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1) PA=FV(1+y1) 95.24=100(1+y1)

Y1=5%

PB=c(1+y1) +c+FV(1+y2)2 107.42=10(1+0.05) +10+100(1+y2)2

Y2=6%

PC=c(1+y1) +c(1+y2)2+ c+FV(1+y3)3 140.51=20(1+0.05) +20(1+0.06)2+ 20+100(1+y3)3

Y3=5%

PD=FV(1+y4)4 85.48=100(1+y4)2

Y4=4%

2) PE=c(1+y1) +c+FV(1+y2)2 FV=100 C=25 PE=25(1+0.05) +25+100(1+0.06)2=135.06

Build a replicating portfolio because arbitrage opportunity only available when selling bonds E and buying a replicating portfolio.

So XA CF1A+XB CF1B=CF1c, XA*100+XB*10=25

XA CF2A+XB CF2B=CF2C, XA+0+XB*110=125

XA=0.1364 XB=1.1364

Arbitrage profit is 136-135.06=0.94 In conclusion, the arbitrage profit is $0.94 when building replicating portfolio whih consist of buying 0.1364 bond A and 1.1364 bond B.

3) P=c(1+y1) +c+FV(1+y2)2 105.6=10(1+y1) +10+100(1+y2)2 123.86=20(1+y1) +20+100(1+y2)2 (1+y2)2= 120123.86-20(1+y1) So, 105.6=10(1+y1) +10+100120123.86-20(1+y1) Y1=4.98% 123.86=20(1+0.0498) +20+100(1+y2)2 Y2=7%

4) FV=100 Coupon rate=10%

A, if 1 year. CF1=C1+P1

CF1=C1+10+100(1+1Y2)2

Finally, we do not know 1Y2 so that we can’t make sure at what price need to sell the bind. This will lead the customer to liquidity risk.

B, if 3 years.

Cause is a 2 years bond.

CF1=10*(1+1Y3)2+110*(1+2Y3)

The investor will face reinvestment risk when they don’t not what rate their cahs flow will reinvested because the question have 2 unknow rate which is 1Y3 and 2Y3.

5) Suppose we have spot rate Ys ,Yt(t>s) and forward rate sft. At the time we invest $1 at t=s and $(1+s ft)t-s.Otherwise, we can invest $1 at the spot rate Yt for t period. Actually two plan generate the same cash flow, so that 1+Yss(1+s ft)t-s=(1+Yt)t

So (1+sft)t-s=(1+Yt)t1+Yss 1+s ft=…...

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