PRMIA 8006 Online Access

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.

Each of the choices describes various scenarios related to the issue of bonds. A when-issued market is a market in government securities where securities are traded as forward contracts prior to their issue. Choice 'c' is the correct answer.

Choice 'd' refers to a 'bought deal'. Choice 'b' refers to the 'grey market', usually in corporate bonds. Choice 'a' refers to a fixed price re-offer mechanism.

The Sharpe ratio is the ratio of the excess returns of a portfolio to its volatility. It provides an intuitive measure of a portfolio's excess return over the risk free rate. The Sharpe ratio is calculated as [(Portfolio return - Risk free return)/Portfolio standard deviation].

The Treynor ratio is similar to the Sharpe ratio, but instead of using volatility in the denominator, it uses the portfolio's beta. Therefore the Treynor Ratio is calculated as [(Portfolio return - Risk free return)/Portfolio's beta]. Therefore Choice 'a' is the correct answer.

Jensen's alpha is another risk adjusted performance measure. It considers only the 'alpha', or the return attributable to a portfolio manager's skill. It is the difference between the return of the portfolio, and what the portfolio should theoretically have earned. Any portfolio can be expected to earn the risk free rate (rf), plus the market risk premium (which is given by [Beta x (Market portfolio's return - Risk free rate)]. Jensen's alpha is therefore the actual return earned less the risk free rate and the beta return.

Refer to the tutorial on risk adjusted performance measures for more details

A residential mortgage carries a prepayment option for the borrower, where in the event of a decrease in interest rates they are likely to repay the mortgage and refinance at the new lower rate. If rates go up, the bank does not have a similar option. If the volatility of the underlying interest rates increases, mortgage holders are more likely to be faced with new rates that are sufficiently lower to persuade them to refinance. This reduces the ability of the bank to continue to earn the higher interest rate it was earning before.

Therefore an increase in volatility of the mortgage interest rates decreases the value of the mortgage portfolio.

The same rationale applies to callable bonds, where the borrower has the option to call the bond.