[ 2009 FRM ] Long Practice Exam 1 Q6-10

6. Consider the following linear regression model: Y = a + b*X + e. Suppose a = 0.05, b = 1.2, Std(Y) = 0.26, Std(e) = 0.1, what is the correlation between X and Y?

A. 0.923

B. 0.852

C. 0.701

D. 0.462

Correct answer is A

The standard deviation of X can be calculated as follows:fficeffice" />

std(X) = SQRT( (std(Y)2 - std(e)2) / b2 ) = SQRT( (0.262 - 0.12) / 1.22) = 0.2

Then, the correlation between X and Y can be calculated as follows:

Corr(X,Y) = b * std(X) / std(Y) = 1.2 * 0.2 / 0.26 = 0.923

7. Two bond traders have USD 100 million invested each in just issued 10-year Microsoft Corp Bonds trading at par. 'A' has exposure in 6% 10-year callable bonds callable at the end of the 1st year at par while 'B' has invested in 5.95% 10-year vanilla bonds. Eleven months later, Microsoft is issuing new 10-year bonds at par paying a coupon of 5.50%. The market value of A's Microsoft bonds is:

A. Almost the same as that of B's Microsoft bonds

B. Much higher than that of B

C. Lower than that of B

D. Nothing can be said from the data given above

Correct answer is C

The market value of bonds in Portfolio 'A' will be very close to par value because they will be 'called' by Microsoft at par (since market yields are much lower now).  On the other hand, Portfolio 'B' will appreciate sharply (nearly 50 basis points yield gain on a 9-year outstanding maturity bond). Hence, portfolio 'B' will have a much higher market value.

Reference: Fixed Income Securities, Tuckman, 2002.

8. Which of the following IBM options has the highest gamma with the current market price of IBM common stock at USD 68?

A. Call option expiring in 10 days with strike USD 70

B. Call option expiring in 10 days with strike USD 50

C. Put option expiring in 10 days with strike USD 50

D. Put option expiring in 2 months with strike USD 70

Correct answer is A

Gamma is highest for at the money options nearing expiration.  The at-the-money options are those with a strike of 70.  The shortest dated options are the 10 day options.  Thus, 'A' is correct. 

Reference: Options, Futures, and Other Derivatives, ffice:smarttags" />Hull, 2006.

9. With any other factors remaining unchanged, which of the following statements regarding bonds is NOT valid?

A. The price of a callable bond increases when interest rates increase

B. Issuance of a callable bond is equivalent to a short position in a straight bond plus a long call option on the bond price

C. The put feature in a puttable bond lowers its yield compared with the yield of an equivalent straight bond

D. The price of an inverse floater decreases as interest rates increase

Correct answer is A

'A' is incorrect.  The price of a callable bond will increase when the interest rate decreases, as the cost of issuing new debt is lower than the current coupon.  Thus, the issuer will 'call' back the bond.

'B' is correct.  The issuance of callable bond is equivalent to a short position in a straight bond plus a long call option on the bond price.

'C' is correct.  The put feature will make the bond more attractive to investors, increasing its price and lowering its yield.

'D' is correct.  As the interest rate increases, the coupon of inverse floater decreases.  In addition, the discount factor increases.  Hence, the value of the inverse floater note must decrease even more than a regular fixed-coupon bond.

Reference: Fixed Income Securities, Tuckman, 2002.

10. The rate of change of duration with respect to the underlying yield of a fixed income bond is called:

A. Convexity

B. Delta

C. Theta

D. DVBP

Correct answer is A

Convexity measures how interest rate sensitivity changes with interest rates.  Mathematically, convexity is defined as:

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where P is the price of the bond and y is the yield-to-maturity.

'B' is incorrect. Delta is the rate of change of the option price with respect to the price of the underlying.

'C' is incorrect. Theta measures the change in an option price with respect to the passage of time.

'D' is incorrect. DVBP refers to the dollar value of a basis point change.

Reference: Fixed Income Securities, Tuckman, 2002.