Given a zero coupon bond with maturity of 5 years and yield of 2% (in annualized units)

a.Calculate the price of this bond in a continuous and discrete models

b.What are the durations and convexity of this bond in discrete and continuous models?

c.Assume that the yield goes up by 0.5% calculate the returns directly and using duration convexity approximation

i.For continuous the direct method gives: (exp(-0.025*5)-exp(-0.02*5))/exp(-0.02*5)=-.2.469%

ii.Using duration convexity approximation we have: -5*0.5%+0.5*25*0.5%*0.5% - 2.468%

2.Now add to it a zero coupon bond maturing in 8 years and yield of 3%

a.Form a duration neutral portfolio and a positive convexity

b.Suppose you pay an interest of 3% on any short or loan youre taking. Assume the yield of the bond moves by 1% down in parallel

c.Calculate the performance of the portfolio using direct calculation ignoring the interest component:

d.Calculate the performance of the portfolio using duration and convexity calculation

e.Assume that the 1% move down took place in 3 months. Calculate the interest expense you will pay on a loan in this period

f.Given of what you see will you recommend implementing this strategy to your trader?

3.Assume you have a 2-year coupon-paying bond that pays 2% each half a year. Assuming the yield equals to 2% calculate the KRD for 1 year point.