Free PRMIA 8006 Practice Exam with Questions & Answers | Set: 7

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.

Professional management that acts as the agent of the shareholders is not likely to protect debt holders from a transfer of wealth to the shareholders. All other mechanisms listed are intended to offset the agency cost for debt holders, ie the expected cost that shareholders and management will transfer wealth away to the detriment of the debt holders.

The price of a treasury bill can be calculated as [Future value / (1 + yield x days-to-maturity/365)] = 100/(1+5%*90/365) = $98.78.

To calculate the Modified Duration from Macaulay's duration, we use the relationship MD = D/(1+r), where MD is the modified duration and D the Macaulay Duration. Therefore Choice 'c' is the correct answer.

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 effectiveness of the hedge is solely determined by the correlation between the position being hedged, and the position being used as the hedge. A hedge can be perfect when correlation is 1, and will be less than perfect when it is anything other than 1.The effectiveness of the optimal hedge is given by the formula √(1-ρ2), where ρ is the correlation between the two. Therefore Choice 'a' is the correct answer. Standard deviations affect the hedge ratio, not the effectiveness of the hedge.

(Note: In other texts, hedge effectiveness is explained to be measured by ρ2, which is essentially the same as √(1-ρ2), both expressions being functions of ρ. You can use either, being aware that one measures the variance explained, and the other is a measure of the unexplained variance.)

The equivalent continuously compounded rate in this case can be calculated as ln(1+5.2%) = 5.07%. The other answers are incorrect.

Refer to the tutorial on interest rates for more details on how continuously compounded rates work.

The efficient frontier is plotted on a graph with portfolio return (mean) as the y-axis and portfolio volatility, or standard deviation, on the x-axis. Asset beta and standard deviation of the market portfolio have nothing to do with the determination of the efficient portfolio.Therefore Choice 'd' is the correct answer, and the rest of the choices are incorrect.

Some parts of this question draw upon contingent claims framework to the value of a firm. According to this framework, the relationship between the debt and equity holders of a firm can be viewed as follows: The equity holders have a call option on the assets of the firm with a strike price equal to the value of the debt, and the debt holders have sold them this call. This is so because should the value of the assets of the firm fall below the value of the debt, the equity holders can walk away by handing over the assets to the debt holders in full extinguishment of their claims. If the value of the firm's assets is greater than the value of debt, the equity holders will exercise their call option. At the same time, it is also possible to view the debtholders as holding an asset and having sold a put on the assets of the firm with a strike price equal to the value of the debt. If the value of the assets of the firm were to fall below the value of the debt, they will end up buying the assets at a price equal to the value of the debt.

An increase in the volatility of returns on the assets of a firm increases the volatility of the asset value. This means the likelihood that the asset value will go below the value of the debt of the firm will increase. Callable debt can be considered to be a summation of two separate securities: a regular debt, for which the firm pays interest and receives a principal loan; and a call option that the debt holders have sold to the firm allowing the firm to buy back the debt. In return, the firm pays an implied 'premium' to the debt holders who have agreed to buy the callable debt. Therefore the total payments by the company to callable debt holders is equal to the interest payments plus the premium payment for the option. An increase in asset volatility will increase the value of this option as it is likely that the assets will increase in value, and strengthen the company's credit, and lower its spread at which time it would like to repay the debt and refinance/roll over at the new lower rate. Therefore an increase in volatility will increase the 'premium' demanded by the callable debt holders, thereby increasing the total yield and lowering the value of the callable debt. Therefore Choice 'b' (An increase in the value of the callable debt of the firm) is incorrect.

An increase in asset volatility will decrease the value of the firm as it is now riskier than before (higher standard deviation, same expected returns). Therefore Choice 'a' (An increase in the value of the equity of the firm) is false too.

The value of the implicit put in the debt of the firm will increase and not decrease as the volatility of the underlying assets increases. Therefore Choice 'c' (A decrease in the value of the implicit put in in the debt of the firm) is incorrect too.

Choice 'd' (A decrease in the value of the non-callable debt issued by the firm) is correct because higher asset volatility will increase the riskiness of the company's debt, making the required yield higher and decreasing its value.

The London Interbank Offered Rate (LIBOR) is published by the British Bankers' Association (BBA). The BBA polls the rates offered by at least eight banks drops the top and bottom quartile, and averages the middle two quartiles of the rates to arrive at the LIBOR.