/i, which means that a 15% coupon perpetual bond will be priced at exactly 3x the price of a 5% coupon bond.

Based on the above, statement I is incorrect, but statement II is correct. Statement III is incorrect because Bond A will be priced at exactly 1/3rd the price of Bond B, and not less than that. Similarly, statement IV is incorrect as well.

Intuitively, a perpetual bond is nothing but a perpetual annuity, which will have a present value equal to 1/i * cash flow (which in this case is the coupon). The coupon rate only sets the cash flow dollar amount - there is really no difference between the two bonds described in the question except that buying one of Bond B is economically identical to buying three of Bond A.

When rates are continuously compounded, we can calculate the marginal rate for year 5 as (5*5% - 4*4%) = 9%. (Note that things would be different if the rates were not continuously compounded, and they were annually compounded. In that case we would need to do a calculation of (1.05^5 / 1.04^4) - 1)

The basis point value is equal to $102 x 5 /10000 = $0.051. Therefore Choice ' d ' is the correct answer.

The basis point value, also called the PV01, is the dollar value change in the price of a bond as a result of a 1 basis point (=1/10000) change in interest rates. Since the modified duration is 5, it means a 1% change in interest rates produces a 5% change in the price of the bond, and a 1 bps change will therefore produce a 0.05% change in the value of the bond. Since the bond is currently valued at $102, the change works out to $102 x 0.05% = $0.051.

Only the butterfly spread has a payoff profile that benefits when prices do not move much. The collar benefits during declining markets, the straddle and the strangle benefit from sharp movements in the markets. Therefore Choice ' c ' is the correct answer.

Investors in CDOs bear credit risk. The SPV is merely a conduit that owns the underlying assets on which the sponsoring institution has bought protection. The investors have sold them this protection, and are on the hook for defaults or other credit events. The reference entity is relevant only to CDSs, not CDOs. Choice ' b ' is the correct answer.

Imagine a bond that provides just two cash flows: $100 in one year and $10 in 10 years. Imagine another bond that pays nothing now but $100 in 10 years. Assume that both have identical yields to maturity. Yet despite the identical YTM, the bonds are quite dissimilar. For the first bond, we face the risk that we would receive the bulk of the present value of the bond in an year ' s time, and while there is a small amount due in 10 years, the first payment may not find an equally attractive investment opportunity. Reinvestment risk refers to the risk that cash flows from a bond may not be investible at the yield to maturity for the bond. In such cases, bonds that have longer durations are preferable.

A coupon bearing bond with a coupon rate lower than our benchmark bond will carry a lower reinvestment risk as its cash flows are weighted more towards the end. An amortizing bond returns a part of the principle periodically, increasing reinvestment risk. A higher coupon bearing bond will have a higher reinvestment risk, and a zero coupon bond will have the least reinvestment risk.

A cash or nothing call is one that pays a fixed amount if the underlying exceeds a certain threshold, or nothing. An asset or nothing call is the same as the cash or nothing call except that instead of paying a fixed amount, it ' pays ' the asset. Therefore the payoff profile of a long asset or nothing call has the same payoff as a long cash or nothing call and a long vanilla call.

This is best considered by building payoff diagrams which will show how the two positions are economically equivalent. Choice ' d ' is the correct answer, and the rest are not.

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.