Explanation
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.

Explanation
The highest possible transformation line, ie the transformation line with the maximum slope, is the transformation line joining the risk free rate on the y-axis and the portfolio with the maximum Sharpe ratio on the efficient frontier. This line is called the 'capital markets line'. Investors can pick any point on this line according to their risk appetite, and doing so would maximize the return they can obtain for their desired level of risk. The capital markets line is tangential to the efficient frontier. The Sharpe ratio stays constant throughout the CML. Therefore statement IV is not true, while the rest are.

Explanation
The price of an interest rate cap is affected by all of the listed choices except the risk free rate. The risk free rate does not come into play in the pricing of caps, and therefore Choice 'b' is the correct answer.

Explanation
This is a straightforward case of basic portfolio math - the only thing being that we are not explicitly given the correlation between the two assets, nor are we given the volatility of the risk free asset. But since the other asset in the portfolio is the risk free asset, it has no risk, ie its volatility is zero, and its correlation with the fund run by the hedge fund manager is also zero. Portfolio returns will be the average returns of the two assets, and portfolio variance will be given by the formula portfolio_vol. Its square root will provide the portfolio volatility.
Therefore the expected returns are = 60%*12% + 40%*4% = 8.8%
The combined volatility of this portfolio will be given by (in Excel formula format) as =SQRT((60%*12%)^2
+ (40%*0%)^2 + 2*0*60%*40%*12%*0%) = 7.2%

Explanation
Choice 'c' correctly describes a 'holder extendible option'. Choice 'd' describes a 'writer extendible option'.
Choice 'a' describes a 'shout option'. Choice 'b' describes a 'knock in' option.