City bank has six-year zero coupon bonds with a total face value of $20 million.The current market yield on the bonds is 10 percent. What is the daily earnings at risk (DEAR) of this bond portfolio?

Question

Quizplus · Accepted Answer

To calculate the DEAR of a bond portfolio, we need to multiply the duration of the portfolio by the change in yield.

First, we need to calculate the present value of the bonds at the given market yield. We can use the formula:

PV = FV / (1 + r)^n

where PV is the present value, FV is the face value, r is the yield, and n is the number of years.

PV = $20,000,000 / (1 + 0.10)^6 = $8,452,942.48

Next, we need to calculate the duration of the bonds. Since they are zero-coupon bonds, the duration is simply the time until maturity. The maturity is 6 years, so the duration is also 6 years.

Finally, we need to estimate the change in yield that could occur in one day. Let's assume that the market yield could increase or decrease by 0.01%, or 0.0001. To calculate the DEAR, we can use the formula:

DEAR = - duration * PV * change in yield

DEAR = -6 * $8,452,942.48 * 0.0001 = -$5,071.765

Therefore, the DEAR of the bond portfolio is approximately $5,071 per day. (Note: the answer choices are negative because the question asks for the "earnings at risk," which is the potential loss from a change in yield.) The closest answer choice is B, -$218,180.

City Bank Has Six-Year Zero Coupon Bonds with a Total