Forward currency rates can be calculated as Spot rate x (1 + rate in domestic currency)/(1 + rate in foreign currency), where the spot rate is the ' direct ' rate. Direct rates are rates that are expressed as the number of domestic currency units that it takes to buy 1 unit of the foreign currency. In this case, considering the US the domestic currency, then the forward rate is given by 0.7 * 1.02/1.035 = 0.6899. Therefore Choice ' b ' is the correct answer.

The efficient frontier is a two dimensional plot with volatility and returns on its axes. For a given level of return, it helps identify the portfolio with the lowest volatility. From the other axis, it helps identify the portfolio with the highest return for a given level of volatility.

Therefore Choice ' b ' is the correct answer. Note that in the exam you may be asked the question slightly differently.

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.

This question requires a calculation of the present value of the future cash flows from the bond. The correct answer is $94.92, calculated as =(5/(1 + 5%)) + (5/(1+ 6%)^2) + (105/(1 + 7%)^3).

All the statements are correct, therefore Choice ' d ' is the correct answer. Let us look at each of these statements one by one.

I. A deep in-the-money call option has a value very close to that of a forward contract with a forward price equal to the exercise price. This is true because a deep in the money call option is most likely to be exercised, and is therefore effectively like a forward contract to buy the stock at the exercise price.

We can also look at this using the BSM formula for a call option. If c be the value of a call option, and all other variables have their usual meaning (S0 is the spot price, K is exercise price, and t is time to expiry), then according to the Black Scholes model the value of a call is given by the following expression:

202.22.e1

As S0 becomes large, d1 and d2 become large, and therefore N(d1) and N(d2) approach 1, leaving the value of the call to be equal to 202.22.e2, which is the formula for a forward contract.

II. If the volatility of a stock goes down to zero, the value of a call option on the stock will tend to be close to that of a forward contract so long as the option is in the money.

Again, this is true because if volatility is low or zero, the stock price will grow at its expected rate, and end up to be what the forward price is (S0 ert). If the option is out of the money, the value of the option will tend to 0.

III. All other things remaining the same, the issue of stock warrants exercisable at a future date will cause a decline in the current stock price.

This is true because the stock warrants are likely to be exercised only when they are in the money, ie when their exercise price is less than the going stock price, and at that time it will dilute the value of the existing shares. However, the reduction in the price is priced into the share price at the time of the issue of the warrants, and it is not that the share price falls the day they are exercised.

IV. Implied volatilities are calculated from market prices of options and are forward looking. This statement is true: historical volatilities calculated from past prices are backward looking, while ' implied volatility ' is the volatility implied from market prices, and is forward looking as it encapsulates the market ' s view of how volatile the future is likely to be.

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.

Since the zero coupon bond has no interim interest payments, its only cash flow is the final payment upon maturity. This would be identical to the spot rate from now till t years, where t is the maturity of the bond.

Forward rates are marginal rates that apply to individual years in a multi-period context. Short rates refer to short term interest rates in money market futures contracts. A zero coupon bond has no coupon.

For fixed income portfolios where standard cash flow discounting models are not available, duration calculations are based upon estimated price moves in response to a change in rates. Recall that we define duration as the percentage change in price expected for a 1% change in yield. In this case, we have three price points known to us:

Line | Price | Yield

a | $102 | r - 45bps

b | $100 | r

c | $ 97 | r + 45bps

(where r is the current yield)

The change in price from line a to line c is $102m - $97m = $5m. We use the middle point, ie $100m, to calculate the percentage change. Therefore the percentage change in price is $5m/$100m = 5%.

The change in yield between lines a and c is 90 basis points [=(r+45bps) - (r-45bps)]. In other words, the change in price is 5% for a 90 bps change in yield. So the duration can be calculated as 5/(90/100) = 5.56. The other answers are incorrect.

The buyer of an FRA is considered ' long ' , and a 3 x 6 FRA allows him or her to borrow funds at the agreed rate starting at the end of month 3 till the end of month 6. (ie, 3 x 6 indicates that the borrowing period commences at 3 months, and ends at 6 months, for a period of 6 - 3 = 3 months). The seller has exactly the opposite position, ie he or she is committed to lend funds at the agreed rate for 3 months starting at the end of 3 months from today (for a 3 x 6 FRA). [Note that the obligation to borrow or lend in and FRA does not mean that either parties will actually do that, instead they will just exchange cash flows to get to get to an identical economic situation.]

Since the seller, or the short, is committed to lending in the future starting 3 months from now, it is akin to borrowing now for 3 months, and investing the borrowed amount for 6 months. During the first 3 months, the amounts borrowed and lent ' cancel ' out (conceptually) and after the 3 months the short returns the amount borrowed, and is left with just the net amount lent, ie the FRA.

Thus the correct answer is Choice ' d ' . Choice ' b ' describes the position of the FRA buyer. Choice ' a ' and Choice ' c ' are nonsensical.

Statement I is correct - since forward prices are determined as (Spot - PV of dividends)*e^(rt), an increase in dividends will reduce forward prices.

Statement II is incorrect as forward prices will be determined by near term interest rates, specifically by the borrowing rate for the period of the contract, and will stay unchanged if near term interest rates do not change.

Statement III is incorrect. Futures exchanges require both buyers and sellers to deposit initial margins as prices can move adversely for either of them.

Statement IV is incorrect, as the margin deposited when a contract is entered into is called initial margin. Margin calls thereafter resulting from movements in prices are called variation margin.

Statement V is incorrect. Most futures exchanges distinguish between hedgers and speculators and require different margins from each.

Statement VI is incorrect. Interest rate futures behave almost identically to their bond counterparts, and carry both duration and convexity.