Question

. Bank Beta has an inventory of AAA-rated zero-coupon bonds with a maturity of 13.42 years and a face value of $127,503,041. The modified duration of these bonds is 12.5 years, the DEAR is $2,150,000, and the potential adverse move in yields is 35 basis points. What is the market value of the bonds, the yield on the bonds, and the duration of the bonds?

Answer 1

Modified duration(MD) = 12.5 years

daily earnings at risk(DEAR) = $2,150,000

Potential movement in yields = 0.35% or 0.0035

First we will calculate price volatiltiy

Price volatility = MD * movement in yield = 12.5 * 0.0035 = 4.375%

We can calculate the market value of bonds by the following formula,

DEAR = Price volatility * value of position/market value

Market value = DEAR/Price volatility = 2,150,000/0.04375 = $49,142,857

Hence the market value of bonds is $49,142,857

We can calculate the yield on the bond by the following formula,

Market value = Face value/(1+yield)^t

t = time to maturity = 13.42 years

Face value = $127,503,041

Putting these values in the formula,

49,142,857 = 127,503,041/(1+yield)^13.42

yield = (127,503,041/49,142,857)^(1/13.42) - 1

Solving this equation, we get

yield = 7.36%

Hence the current yield on the bond is 7.36%

We can calculate the duration of the bonds by the following formula,

MD = Duration/(1+yield)

12.5 = Duration/1.0736

Duration = 12.5 * 1.0736 = 13.42 years

Hence the duration on the bonds is 13.42 years.

If you have any doubts please let me know in the comments. Please give a positive rating if the answer is helpful to you. Thanks.