Q11. A 30-year semi-annual coupon bond issued today with market rates at 6.75% pays a 6.75% coupon. If the market yield declines by 30 basis points, the price increases to $1,039.59. If the market yield rises by 30 basis points, the price decreases to $962.77. Which of the following choices is closest to the approximate percentage change in price for a 100 basis point change in the market interest rate?

A)   12.80%.

B)   3.84%.

C)   1.28%.

Q12. Joshua Reynaldo is a fixed income portfolio manager for Golden Apple Capital Management. The portfolio is valued at $900 million, of which $840 million is currently invested. Fiona Campbell, the firm’s strategist, is becoming concerned about the possibility of an increase in interest rates. Reynaldo agrees, and this makes him nervous because the effective duration of his current portfolio investments is 10.315. However, his portfolio is presented to clients as a long-term fund, so there are limits to how short he can make the duration of the portfolio and still stay within the investment policy guidelines.

Reynaldo needs to invest the $60 million cash currently in the portfolio, and wants to do it in a way that will minimize the portfolio’s downside risk in a rising rate environment. He considers two different bonds. Both trade at their $1,000 par value and make coupon payments semiannually.

The first bond is a 12-year issue of Yorkville Technologies. Reynaldo likes the bond because of its attractive 5.9% coupon. He is concerned, however, because Yorkville is only rated Baa and Campbell is expecting a deterioration in credit quality as part of her economic outlook.

The second bond is also a 12-year maturity, but issued by Mountain States Electric & Gas, an Aaa utility. The 5.2% yield is not as attractive as the lower quality issue, but the Mountain States bond would represent a safe haven if credit spreads begin to widen, as both he and Campbell expect. Reynaldo’s only concern about the Mountain States bond is that it is callable any time at 102.

Discussing these possibilities with Campbell, Reynaldo tells her, “I ran my calculations assuming rates rise or fall by 50 basis points, and found that the effective convexity of the Mountain States bond is ten times the effective convexity of the Yorkville bond.” Campbell adds, “But the signs are opposite – the Mountain States bond has negative convexity and the Yorkville bond has positive convexity.” 

Reynaldo continues, “I haven’t done a full valuation yet, but using my figures for duration and assuming convexity is 46, it looks like a 100 basis point rise in rates would cause the price of the Yorkville bond to fall by 6.73%.” Campbell, looking over his shoulder at his calculations, adds, “The dollar value of an 01 for the Yorkville bond is only 0.063, though.”

Reynaldo decides to invest in the Yorkville bond.

Which statement about how duration tends to predict price changes for large swings in yield is most accurate? Duration:

A)   overestimates the increase in price for increases in yield.

B)   underestimates the increase in price for decreases in yield.

C)   overestimates the increase in price for decreases in yield.

Q13. Using a 50 basis point change in interest rates, what is the difference in effective duration between the Mountain States bond and the Yorkville bond? The effective duration of the:

A)   Mountain States bond is 0.34 lower than the effective duration of the Yorkville bond.

B)   Yorkville bond is 2.21 higher than the effective duration of the Mountain States bond.

C)   Mountain States bond is 0.34 higher than the effective duration of the Yorkville bond.

Q11. A 30-year semi-annual coupon bond issued today with market rates at 6.75% pays a 6.75% coupon. If the market yield declines by 30 basis points, the price increases to $1,039.59. If the market yield rises by 30 basis points, the price decreases to $962.77. Which of the following choices is closest to the approximate percentage change in price for a 100 basis point change in the market interest rate?fficeffice" />

A)   12.80%.

B)   3.84%.

C)   1.28%.

Correct answer is A)

Approximate % change in price =
(price if yield down – price if yield up) / (2 × initial price × yield change expressed as a decimal).
Here, the initial price is par, or $1,000 because we are told the bond was issued today at par. So, the calculation is: (1039.59 – 962.77) / (2 × 1000 × 0.003) = 76.82 / 6.00 = 12.80.

Q12. Joshua Reynaldo is a fixed income portfolio manager for Golden Apple Capital Management. The portfolio is valued at $900 million, of which $840 million is currently invested. Fiona Campbell, the firm’s strategist, is becoming concerned about the possibility of an increase in interest rates. Reynaldo agrees, and this makes him nervous because the effective duration of his current portfolio investments is 10.315. However, his portfolio is presented to clients as a long-term fund, so there are limits to how short he can make the duration of the portfolio and still stay within the investment policy guidelines.

Reynaldo needs to invest the $60 million cash currently in the portfolio, and wants to do it in a way that will minimize the portfolio’s downside risk in a rising rate environment. He considers two different bonds. Both trade at their $1,000 par value and make coupon payments semiannually.

The first bond is a 12-year issue of Yorkville Technologies. Reynaldo likes the bond because of its attractive 5.9% coupon. He is concerned, however, because Yorkville is only rated Baa and ffice:smarttags" />Campbell is expecting a deterioration in credit quality as part of her economic outlook.

The second bond is also a 12-year maturity, but issued by Mountain States Electric & Gas, an Aaa utility. The 5.2% yield is not as attractive as the lower quality issue, but the Mountain States bond would represent a safe haven if credit spreads begin to widen, as both he and Campbell expect. Reynaldo’s only concern about the Mountain States bond is that it is callable any time at 102.

Discussing these possibilities with Campbell, Reynaldo tells her, “I ran my calculations assuming rates rise or fall by 50 basis points, and found that the effective convexity of the Mountain States bond is ten times the effective convexity of the Yorkville bond.” Campbell adds, “But the signs are opposite – the Mountain States bond has negative convexity and the Yorkville bond has positive convexity.” 

Reynaldo continues, “I haven’t done a full valuation yet, but using my figures for duration and assuming convexity is 46, it looks like a 100 basis point rise in rates would cause the price of the Yorkville bond to fall by 6.73%.” Campbell, looking over his shoulder at his calculations, adds, “The dollar value of an 01 for the Yorkville bond is only 0.063, though.”

Reynaldo decides to invest in the Yorkville bond.

Which statement about how duration tends to predict price changes for large swings in yield is most accurate? Duration:

A)   overestimates the increase in price for increases in yield.

B)   underestimates the increase in price for decreases in yield.

C)   overestimates the increase in price for decreases in yield.

Correct answer is B)

For large swings in yield, duration tends to underestimate the increase in price when yield decreases and overestimate the decrease in price when yield increases. This is because duration is a linear estimate and does not account for the curvature in the price/yield relationship.

Q13. Using a 50 basis point change in interest rates, what is the difference in effective duration between the Mountain States bond and the Yorkville bond? The effective duration of the:

A)   Mountain States bond is 0.34 lower than the effective duration of the Yorkville bond.

B)   Yorkville bond is 2.21 higher than the effective duration of the Mountain States bond.

C)   Mountain States bond is 0.34 higher than the effective duration of the Yorkville bond.

Correct answer is B)

In order to calculate effective duration, we first need to know the bond price if interest rates rise or fall by 50 basis points.

For the Yorkville bond:

N = 24; PMT = (0.059 coupon × $1,000 par value / 2 payments per year =) 29.50; FV = 1,000

If rates rise by 50 basis points, I = ((5.9% + 0.50 =) 6.4% / 2 payments per year =) 3.2%; PV = -958.56.
Since the bond has a par value of $1,000, the estimated price will be (958.56 / 1,000 × 100 =) 95.86.

If rates fall by 50 basis points, I = ((5.9% ? 0.50 =) 5.4% / 2 payments per year = ) 2.7%; PV = -1043.74.
Since the bond has a par value of $1,000, the estimated price will be (1043.74 / 1,000 × 100 =) 104.37.

Now that we have the prices, we can use the formula for effective duration (ED):

ED = (104.37 – 95.86) / (2 × 100 × 0.005)
ED = 8.51 / 1
ED = 8.51

For the Mountain States bond:

N = 24, PMT = (0.052 coupon × $1,000 par value / 2 payments per year =) 26.00, FV = 1,000

If rates rise by 50 basis points, I = ((5.2% + 0.50 =) 5.7% / 2 payments per year =) 2.85%; PV = -956.97.
Since the bond has a par value of $1,000, the estimated price will be (956.97 / 1,000 × 100 =) 95.70.

If rates fall by 50 basis points, I = ((5.2% ? 0.50 =) 4.7% / 2 payments per year =) 2.35%; PV = -1045.46.
Since the bond has a par value of $1,000, the estimated price will be (1045.46 / 1,000 × 100 =) 104.55
However, since the bond is callable at 102, the price will be 102, not 104.55.

ED = (102 – 95.70) / (2 × 100 × 0.005)
ED = 6.30 / 1
ED = 6.30

The ED of the Yorkville bond is (8.51 – 6.30 =) 2.21 higher than the ED of the Mountain States bond.

thanks