Pass the PRMIA PRM Certification 8006 Questions and answers with ExamsMirror

This is a two step problem:

First, calculate the bond price using the yield information, then

Second, once you know the bond price, calculate the 18 month zero rate using the bootstrap method.

Step 1: Bond valuation: All variables required for pricing the bond are known. The coupon payments will be $1.50 in 6 months and 1 year from now, and a final paymento of $101.50 will be received in an year's time. This can be discounted at the yield provided as follows, and summed together to get the bond price of $97.14.

Step 2: Boot strapping: Discount the 6 month and 12 month coupons at the zero rates for those periods, and subtract the total of these PVs from the bond price. These work out to 1.5/(1+2%/2) = 1.485, and 1.5/(1+3%/2)^2=1.456. That gives us the present value, $97.14 - $1.485 - 1.456 = $94.203, which grows to the final payment of $101.50 at the end of 18 months. The zero rate inherent in this price can then be worked out as we know that (1+r/2)^3 = 101.5/94.203, or r = 5.03%.

The correct answer is Choice 'b', as this question is merely asking for the forward rate based on known spot rates. The forward rate applicable to the three month period commencing in 3 months time is given by [(1 + 6%*6/12)/(1 + 5%*3/12) - 1]*4 = 6.91%. Thus Choice 'b' is the correct answer.

Here is a step by step way to think about it: $1 invested now at 6% for 6 months grows to (1 + 6%*6/12)=1.03. At the same time, using the 3 month rate, $1 invested now at 5% for 3 months grows to (1 + 5%*3/12)=1.0125. Effectively, this means that the 1.0125 at the end of 3 months grow to 1.03 at the end of 6 months, implying the rate of interest during the 3 months from 3 to 6 months is (1.03/1.0125 - 1)*4 = 6.91%.

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.

For a deep in the money option, the option value changes in line with the value of the underlying because at this point the option is effectively behaving like the underlying. Therefore its delta is the same as the delta of the underlying, ie 1. In the same way, its gamma will be the same as the gamma of the underlying, which is 0. Therefore Choice 'b' is the correct answer.

The minimum variance hedge ratio is effectively the beta between the asset to be hedged and the asset used as a hedge, calculated as [correlation between the hedge and the asset to be hedged x volatility of the asset to be hedged/volatility of the hedge].The effectiveness of the hedge depends upon the correlation between the two, ie the asset to be hedged and the hedge. The minimum variance hedge ratio can be 1.0 even in situations where the correlation between the asset and the hedge is low, and as such does not mean much unless we know the hedge effectiveness (ie, the correlation).

It is therefore not possible to draw any certain conclusions based on the minimum variance hedge ratio alone. IV therefore is the only correct answer.

Choice 'b' lists all the factors that affect the forward price of a physical asset and is the most complete answer. Forward prices for physical assets are not affected by volatility (only options are), nor are they arbitrarily decided by any prevailing 'views'.

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.

The security market line is generally shown graphically with returns on the y-axis and the asset's beta on the x-axis. The correct answer is Choice 'a'.

Note the difference between the SML and the CML (the capital markets line). The CML 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, and expresses the relationship between risk and return.

This question requires us to use the CAPM.

Recall that according to CAPM the expected return on an asset = The risk free rate + β x Market risk premium.

Using the beta and expected return of security A, we can determine the market risk premium to be (8% - 3%)/1.2 = 4.1667%. The excess return is the return over the risk free rate, and for security B, this is nothing but the beta multiplied by the market risk premium. Therefore the correct answer is 4.1667% x 1.5 = 6.25%. Note that this is the 'excess return', and not the total return. (Total return will include the risk free rate).

Eurodollar deposits refer to US dollar denominated deposits outside the US, for example in a banking center such as London, and held by a non-US bank or a foreign branch of a US bank. Choice 'b' is the correct answer.