问一个有关债券的问题同学做的但是觉得有的地方想探究下感觉总是怪怪的?AgovernmenthasissuedasetofTreasurybondswhichhaveexactly4yearstomaturity.Thecouponrateonthesebondsis3.5%peryearandcouponsar

Question

问一个有关债券的问题 同学做的 但是觉得有的地方想探究下 感觉总是怪怪的?
A governmenthas issued a set of Treasury bonds which have exactly 4 years to maturity.Thecoupon rate on these bonds is 3.5% per year and coupons are paid annually.Theface value of the Treasury Bond is $1000.Below are the prices of zero-couponbonds with identical face value to the Treasury bond:
Maturity Price
1 963.855
2 926.337
3 888.996
4 863.073
(a) Thecurrent market price for the Treasury bond is $985.Is this price fair?
(b) If the answer tothe above is `no',devise a trading strategy that can be used to generate profits
（a）不说了折下 是990.548
Because 990.548〉985
So the price is not fair.
（b) he trading strategy should be:
At the first year we sold out a one year maturity zerocoupons T-bonds that worth 35 pounds,and two years,three years’ T -bondsrespectively (all worth 35pounds),plus a four years maturity T-bonds of1035pounds and get the present value of 990.548,Then we can buy the Treasurybond with the market price of 985.
感觉总是哪儿有问题.这种说法 是不是不对.
如果是对的能否详细解释下为啥今天卖了35X4+1000债券 又折到今天是990.548 不太懂

Answer 1

The bond fair price should be 990.55,which is greater than the market price 985.That is,the bond is under-priced.We would long (hold) the bond,and short (sell short) those zero-coupon bonds.


Strategy:
buy the Treasury at the price 985.

short one year zero-coupon bond that has face value $35;
short two year zero-coupon bond that has face value $35;
short three year zero-coupon bond that has face value $35;
short four year zero-coupon bond that has face value $1035;
This is a risk-free arbitrage.