b_c5.pdf

Bachelor Studies in Finance

Year 2

Spring 2012

BANKING

Class assignment #5

Due April 16 (group 1) and April 23 (group 2)

1. Bank ONE has a €1 million position in a five-year, zero-coupon bond that is trading at a

yield to maturity of 7 percent. The historical mean change in daily yields is 0.0 percent,

and the standard deviation is 12 basis points.

a. What is the modified duration of the bond?

b. What is the maximum adverse daily yield move given that we desire no more than a 5

percent chance that yield changes will be greater than this maximum?

c. What is the price volatility of this bond?

d. What is the daily earnings at risk for this bond?

2. Bank TWO has a portfolio of AAA-rated, 15-year zero-coupon bonds with a face value of

€400 million. The bonds currently are yielding 9.5% in the over-the-counter market.

a. What is the modified duration of these bonds?

b. What is the price volatility if the potential adverse move in yields is 25 basis points?

c. What is the DEaR?

d. If the price volatility is based on a 90 percent confidence limit and a mean historical

change in daily yields of 0.0 percent, what is the implied standard deviation of daily

yield changes?

3. Bank THREE has a portfolio of bonds with a market value of €200 million. The bonds

have an estimated price volatility of 0.95 percent. What are the DEaR and the 10-day VaR

for these bonds?

4. Calculate the DEaR for the following portfolio of stocks (S), foreign currencies (FX) and

bonds (B) with and without the correlation coefficients (ρ S,FX , ρ S,B , ρ FX,B ). What is the

amount of risk reduction resulting from the lack of perfect positive correlation between

the given assets?

Correlation coefficients

Assets

DEaR

ρ S,FX ρ S,B

ρ FX,B

Stocks (S)

€300,000

–0.10

0.75

0.20

Currencies (FX)

€200,000

Bonds (B)

€250,000

5. A bank has a bond whose historical mean change in daily yields is 0 percent and the

standard deviation is 12 basis points. What is the maximum adverse daily yield move

given that we desire no more than a 5 percent chance that yield changes will be greater

than this maximum?

6. The DEaR for a bank is $8,500. What is the VaR for a 10-day period? A 20-day period?

Why is the VaR for a 20-day period not twice as much as that for a 10-day period?

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