Baran

 

4、A 12-year, 6 percent, option-free bond is currently trading at par. The bond has a duration of 8.38 years and a convexity of 91.93. Your estimate of the percent price change (PPC) associated with a 100 basis point decrease in yield is closest to:

A) 7.92 percent increase.  

B) 8.84 percent decrease. 

C) 7.92 percent decrease.  

D) 8.84 percent increase.

Baran

 

The correct answer is D

 

ΔV-% ≈ [-duration×(Δy)×100]+[0.5×convexity×(Δy)2×100]=[-8.38×(-0.01) ×(100)]+[0.5×(91.93)×(-0.01)2×100]=8.84.

Baran

 

5、A bank has $100 million in assets with modified duration of 8.5, and $90 million of liabilities with modified duration of 6.5. Accounting only for duration effects, a 50 basis point parallel downward shift would impact the bank’s equity position by an amount closest to a:

A) $10 million increase in equity.  

B) $1.325 million increase in equity.

C) $100 million decrease in equity.  

D) $90 million increase in equity.

[此贴子已经被作者于2009-6-27 14:47:18编辑过]

Baran

 

The correct answer is B

 

The change in assets would be an increase of ($100)(8.5)(0.005) = $4.25 million, whereas the change in liabilities would be an increase of ($90)(6.5)(0.005) = $2.925 million. The net effect would be an increase in equity of $1.325 million.

Baran

 

AIM 8: Compute the duration of a portfolio.

 

1、A bond portfolio consists of a AAA bond, a AA bond, and an A bond. The prices of the bonds are $1,050, $1,000, and $950 respectively. The durations are 8, 6, and 4 respectively. What is the duration of the portfolio?

A) 6.00.

B) 6.07.

C) 6.67.

D) 18.20.

[此贴子已经被作者于2009-6-27 14:48:08编辑过]

Baran

 

The correct answer is B

 

The duration of a bond portfolio is the weighted average of the durations of the bonds in the portfolio. The weights are the value of each bond divided by the value of the portfolio: portfolio duration = 8*(1050/3000)+6*(1000/3000)+4*(950/3000) = 2.8+2+1.27 = 6.07.

Baran

 

2、Suppose you have a two-security portfolio containing bonds A and B. The book value of bond A is $20 and the market value is $35. The book value of bond B is $40 and the market value is $50. The duration of bond A is 4.7 and the duration of bond B is 5.9. Which of the following amounts is closest to the duration of the portfolio?

A) 5.3.  

B) 5.5.

C) 5.4.  

D) 5.6.

Baran

 

The correct answer is C

 

Market values (not book values) should be used to calculate effective portfolio duration.

(35/85 × 4.7) + (50/85 × 5.9) = 5.41

Baran

 

3、Suppose you have a three-security portfolio containing bonds A, B and C. The effective portfolio duration is 5.9. The market values of bonds A, B and C are $60, $25 and $80, respectively. The durations of bonds A and C are 4.2 and 6.2, respectively. Which of the following amounts is closest to the duration of bond B?

A) 9.0.  

B) 1.4. 

C) 7.1.

D) 7.4.

Baran

 

The correct answer is A

 

Plug all the known figures and then solve for the one unknown figure, the duration of bond B.

Proof: (60/165 × 4.2) + (25/165 × 9.0) + (80/165 × 6.2) = 5.9