Basis risk between spot and futures prices is the risk that the prices of the futures contract will not move in lockstep with the spot prices. Basis risk creates a problem when investors are trying to get exposure to a stock price through a futures contract, or are trying to hedge a position using a futures contract, and over time the prices of these two diverge.

To understand why basis risk arises, we need to think about how futures prices are determined. Futures prices are nothing but the spot prices plus the carrying cost, ie what it would cost for the seller of the contract to buy the spot security and hold it till the time of delivery in the future. During this holing period, the seller of the contract has to pay interest to fund his purchase in the spot market, and also receives and distributions such as dividends. In the case of commodity futures, he may also have to pay storage charges. When determining the futures prices, it is not known with complete certainty as to what the carrying costs will ultimately turn out to be - interest rates may change, dividends may turn out to be more or less, leading to changes in the futures prices without changes in the spot prices. This gives rise to basis risk.

Therefore changes to the risk free rate, which is a proxy for the true funding cost of the futures position and changes in expected dividends creates basis risk. Volatility of the underlying is irrelevant for futures.

Therefore Choice 'b' is the correct answer.

Kappa indices, which include the Sortino ratio and the Omega statistic, consider semi-variance, ie variance calculated only in respect of the downside risk instead of variance (which includes both upside and downside). This is because one criticism of other risk adjusted performance measures is that they take both upside and downside risk into account, even though a portfolio manager or investor is only concerned with managing the downside. The Kappa indices consider returns that are below a threshold to measure performance by. Therefore statement I is correct.

The Treynor ratio is calculated as [(Portfolio return - Risk free return)/Portfolio's beta]. It therefore calculates the excess return per unit of systematic risk and not specific risk. Therefore statement II is not correct.

Increasing portfolio leverage, ie borrowing to invest more in the portfolio, will increase the excess return of the portfolio in a linear fashion. However, it will also increase the volatility of such a portfolio in an identical linear way. Since Sharpe ratio is the ratio of 'excess returns' to standard deviation, the Sharpe ratio will stay constant. In other words, leverage does not impact Sharpe ratio, which is an attribute of this measure that allows us to compare performance across managers and funds regardless of leverage used. Statement III is not correct.

Jensen's alpha results from security selection, ie from specific risk the manager has taken. In a market portfolio, all specific risk is diversified away and only systematic risk remains. Therefore, statement IV is correct.

Choice 'b' is the correct answer. The other relationships are not correct.

The efficient markets hypothesis states that all known information is captured in the prices of a security. It does not explain the shape of the yield curve.

The expectations hypothesis, the LPT and the market segmentation theory are all attempts to explain the shape of the term structure of interest rates.

Therefore Choice 'c' is the correct answer as it does not explain the shape of the yield curve.

The stock has a beta of 1.2, therefore intuitively it can be expected to earn more than the broad market index. It will earn the risk free rate, ie 3%, and 1.2 times the equity risk premium of 5% (8% - 3%). The expected returns from the stock therefore are 3% + (8% - 3%)*1.2 = 9%

An yield curve would be meaningless if it combines, for example, the yield on a AAA bond with the yield on a bond near default on the same curve. Therefore statement I is incorrect as any typical yield curve generally refers to similar instruments, and similarity includes similarity of issuer type and credit risk profiles.

Statement II accurately describes an yield curve, and statement IV explains what the term structure is.

Statement III is incorrect as the liquidity preference theory offers an explanation for an upward sloping yield curve and not a downward sloping one.

Interest rate caps are effectively call options on an underlying interest rate that protect the buyer of the cap against a rise in interest rates over the agreed exercise rate. As with options, the premium on the cap depends upon the volatility of the underlying rates as one of its variables. A floor is the exact opposite of a cap, ie it is effectively a put option on an underlying interest rate that protects the buyer of the floor against a fall in interest rates below the agreed exercise rate. Therefore statements I and II are correct.

A cap protects a borrower against a rise in interest rates beyond a point, and a floor protects a lender against a fall in interest rates below a point.

A collar is a combination of a long cap and a short floor, the idea being that the premium due on the cap is offset partly by the premium earned on the short floor position. Therefore a collar is less expensive than a cap or a floor.

Caps, floors and collars provide a hedge against interest rate risks. Therefore statement III is correct too. However. they do not always provide protection against spreads changing, as the rate other than the one referenced by the cap or the floor may change causing the spread to change. Therefore statement IV is incorrect.

The lowest achievable standard deviation will be lowest when the assets are perfectly negatively correlated, ie when correlation = -1. In the case of the above choices, the lowest correlation is -0.33, which is the correct choice.

T-bill futures 'discount' can be converted to a price for the bill using the formula Price = [1 - discount * number of days/360]. In this case, this works out to (1- 10% *90/360) * 100 = $97.50. Choice 'd' is the correct answer.

Consider a long vanilla call at a strike of K1, and a short call with a strike price of K2 so that K2 > K1. If you construct the payoff diagrams for these option positions, you will see that the combined payoff resembles very closely the payoff of a digital cash-or-nothing option. By bringing K2 and K1 closer together, we can make it very close to a digital cash-or-nothing option. Therefore Choice 'c' is the correct answer.