8006 Exam Dumps - Exam I: Finance Theory Financial Instruments Financial Markets - 2015 Edition

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.

A utility function is graphed with utility on the y-axis and the variable driving utility (generally wealth) along the x-axis.

A concave utility function, ie a function with a downward sloping curve, indicates risk aversion. A convex utility function indicates a risk seeking attitude and a straight line (ie no curvature) indicates a risk neutral attitude.

Choice 'a' is the correct answer as the issue of the floating rate note will provide the utility with the funds it needs, and the interest rate swap would offset the floating rate payment and leave it with a net fixed payment.

Choice 'd' is incorrect as the swap is in the wrong direction.

Choice 'c' is incorrect as buying and selling a floating rate bond would mean the utility will not have any funds that it wants to issue the note for, and combining it with interest rate futures would be just absurd.

Choice 'b' is incorrect as buying a floating rate note would use funds while the utility is trying to raise funds.

The key point in this question is that the bond is zero coupon, and can only be called at face value. Since the bond is zero coupon, its value will always be less than its par value at any time during its existence (as any interest rate will be a positive number). Therefore the issuer will never exercise the call. Thus the bond will have a duration equal to what an equivalent non-callable bond would have.

Since zero coupon bonds have a duration equal to their maturity, the bond's duration is 10 years.

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.

The transformation line represents the various possible combinations of the 'risky bundle' and the risk free asset. Investors can choose different combinations of the risky and risk-free asset depending upon their risk appetite. The transformation line meets the y-axis (portfolio returns) at the point equal to the risk free rate. Choice 'a' is the correct answer and the rest are incorrect.

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.

Remember that the transformation line and the capital markets lines are different from each other - there is only one CML for an efficient frontier, whereas there can be multiple transformation lines.

The effect of higher convexity is that when yields rise, the price decrease is lower than the increase in yields, and when yields fall, the increase in price is greater than the fall in yield. In either case, it benefits the holder of the fixed income instrument that carries such positive convexity. The converse is true for someone short a bond - such an investor would prefer lower convexity to higher convexity. Therefore statement I is not true for an investor who is short a bond.

An increase in yields makes bond prices decrease, something that would benefit the short. Therefore statement II is true for an investor short a bond.

Negative convexity has exactly the opposite effect as the one described for positive convexity for statement I above. An investor short a bond would prefer negative convexity (which by the way is exhibited by very few fixed income instruments such as mortgages) to positive convexity, therefore statement III is true for such an investor.

Choice 'b' is the correct answer.

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.