PRMIA 8006 Exam I: Finance Theory, Financial Instruments, Financial Markets – 2015 Edition Exam Practice Test

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Total 287 questions
Question 1

For an investor short a bond, which of the following is true:

1. Higher convexity is preferable to lower convexity

II. An increase in yields is preferable to a decrease in yield

III. Negative convexity is preferable to positive convexity



Answer : B

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.


Question 2

[According to the PRMIA study guide for Exam 1, Simple Exotics and Convertible Bonds have been excluded from the syllabus. You may choose to ignore this question. It appears here solely because the Handbook continues to have these chapters.]

A digital cash-or-nothing option can be hedged reasonably effectively using:



Answer : C

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.


Question 3

Which of the following expressions represents the Sharpe ratio, where is the expected return, is the standard deviation of returns, rm is the return of the market portfolio and if is the risk free rate:

A.

B.

C)

D)



Answer : C

The Sharpe ratio is the ratio of the excess returns of a portfolio to its volatility. It provides an intuitive measure of a portfolio's excess return over the risk free rate. The Sharpe ratio is calculated as [(Portfolio return - Risk free return)/Portfolio standard deviation]. Therefore Choice 'c' is the correct answer.

The Treynor ratio is similar to the Sharpe ratio, but instead of using volatility in the denominator, it uses the portfolio's beta. Therefore the Treynor Ratio is calculated as [(Portfolio return - Risk free return)/Portfolio's beta].

Jensen's alpha is another risk adjusted performance measure. It considers only the 'alpha', or the return attributable to a portfolio manager's skill. It is the difference between the return of the portfolio, and what the portfolio should theoretically have earned. Any portfolio can be expected to earn the risk free rate (rf), plus the market risk premium (which is given by [Beta x (Market portfolio's return - Risk free rate)]. Jensen's alpha is therefore the actual return earned less the risk free rate and the beta return.

Refer to the tutorial on risk adjusted performance measures for more details.


Question 4

[According to the PRMIA study guide for Exam 1, Simple Exotics and Convertible Bonds have been excluded from the syllabus. You may choose to ignore this question. It appears here solely because the Handbook continues to have these chapters.]

Which of the following is not an approach to attempt to value to a convertible security:



Answer : B

Bootstrapping is not one of the various approaches to try to value a convertible security. The rest of them are, and therefore Choice 'b' is the correct answer.


Question 5

If the continuously compounded risk free rate is 4% per year, and the continuous rate of dividend on a broad market index is 1% annually, what is the no-arbitrage 6-month futures price of the index if its spot value is $1000?



Answer : A

The no-arbitrage futures price is given by exp(0.5*(4%-1%))*$1000 = $1015.11. Therefore Choice 'a' is the correct answer.


Question 6

If the 1-year forward rates for years 1,2,3 and 4 are 2%, 3%, 4% and 5% respectively, what is the zero coupon spot rate for 4 years



Answer : A

The zero coupon spot rate for 4 years can be calculated as = (1.02*1.03*1.04*1.05)^(1/4) - 1 = 3.49%, which is the correct answer. (3.50% is just the mathematical average of the rates for the four years and is not correct, even though close.)


Question 7

Which of the following statements are true in respect of a fixed income portfolio:

1. A hedge based on portfolio duration is valid only for small changes in interest rates and needs periodic readjusting

II. A duration based portfolio hedge can be improved by making a convexity adjustment

III. A long position in bonds benefits from the resulting negative convexity

IV. A duration based hedge makes the implicit assumption that only parallel shifts in the yield curve are possible



Answer : C

A hedge based on portfolio duration alone makes the assumption that the price/yield relationship is linear, and ignores the convexity or non-linearity of the price/yield relationship. As prices change beyond small changes, the non-linear effect kicks in, which can be offset by making a convexity adjustment to the hedge. Therefore statements I and II are correct.

Statement III is incorrect - negative convexity has an adverse effect on bond prices regardless of whether prices rise or fall.

Statement IV is correct, a bond hedge based on duration alone may be mismatched along the yield curve (eg, hedging a 10 year maturity bond with a 3 year futures contract, even though of identical total durations), which is based upon the implicit assumption that all rates will move together (ie parallel shifts).


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