Security A 'dominates' security B, ie it offers the most return per unit of volatility. However, because it is less volatile, its returns are likely to be more concentrated around its mean compared to Security B which will have 'fatter tails' compared to Security A. Therefore Security B will offer a much better chance of making the desired 25% return. Of course, this also means that Security B is much more likely to lose a lot more money than Security A. However, if the portfolio manager is only interested in maximizing his chances of making a 25% or greater return, he should select Security B. The answer can be verified using Excel's Normdist formula, and probability of exceeding 25% will be given by [=1-NORMDIST(0.25,0.1,0.1,TRUE)] for Security A and =1-NORMDIST(0.25,0.1,0.2,TRUE)] for Security B. A combined portfolio of the two will have a return of 10% and variance less than that of Security B (or at the most equal to the weighted average of the two variances, even if their correlation is 1), which means a combined portfolio will also have a lower probability of exceeding a 25% return.

This question reflects how portfolio managers may be tempted to make sub-optimum decisions for their investors by swinging for the fences by taking large bets, for example, when they have had a big drawdown and have to make it up to the high water mark levels before they earn performance fees.

The futures price of the contract will be the future value of the spot price, calculated at a net rate equal to the cost of funding the futures position, less any dividends or other distributions. Also note that when rates are continuously compounded, Future Value = Present Value x (exp(rate x time)).

Therefore in this case the futures price for the S & P = 1000 * exp((5%-2%)*3/12) = 1007.53

According to the dividend discount model, the spot share prices represent the present value of all the future cash flows from the stock. If held till perpetuity, this becomes an annuity equal to the dividend, growing at its expected growth rate. Therefore Choice 'a' is the correct answer. Choice 'c' would represent the total market cap, and not the value per share that the question asks.

The mean can be calculated quite easily as a weighted average, and in this case it is 0.6*5% + 0.4*3% = 4.2%.

The variance can be calculated with the formula for portfolio variance as = (0.6^2)*(20%^2) + (0.4^2)*(5%^2) + 2*(-0.6)*0.6*0.4*20%*5%=0.01192. Therefore the volatility of this portfolio is SQRT(0.01192)=10.92%

A CDS contract provides exposure to default risk and the credit spread for a particular credit. It does not provide an exposure to the risk of interest rates going up or down. It is an instrument that allows institutions to take a view on the price of credit risk alone. Therefore statement I is false and statement II is true.

A total return swap (TRS) exchanges the return from an asset for a fixed or floating exchange rate. It is in essence a financing arrangement where one party pays the other interest to earn a return on an asset that it does not wish to hold itself, perhaps for liquidity reasons. The financed asset is held by the party paying the asset's returns, effectively creating a 'collateral'. Therefore statement III is correct.

A credit linked note is a funded instrument where the sellers of the protection have put up the money upfront in the form of a subscription to a note in case the credit losses are realized. Therefore statement IV is not correct.

Statement I is correct. If daily returns are not independent, variances cannot simply be added up over the period, and the square root of time rule is not appropriate to use to scale volatility. Statement II is incorrect. Statement III is correct. If daily returns are positively correlated, it means that a high return on one day will likely cause a higher return the next day, and likewise for low or negative returns. Intuitively, it means that a 'trend' will be created and volatility will be higher than in a case where daily returns were not correlated. Therefore statement II is not correct. By the same logic, negative correlation between daily returns would mean a higher return on one day would likely be followed by lower returns the next day, ie a reversion to mean will result causing the volatility to be lower than the case when the returns are uncorrelated. (The correlation between the daily returns is called the 'autocorrelation coefficient'.) Statement IV is false because while the random walk of prices does imply independence, it says nothing about the expected value of returns. It does not imply that the returns will have an expected value of zero (or any other value). Thus Choice 'c' is the correct answer and the rest are incorrect.

The loss to the fund manager is $20*100 = $2,000. The initial margin placed was $5,000. After the loss is charged to his account, the margin balance is only $3,000 ($5,000 - $2,000). The margin to be maintained is $5,000. Therefore the margin call is $2,000.

Note that there would have been no margin call till the balance in the margin account had reduced to the 'maintenance' level of $4,000. So if the price had fallen by $5, and the loss had been $500, there would have been no margin call. But when the margin call would be made, it would require the balance to be brought up to the initial margin of $5,000 (and not the maintenance margin of $4,000).

All the statements given are true, except that standard deviations cannot be averaged to get the portfolio standard deviation unless the assets are perfectly positively correlated. Therefore Choice 'd' is the false statement, and the correct answer.

For a portfolio of uncorrelated assets, ie correlations being equal to zero, variances can be added together to get portfolio variance. Also, regardless of correlations, portfolio returns are always the weighted average of asset returns, and just averages will do in this case as the portfolio is said to be equally weighted across the assets. A correlation of zero produces a risk level less than that possible with positive correlations.

There are two ways to think about this question: First, because the asset manager thinks that interest rates are going to decline, his profit will be maximized if he buys the bond with the greatest duration. The zero coupon bond has the greatest duration among the alternatives listed. Therefore Choice 'c' is the correct answer.

The second way to look at this question is to consider what is called 'reinvestment risk'. Yields to maturity calculations have an implicit assumption that any cash flows received prior to maturity are investible at the ytm rate. Thus, an yield to maturity calculation for a coupon bearing bond assumes that coupon payments get invested at the same rate as the calculated ytm from the time they are received till the time the bond matures. In an environment where interest rates fall, this assumption will not hold true. Reinvestment risk is the risk that coupons will not be able to earn the ytm that the bond was brought at - and the investor will be at a loss to the extent the money does not earn the ytm rate till the end of the investment. One way to reduce reinvestment risk is to minimize coupon receipts so the money stays invested as part of the bond, and the zero coupon bond helps to do exactly that.

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.